Description
The purpose of this paper is to create an endurance index of housing investor sentiment and use
it to forecast housing stock returns. This study performs not only in-sample and out-of-sample forecasting,
like many previous studies did, but also a true forecasting by using all lag terms of independent variables. In
addition, an evaluation procedure is applied to quantify the quality of forecasts.
Journal of Financial Economic Policy
Forecasting of housing stock returns and housing prices: Evidence from the
endurance index of housing investor sentiment
Ling T. He
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Ling T. He , (2015),"Forecasting of housing stock returns and housing prices", J ournal of Financial
Economic Policy, Vol. 7 Iss 2 pp. 90 - 103
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Forecasting of housing stock
returns and housing prices
Evidence from the endurance index of
housing investor sentiment
Ling T. He
Department of Economics & Finance, University of Central Arkansas,
Conway, Arkansas, USA
Abstract
Purpose – The purpose of this paper is to create anendurance indexof housinginvestor sentiment anduse
it to forecast housing stock returns. This study performs not only in-sample and out-of-sample forecasting,
like manyprevious studies did, but also a true forecastingbyusingall lagterms of independent variables. In
addition, an evaluation procedure is applied to quantify the quality of forecasts.
Design/methodology/approach – Using a binomial probability distribution model, this paper creates
anendurance indexof housinginvestor sentiment. The indexrefects the probabilityof the highor lowstock
price beingthe close price for the Philadelphia StockExchange HousingSector Index. This housinginvestor
sentiment endurance index directly uses housing stock price differentials to measure housing investor
reactions to all relevant news. Empirical results in this study suggest that the index can not only play a
signifcant role in explaining variations in housing stock returns but also have decent forecasting ability.
Findings – Results of this study reveal the considerable forecasting ability of the index. Monthly
forecasts of housing stock returns have an overall accuracy of 51 per cent, while the overall accuracy of
8-quarter rolling forecasts even reaches 84 per cent. In addition, the index has decent forecasting ability
on changes in housing prices as suggested by the strong evidence of one-direction causal relations
running from the endurance index to housing prices. However, extreme volatility of housing stock
returns may impair the forecasting quality.
Practical implications – The endurance index of housing investor sentiment is easy to construct and
use for forecasting housing stock returns. The demonstrated predictability of the index on housing stock
returns in this study can have broad implications on housing-related business practices through providing
an effective forecasting tool to investors and analysts of housing stocks, as well as housing policy-makers.
Originality/value – Despite different investor sentiment proxies suggested in the previous studies,
few of them can effectively predict stock returns, due to some embedded limitations. Many increases
and decreases inn prices cancel out each other during the trading day, as many unreliable sentiments
cancel out each other. This dynamic process reveals not only investor sentiment but also resilience or
endurance of sentiment. It is only long-lasting resilient sentiment that can be built in the closing price.
It means that the only feasible way to use investor sentiment contained in stock prices to forecast future
stock prices is to detach resilient investor sentiment from stock prices and construct an index of
endurance of investor sentiment.
Keywords Forecasting and simulation, Financial forecasting, Real estate services
Paper type Research paper
JEL classifcation – E37, G17, L85
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1757-6385.htm
JFEP
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90
Received10 January2014
Revised5 March2014
16 June 2014
Accepted7 July2014
Journal of Financial Economic
Policy
Vol. 7 No. 2, 2015
pp. 90-103
©Emerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-01-2014-0004
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1. Introduction
Researchers have studied the predictability of housing market and housing stocks for
long time. In early studies, Case and Shiller (1989, 1990) argue that the housing market
is not effcient and that price changes display positive autocorrelation. Therefore, the
housing market may be predictable. The authors report that the ratio of construction to
price, changes in adult population and real per capita income have forecasting ability on
housing price changes. As then many researchers, including Dua et al. (1999), Goyal and
Welch (2003, 2008), Gallin (2008), Campbell et al. (2009), Rapach and Strauss (2009),
Cochrane (2011), Gupta et al. (2011) and Ghysels et al. (2012), use different variables, such
as the price-rent ratio, leading indicators and different regression models, to predict
changes in the housing prices and home sales. Furthermore, He (2000) reports causal
relationships between residential real estate and securitized real estate (stocks). Piazzesi
et al. (2007), with their consumption-based asset pricing model, fnd that the “housing
share can be used to forecast excess returns on stocks”.
The extension of housing research to including securitized real estate prompts
research interests on forecastability of securitized real estate, such as real estate
investment trusts (REIT) stocks. Many previous studies, based on different variables
and estimation models, fnd that returns of securitized real estate may be predictable
because they are signifcantly correlated with other assets and affected by investor
responses to important economic as well as frm-specifc information. Examples include
Liu and Mei (1992, 1994), Li and Wang (1995), Nelling and Gyourko (1998), Brooks and
Tsolacos (2003), He and Webb (2006), He (2007) and Cabrera et al. (2011). However,
results on predictability of REITstock returns are inconsistent. Ling et al. (2000) offer an
explanation claiming that predictability of REIT stock returns is time-varying, due to
the instability or dynamics of stock prices. It is consistent with Welch and Goyal’s (2008)
fnding that equity premium prediction models in the academic literature are unstable
and produce poor in-sample and out-of-sample forecasts for 30 years.
There is a consensus that the dynamics of stock returns are determined by investor
reactions to information. Creating accurate measurements of investor reactions to
important news is certainly a vital issue in forecasting stock returns. However, there is
no agreement on what kind of information that causes fuctuations in the stock prices.
For example, Fama and French (1993, 1996 and 1997) develop their three-factor model to
explain and predict factor betas and excess returns of stocks, while other researchers use
frm-specifc variables, instead of macro variables, to explain and forecast stock returns.
Daniel and Titman (1997) argue that information about frm characteristics can better
explain variations in cross-sectional stock returns. In fact, investors respond to all
pertinent information, not just frm-specifc information. To improve forecasting
quality, this study uses a comprehensive measure of investor reactions to all sorts of
relevant information, macro and frm-specifc, to predict changes in housing stock
returns.
According to Delong et al. (1990), the underlying issue of investor reaction to news or
investor sentiment essentially is about howinvestors interpret news to formtheir beliefs
about future cash fows and investment risks. However, this process is not linear.
Investors may underreact to news when stock prices slowly refect news; on the other
hand, investors might consistently overreact to news in the same direction over long
horizons and cause stocks overpriced (Barberis et al., 1998). Obviously, it is investor
sentiment that drives stock prices. There are many different kinds of investor sentiment
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indexes created and reported in the literature. For example, Baker and Wurgler (2007)
listed various widely used investor sentiment proxies, such as investor survey, investor
mood, retail investor trades, mutual fund fows, trading volume, dividend premium,
close-end fund discount, opinion implied volatility, initial public offering (IPO) frst-day
returns, IPO volume, equity issues over total new issues and insider trading. The
investor sentiment indexes and their lagged terms are often used as predictors for stock
market returns or portfolio returns (Baker and Wurgler, 2006).
Despite different investor sentiment proxies suggested in the previous studies, fewof
them can effectively predict stock returns, due to some embedded limitations. The
existing sentiment indexes are either event-based or opinion- and mood-based. Indexes
based on individual events cannot serve as a measure of a continuous process, because
different events have their own frequencies, regularly or irregularly. In contrast,
changes in stock prices follow a continuous process which refects the way investors to
react to news, i.e. continuously changing bid and ask prices. During a trading day,
investors have to constantly analyze and respond to different kinds of news, and their
reactions are instantaneously quantifed into stock prices, no matter the reactions are
rational or irrational, optimistic or pessimistic. Apparently, the event-based sentiment
indexes, as a non-continuous measure, cannot effectively forecast stock returns. In
addition, stock price dynamics essentially is a result of investor reactions to all relevant
important information, not just to a particular type of news. Investor reaction,
determined by its nature, is not constant but time-varying. The time-varying nature
makes some opinion- and mood-based sentiments short-lived and unreliable. That is,
these sentiments may not be refected into the closing price which is the only one that
can evaluate persistence of investor reactions to all signifcant events and news during
the entire trading day. Many other prices cancel out each other during the trading day,
as many unreliable sentiments cancel out each other.
Although many prices between the high and low prices are going to cancel out each
other during a trading day, He (2012) argues that some of them can form a lasting
momentumor force that drives stock prices more or less inclining to the high or lowprice
until the closure of the stock market. This dynamic process reveals not only
time-varying investor sentiments but also the resilience or endurance of sentiments,
which is built on signifcant pertinent information. The long-lasting resilient sentiment
cannot be offset and only refected in the closing price, the price at the end of a trading
day. Therefore, the probability of the high or lowprice being the closing price is used to
quantify the endurance of investor sentiment. It is an effective way to detach resilient
investor sentiment from stock price dynamics. He (2012) provides evidence that the
endurance index has decent forecasting power on returns of the stock market
represented by the S&P 500 Stock Index. Can the endurance index also effectively
predict stock returns in major industries or sectors? This study is to empirically examine
the issue.
Applying the endurance index of investor sentiment to forecast housing stock
returns and housing prices is an interesting and important endeavor. First, this
sentiment endurance-based forecasting approach is completely different from all
housing-related forecasting models reported in the literature. According to Welch and
Goyal’s (2008), equity premium prediction models in the academic literature are
unstable, and for long time, they produce poor in-sample and out-of-sample forecasts.
Given the fact that the endurance index model can produce decent forecasts on stock
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market returns (He, 2012), it is reasonable to expect the model that can demonstrate the
similar or even better forecasting ability on housing stock returns and housing prices.
Second, using endurance index model to enhance the forecasting ability on securitized
and unsecuritized housing market has valuable implications to many stakeholders in
the housing sector. The housing sector is one of major pillars of the US economy. The
sector covers several important industries, such as home building, fnancial services
(mortgage lending, home insurance, etc.) and building materials. The demonstrated
predictability of the index on housing stock returns and home prices in this study can
have broad infuences on housing-related business practices, including decisions on
hiring employees, as well as housing and fnancial policy-makers through providing a
near-termindicator of health of the housing market. Finally, additional beneft provided
by the endurance index of housing investor sentiment is that it is easy to construct and
can be used as an effective forecasting tool for investors and analysts of housing stocks,
as well as housing policy-makers.
The main purpose of this study is to create an endurance index of housing investor
sentiment and use it to forecast housing stock returns. This study performs not only
in-sample and out-of-sample forecasting, like many previous studies did, but also a true
forecasting by using all lag terms of independent variables. In addition, an evaluation
procedure is applied to quantify the quality of forecasts. Finally, causality tests are
conducted to verify if variations in the sentiment endurance (SE) index can
Grange-cause changes in housing prices.
The remainder of the paper is organized as the follow. Section 2 describes the
methods and data used in this study. Section 3 discusses empirical results, and Section
4 concludes major fndings.
2. Methods and data
The SE index essentially measures the probabilities of the most optimistic and
pessimistic sentiments, quantifed by the high and low prices, respectively, being the
closing price. The following is the binomial probability distribution model developed by
He (2012):
P
t
? H
t
? (1 ? P
t
) ? L
t
? C
t
, (1)
where P
t
represents the probability of the high price ( H
t
) being the closing price ( C
t
) and
takes a value between zero to one; and ( 1 ?P
t
) is the probability of the low price ( L
t
)
being the closing price. When P
t
? 0.5, the overall investor sentiment is neutral; if
P
t
? 0.5, the overall sentiment is considered optimistic, while P
t
? 0.5 indicates the
overall pessimistic sentiment. Therefore, the index of investor SEat time t is revealed in:
SE
t
? (P
t
? 0.5). (2)
A positive SE indicates a positive sentiment toward the closing price, while a negative
SErepresents a higher probability of the lowprice being the closing price. This SEindex
can effectively quantify investors’ continuous momentous reactions to all important
news. The persistence or endurance of these reactions, implied in closing prices, largely
shape the dynamics of stock market returns.
The primary data set used in this study is the Philadelphia Stock Exchange (PHLX)
Housing Sector Index (HGX) which comprises 19 companies that work directly in
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housing-related industries, such as construction of residential homes, mortgage
insurance and supply of building materials. The index has the potential to track the
strength of the housing market, such as home sales and residential real estate values.
Obviously, it is a better proxy for securitized residential real estate than equity REITs,
a widely used proxy, which essentially concentrates on commercial real estate. This is
the main reason why the HGX index, as a portfolio of housing stocks, can better serve
the purpose of predicting securitized residential real estate and home prices. The index
began in 2002. This study covers a period of November of 2002 through December of
2012. Data availability dictates the sample period. The index numbers include high, low
and closing prices. The daily indexes are averaged into monthly and quarterly series.
The monthly and quarterly SE indexes are constructed based on equations (1) and (2).
First, the high (H), low (L) and close (C) prices are plugged into equation (1) to solve the
probability (P), then, subtracting 0.5 from P to get SE index.
The monthly and quarterly endurance indexes of housing investor sentiment and the
lag terms of the indexes are then used to explain changes in monthly and quarterly
housing stock returns represented by percentage changes in the HGX, to examine the
explanatory power of each independent variable. Regression results indicate that only
the current term and one-period lagged term of SE (SEL) have signifcant infuence on
housing stock returns. The result is in line with fndings in previous studies. For
example, He (2012) reports that both the SE and lagged SE can explain a signifcant
portion of variation in the stock market which is represented by the S&P 500 Stock
Index and Baker and Wurgler (2006) fnd that their lagged sentiment index has a
negative impact on returns of some stock portfolios.
This study assesses the forecasting ability of SE to justify the relevancy or
importance of the endurance index to housing stock investing professionals. The
forecasting starts with applying different rolling periods to estimate coeffcients of the
following regression model:
R
t
? a
t
? b
t
SE
t
? c
t
SE
t?1
? e
t
, (3)
where R
t
represents housing stock returns at time t. The rolling coeffcient estimates of
SEand SEL, together with the rolling constant terms, are used to forecast housing stock
returns based on different forecasting methods. First, the in-sample forecasting which
uses rolling coeffcients at time t to predict housing stock returns at time t. There is no
time lag between predicting variables and the variable to be predicted. In fact, the
in-sample forecasting is simply a test for the goodness of ft. Second, the out-of-sample
forecasting that uses one-period lagged rolling coeffcients and constant terms to predict
changes in the housing stocks:
F
t
? a
t?1
? (b
t?1
? SE
t
) ? (c
t?1
? SE
t?1
). (4)
The out-of-sample forecasting demonstrates some forecasting ability of rolling
coeffcients, as it is widely used as a forecasting tool in previous studies, such as Fama
and French (1997). Nevertheless, there exists a potential problemthat SEat time t is still
used in predicting of housing stock returns at time t. A true feasible forecasting model
should use all lagged variables to forecast current changes in the housing stocks. That
leads to the third model which may be considered as a true forecasting model:
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F
t
? a
t?1
? (b
t?1
? SE
t?1
) ? (c
t?1
? SE
t?1
). (5)
In equation (5), the SEL substitutes SE and multiplies with the one-period lagged
coeffcient of b. Equation (5) is not completely consistent with the rolling regression
model, equation (3), in which coeffcient of b represents sensitivity of housing stock
returns to the current term of SE, not the SEL. However, if SE is stable at times of t and
t?1, that may warrant the feasibility of equation (5).
A simple equality test can assess the quality of the above rolling forecasts. This
paper uses the t-test without the assumption of equal variances between the two series
in analysis of variance to examine if the averages of rolling forecasts are statistically
indifferent fromthe actual housing stock returns. An insignifcant test statistic indicates
that the forecasts, on average, are not considerably deviated from the actual housing
stock returns and, therefore, are statistically accurate. As He (2012) points out there is a
potential faw involved in this approach, that is extremely positive and negative
inaccurate forecasts may cancel out each other and result in an average of forecasts close
to the mean of actual housing stock returns. The procedure of calculating accuracy ratio
developed by He (2012) can effectively eliminate the conceivable unreliable and
misleading equality test results.
The procedure starts with sorting both series of stock return forecasts and actual
housing stock returns by forecast errors (forecasts – actual returns) in an ascending
order (smallest to largest). Forecasts with negative errors are known as under-forecasts
(UF), while those with positive errors are referred as over-forecasts. Then, all
observations associated with positive forecast errors (the bottompart of the sample) are
deleted. The remaining observations with negative forecast errors are in a sequence of
the smallest (most inaccurate) to the largest (most accurate). The equality test for the
forecasts and their corresponding real housing stock returns is performed repeatedly in
a loop that begins with all UFand their corresponding stock returns. If the statistic of the
frst test is signifcant, observation one of both variables goes out. If the second test
statistic remains signifcant, observation two is out. As more inaccurate forecasts are
thrown out, the signifcance level of the test statistic keeps going down, from the 1, 5 to
10 per cent. When the test statistic is not signifcant at the 10 per cent level, that is the
null hypothesis of equal means of the forecasts and their corresponding housing stock
returns cannot be rejected at the 10 per cent level, the loop stops. The remaining UF are
statistically considered accurate.
The above process is repeated one more time with variables sorted by positive
forecast errors from the largest to the smallest to identify accurate over-forecasts. The
number of accurate over-forecasts (OF) plus the number of accurate UF from the
previous process equals the total number of accurate forecasts. The total number of
accurate forecasts is then divided by the total number of forecasts to get the accuracy
ratio which effectively removes the problemof cancellation between extreme under- and
over-forecasts. Compared with the traditional forecast quality measure, the absolute
forecast error, the above forecast quality assessment reports not only the overall
forecast accuracy which is also refected in the absolute forecast error but also the
unique distribution of accurate forecasts by showing the numbers of accurate over- and
under-forecasts.
This study performs the Granger-causality test to examine the causal relations
between the endurance index of housing invest sentiment and housing prices. Three
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housing price indexes compiled by the Federal Housing Finance Agency (FHFA) are
used in the test, the Purchase-only Housing Price Index (SALES), the Expanded-data
Housing Price Index (EXPANDED) and the All-transaction Housing Price Index
(ALLTRANSAC). Due to the unavailability of the high and low housing prices, it is
impossible to build an endurance index derived from housing prices. This is the
reason why the causality test is used to replace a true forecasting on housing prices.
3. Results
3.1 Correlations between the SE index and housing stock returns
The descriptive statistics for the period of November 2002 through December 2012
(Table I) suggest optimistic sentiment of housing investors as evidenced with positive
monthly and quarterly average SE, the investor SE index and the SEL index. If
the investor SE index can effectively capture the overall investor reactions to news, the
positive investor sentiment should be refected in high stock returns. The average
monthly housing stock returns of 0.64 per cent and quarterly returns of 1.85 per cent
over the sample period provide supportive evidence. The fact that both monthly and
quarterly series of SE and SEL share sizable positive coeffcients of correlation (ranged
from 43 to 61 per cent) with housing stock returns indicates the relevance and
importance of SE index in driving housing stock prices. Nonetheless, the correlation
between SE and SEL is low, 6.45 per cent in the monthly series and 7.29 per cent in the
quarterly data set. It means that SE and SEL may have independent explanatory power
on variations in housing stock prices. Results of regression equation (3) confrm that
Table I.
Descriptive statistics
and regression
coeffcients of SE
index
Monthly data (2002.11-2012.12) Quarterly data (2003.Q1-2012.Q4)
N Mean SD N Mean SD
Return 121 0.0064 0.0773 39 0.0185 0.1282
SE 121 0.0225 0.0795 39 0.0239 0.0483
SEL 121 0.0223 0.0794 39 0.0237 0.0484
Coeffcients of correlation
Return 1.0000 1.0000
SE 0.5240 1.0000 0.6139 1.0000
SEL 0.4260 0.0645 1.0000 0.4531 0.0729 1.0000
SE SEL Constant R
2
Coeffcient estimates of model (3) with the dependent variable of return
Monthly regression 0.4852 0.3834 ?0.0130 0.4290
(7.152)*** (5.650)*** (?2.268)**
Quarterly regression 1.5491 1.0884 ?0.0443 0.5444
(5.177)*** (3.639)*** (?2.573)**
Notes: Return ? percentage changes of the Nasdaq Housing Indexes; SE ? sentiment endurance
index from equations (1) and (2); SEL ? one-term lagged SE; N ? number of observations used in
calculations, the frst observationis excludedfromcalculations because of the use of SEL, the laggedSE;
t-values are inparentheses andall of themare signifcant at the 1 %level; **, ***represent the 5%and
1% signifcance levels, respectively
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both the current termof the SEindex and SELindex have signifcant explanatory power
on the housing stock returns based on either monthly or quarterly data. The two
variables can explain about 43 per cent of variation in the monthly housing stock returns
and 54 per cent in quarterly returns (Table I).
The descriptive statistics indicate some differences between the monthly and quarterly
series of SE. For instance, the standard deviation is about 4.8 per cent for the quarterly SE
andSELand8.0per cent for monthlySEandSEL. It suggests that the quarterlySEandSEL
are much less volatile than the monthly SEand SEL. Furthermore, the correlations between
housing stock returns and quarterly SEand SEL (61 and 45 per cent) seemhigher than that
between the monthly SE and SEL and housing stock returns (52 and 43 per cent). Those
differences canaffect forecastingqualityandmake the quarterlySEandSELmore accurate
predictors of future housing stock returns.
3.2 Rolling forecasts of housing stock returns
The forecasting ability of SE is the most crucial factor in verifying its importance to the
housing stock investors. To generate forecasts, equation (3) is frst estimated on a rolling
basis to get a set of coeffcient estimates of SE and SEL, and then, the coeffcients are
multipliedwithSEandSEL, combinedwiththe constant terms, to formin-sample forecasts.
All in-sample forecasts, 6- and 12-month and 4-, 6- and 8-quarter rolling forecasts, are
statistically indifferent from the actual housing stock returns (Table II). The results are
expected because the in-sample forecasting is merely about testing the goodness of ft for
data. To examine forecasting power of estimated rolling coeffcients of SEand SEL, lagged
coeffcients andconstant terms must replace the current ones. Table II reports out-of-sample
forecasts that are basedonone-periodlaggedcoeffcients. Althoughthe averages of absolute
errors for different kinds of out-of-sample forecasts are larger than that for the in-sample
forecasts, t-statistics of the equalitytest without anassumptionof equal variance once again
fail to reject the null hypothesis of equal means of Forecast and Return for all rolling
out-of-sample forecasts. The same results are obtained for the true forecasts that use only
one-period lagged coeffcients and intercepts as well as the one-period lagged independent
variable, SE. Overall, results reported in Table II suggest the decent forecasting ability for
SE. Nevertheless, the equality test perhaps exaggerate the accuracy of forecasting because
the test simply compares the mean of rolling forecasts with the mean of actual returns;
therefore, the test result may be skewed by the potential cancelations of extreme under- and
over-forecasts. The overstated accuracy is evidenced with high average absolute forecast
errors (over 10 per cent) for all quarterly rolling out-of-sample and true forecasts (Table II).
3.3 Quality of forecasts of housing stock returns
To eliminate the cancellation bias in assessing the forecasting ability of SE, this study
calculates accuracy ratios, the number of accurate forecasts versus the number of total
forecasts, for various kinds of rolling true forecasts. The accurate forecasts are defned as
those with an average value close to that of actual returns as suggested by the equality test.
There are two kinds of forecasts, UF with negative forecast errors and OF with positive
forecast errors. For example, the total number of 6-month rolling true forecasts is 116 in
which57 are UFand59 OF(Table III). After large under- andOFare rejectedbythe equality
test at the 10per cent signifcance level inseparate testingloops, the retainedUFare 32while
retained OF 27. Those retained UF and OF are statistically indifferent from the actual
housing stock returns. Therefore, the accuracy ratio for UF is 0.5614 (32/57) and for OF is
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0.4576 (27/59). The overall accuracy ratio for the combination of UF and OF is 0.5086 (59/
116). In contrast, the 12-month rolling true forecasts generate higher OF accuracy (0.5577)
and lower UF accuracy (0.4655); however, the overall accuracy remains the same (0.5091).
The quality of 6-month rolling forecast is better if the mean absolute forecast error (MAFE)
is considered. Fama and French (1997) report about 2.98 per cent and 2.77 per cent for the
average monthly rolling forecast errors for 48 industries based on the capital asset pricing
model (CAPM) and their 3-factor model, respectively. MAFE (2.31 per cent) for 6-month
rolling forecasts in Table III is much lower, about17%-22 per cent, than that. But MAFE is
about 2.73 per cent for 12-month rolling forecasts.
All 4-, 6- and 8-quarter rolling forecasts exhibit high accuracy. They have overall
accuracy ratios of 0.6944, 0.7941 and 0.8438, respectively (Table III). In fact, all three
quarterly forecasts enjoy considerable higher accuracy ratios in almost all aspects than
that for the monthly forecasts. The quarterly MAFE, range from 6.65 - 7.02 per cent, is
equivalent to a monthly MAFE of 2.31 per cent. The better forecasting ability of the
quarterly forecasts is consistent with the lower standard deviation of quarterly SE,
higher correlations between housing stock returns and quarterly SE and SEL, and
higher explanatory power of regression model, compared with monthly SE (Table I). It
Table II.
Results of equality
test for forecast and
return based on
different rolling
regressions in
equation (3)
Forecast Return t-stat P-value AbsError N
6-month rolling regressions
In-sample 0.0091 0.0069 0.2246 0.8225 0.0310 117
Out-of-sample 0.0163 0.0062 0.9450 0.3457 0.0604 116
True forecasting 0.0142 0.0062 0.7234 0.4702 0.0679 116
12-month rolling regressions
In-sample 0.0057 0.0039 0.1893 0.8500 0.0364 111
Out-of-sample 0.0065 0.0031 0.3468 0.7291 0.0478 110
True forecasting 0.0063 0.0031 0.2950 0.7683 0.0659 110
4-quarter rolling regressions
In-sample 0.0087 0.0111 ?0.0846 0.9328 0.0340 37
Out-of-sample 0.0050 0.0061 ?0.0309 0.9755 0.1473 36
True forecasting 0.0235 0.0061 0.5080 0.6131 0.1268 36
6-quarter rolling regressions
In-sample ?0.0042 0.0044 ?0.3018 0.7637 0.0578 35
Out-of-sample ?0.0092 0.0047 ?0.4580 0.6484 0.1075 34
True forecasting ?0.0085 0.0047 ?0.3914 0.6968 0.1154 34
8-quarter rolling regressions
In-sample ?0.0032 0.0042 ?0.2538 0.8005 0.0621 33
Out-of-sample ?0.0009 0.0011 ?0.0670 0.9468 0.1051 32
True forecasting 0.0042 0.0011 0.0931 0.9254 0.1092 32
Notes: In-sample forecasting ?constant
t
?[(coeffcient of SE)
t
*SE)] ?[(coeffcient of SEL)
t
*SEL)];
out-of-sample forecasting ?constant
t-1
?[(coeffcient of SE)
t-1
*SE] ?[(coeffcient of SEL)
t-1
*SEL]; true
forecasting ?constant
t-1
?[(coeffcient of SE)
t-1
*SEL] ?[(coeffcient of SEL)
t-1
*SEL]; SE ?sentiment
endurance index from equations (1) and (2); SEL ?one-term lagged SE; AbsError ?absolute value of
(Forecast and Return); N?number of observations used in calculations; t-stat ?statistic of the test for
equal means (Forecast and Return) without an assumption of equal variance
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is interesting to point out that the quarterly forecasts tend to generate higher accuracy
for under-forecasts (Table III).
In contrast to Fama and French’s (1997) fnding that length of the rolling estimation
period has no impact on forecasting accuracy, accuracy ratios for both OF and UF of
quarterly rolling forecasts in this study indicate that the length of the rolling estimation
period can affect the accuracy of forecasting. Results in Table III suggest that the
8-quarter rolling estimation period is more appropriate to predict future changes in
housing stock prices because it produces higher accuracy for UF, OF, and total forecasts
than for 4- and 6-quarter rolling forecasts.
Results in Table III validate the overall decent forecasting ability of the endurance
index. However, persistent extreme changes in housing stock market may severely
thwart the accuracy of rolling forecasts in tremendous volatile periods. Results in
Table IV indicate that most inaccurate forecasts are generated in the extraordinarily
volatile period of 2008 through 2009. For example, three out of fve most inaccurate
8-quarter rolling forecasts appear in the period which also contains most inaccurate 4-
and 6-quarter rolling forecasts. Clearly, the endurance index fails to predict the collapse
of the housing market in 2008. All three rolling forecasts for the fourth quarter 2008
greatly overestimate housing stock returns, as evidenced by the gigantic forecast errors
ranging from 44.78 to 65.70 per cent.
3.4 Forecasting housing prices
The overall decent forecasting ability of the endurance index may also be demonstrated
in the housing market. Past empirical evidence suggests that changes in housing prices
can signifcantly infuence corporate earnings and stock prices in the housing sector; if
the endurance index of housing investor sentiment can predict housing stock returns,
Table III.
Accuracy ratios for
different kinds of
rolling true forecasts
6-month 12-month 4-quarter 6-quarter 8-quarter
UF 57 58 20 21 18
Retained UF 32 27 17 17 16
Accuracy ratio 0.5614 0.4655 0.8500 0.8095 0.8889
Average error ?0.0233 ?0.0229 ?0.0715 ?0.0661 ?0.0722
OF 59 52 16 13 14
Retained OF 27 29 8 10 11
Accuracy ratio 0.4576 0.5577 0.5000 0.7692 0.7857
Average error 0.0229 0.0313 0.0559 0.0773 0.0646
Retained UF and OF 59 56 25 27 27
Total forecasts 116 110 36 34 32
Accuracy ratio 0.5086 0.5091 0.6944 0.7941 0.8438
MAFE 0.0231 0.02725 0.0665 0.0702 0.0691
Notes: UF ?number of forecasts that are smaller than actual returns; OF ?number of forecasts that
are greater than actual returns; retained UF?number of UFthat are statistically indifferent fromactual
returns, after excluding large UF at the 10 % signifcance level; retained OF ?number of OF that are
statistically indifferent from actual returns, after excluding large OF at the 10% signifcance level; UF
retain ratio ?retained UF/UF; OF retain ratio ?retained OF/OF; accuracy ratio ?ratio of retained UF
or OF to the number of forecasts; average error ?average of (Forecast and Return) for retained UF or
retained OF; MAFE ?mean absolute forecast error
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the index should be able to validate its forecasting ability on housing prices as well.
However, technically, it is impossible to construct the endurance index based on housing
prices because of the unavailability of the high and low housing prices. Therefore, this
study examines the causal relations between the endurance index of housing investor
sentiment and housing prices instead of conducting the true forecasting (equation [5])
that requires an endurance index based on housing prices.
Three housing price indexes compiled by the FHFA are used in the Granger-
causality test, the SALES, the EXPANDEDand the ALLTRANSAC. Results in Table V
show that SE and four lagged terms of SE have substantial explanatory power on all
three housing price indexes, supported by highly signifcant F-statistics and above
35 per cent R-squares. Results of the Granger-causality test based on 2- and 4-quarter lag
lengths indicate signifcant one-direction causal relations running from the endurance
index of housing investor sentiment to all three housing price indexes, except for
ALLTRANSAC which might Granger-cause changes in the endurance index up to four
quarters; nonetheless, the relation is signifcant only at the ten per cent level. The strong
evidence of one-direction causal relations reinforces that the endurance index of housing
investor sentiment has the decent forecasting ability on housing prices.
4. Concluding comments
Based on the PHLX HGX, this study creates a binomial probability distribution-based
endurance indexof housinginvestor sentiment to measure the probabilityof the highor low
housing stock price being the closing price. This housing investor SE index directly uses
housing stock price differentials to measure housing investor reactions to all relevant news.
Empirical results in this study suggest that the index not only plays a signifcant role in
explaining variations in housing stock returns but also has decent forecasting abilities.
To eliminate potential limitations in conventional forecasting assessment approach, this
study adopts forecasting and forecast-quality assessing methods developed by He (2012),
which use all lagged independent variables to forecast housing stock returns and a rigorous
procedure that excludes bias of offsets between extreme over- and under-forecasts to assess
the quality of forecasting. Results of the assessment indicate the following:
Table IV.
Distribution of
rejected inaccurate
quarterly rolling
forecasts
4-quarter 6-quarter 8-quarter
2004 Q1 (0.1147)
2005 Q4 (0.2075)
2006 Q3 (0.3356) Q2 (0.2182) Q2 (0.2148)
2007 Q3 (0.1769)
2008 Q4 (0.4478) Q4 (0.5185) Q4 (0.6570)
2009 Q1 (0.1315)
Q2 (?0.2379) Q2 (?0.2861) Q2 (?0.2899)
Q3 (?0.2954) Q3 (?0.3090) Q3 (?0.2495)
2010 Q4 (0.4513) Q1 (?0.2345)
2011 Q4 (?0.2206) Q4 (?0.2309)
2012 Q2 (0.2824) Q2 (0.2288) Q2 (0.2151)
Total number of rejected forecasts 11 7 5
Note: Forecast errors (Forecast and Return) are in parentheses
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• The 8-quarter rolling forecasts have the highest quality with an overall accuracy
ratio of 84.38 per cent, while the ratio (69.44 per cent) is the lowest for the 4-quarter
rolling forecasts.
• Quarterly forecasts are more accurate than monthly forecasts which have
accuracy ratios around 51 per cent.
• Extreme volatility of housing stock returns may impair the quality of forecasting
as suggested by the result that most inaccurate quarterly forecasts are
concentrated in the extraordinarily volatile years, 2008 and 2009.
• The decent forecasting ability of the endurance index of housing investor
sentiment on housing prices is refected in the signifcant one-direction causal
relations running from the index to all three housing price indexes.
Table V.
Quarterly OLS
coeffcients of SE and
its lag terms (2002.4-
2012.4)
Dependent variables
SALES EXPANDED ALLTRANSAC
SE ?0.0200 ?0.0005 0.0077
(?0.318) (?0.007) (0.144)
SE-1 0.0997 0.1266 0.0070
(1.624) (1.889)* (0.033)
SE-2 0.1621 0.1486 0.1204
(2.651)** (2.227)** (2.298)**
SE-3 0.1297 0.1696 0.1291
(2.114)** (2.534)** (2.457)**
SE-4 0.0332 0.0569 0.1375
(0.528) (0.828) (2.549)**
Constant term ?0.0066 ?0.0105 ?0.0055
(?1.667) (?2.455)** (?1.648)
SUM (COEFS) 0.4048 0.5012 0.4017
(3.27)*** (3.71)*** (3.78)***
F-statistic 3.34*** 3.69*** 3.99***
R
2
(%) 35.02 37.34 39.15
Granger causality tests Lag length ?2 Lag length ?4
Null hypothesis F-statistic P-value F-statistic P-value
SE does not Granger-cause SALES 4.0098 0.0273 2.4782 0.0669
SALES does not Granger-cause SE 1.6952 0.1987 2.1271 0.1039
SE dose not Granger-cause EXPANDED 3.0565 0.0602 3.1286 0.0302
EXPANDED does not Granger-cause SE 1.7470 0.1869 1.5287 0.2209
SE does not Granger-cause ALLTRANSAC 3.8754 0.0305 3.1835 0.0283
ALLTRANSAC does not Granger-cause SE 1.3569 0.2710 2.3072 0.0828
Notes: SE?sentiment endurance index fromequations (1) and (2); SALES ?Purchase-only Housing
Price Index by FHFA; EXPANDED ?Expanded-data Housing Price Index by FHFA; ALLTRANSAC ?
All-transaction Housing Price Index by FHFA; t-values are in parentheses; OLS ? ordinary least
squares; *, **, ***represent the 10%, 5% and 1% signifcance levels, respectively
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Findings of this study evidently suggest that, except for some extremely volatile
periods, the housing investor SE index can be used to predict, with decent accuracy,
future changes in the housing stock prices on a monthly or quarterly basis as well as
quarterly changes in the housing prices. Those projections are valuable to housing stock
investors and housing policy-makers.
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Corresponding author
Ling T. He can be contacted at: [email protected]
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doc_857766129.pdf
The purpose of this paper is to create an endurance index of housing investor sentiment and use
it to forecast housing stock returns. This study performs not only in-sample and out-of-sample forecasting,
like many previous studies did, but also a true forecasting by using all lag terms of independent variables. In
addition, an evaluation procedure is applied to quantify the quality of forecasts.
Journal of Financial Economic Policy
Forecasting of housing stock returns and housing prices: Evidence from the
endurance index of housing investor sentiment
Ling T. He
Article information:
To cite this document:
Ling T. He , (2015),"Forecasting of housing stock returns and housing prices", J ournal of Financial
Economic Policy, Vol. 7 Iss 2 pp. 90 - 103
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dx.doi.org/10.1108/J FEP-10-2014-0056
Santi Gopal Maji, Utpal Kumar De, (2015),"Regulatory capital and risk of Indian banks: a
simultaneous equation approach", J ournal of Financial Economic Policy, Vol. 7 Iss 2 pp. 140-156
http://dx.doi.org/10.1108/J FEP-06-2014-0038
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Forecasting of housing stock
returns and housing prices
Evidence from the endurance index of
housing investor sentiment
Ling T. He
Department of Economics & Finance, University of Central Arkansas,
Conway, Arkansas, USA
Abstract
Purpose – The purpose of this paper is to create anendurance indexof housinginvestor sentiment anduse
it to forecast housing stock returns. This study performs not only in-sample and out-of-sample forecasting,
like manyprevious studies did, but also a true forecastingbyusingall lagterms of independent variables. In
addition, an evaluation procedure is applied to quantify the quality of forecasts.
Design/methodology/approach – Using a binomial probability distribution model, this paper creates
anendurance indexof housinginvestor sentiment. The indexrefects the probabilityof the highor lowstock
price beingthe close price for the Philadelphia StockExchange HousingSector Index. This housinginvestor
sentiment endurance index directly uses housing stock price differentials to measure housing investor
reactions to all relevant news. Empirical results in this study suggest that the index can not only play a
signifcant role in explaining variations in housing stock returns but also have decent forecasting ability.
Findings – Results of this study reveal the considerable forecasting ability of the index. Monthly
forecasts of housing stock returns have an overall accuracy of 51 per cent, while the overall accuracy of
8-quarter rolling forecasts even reaches 84 per cent. In addition, the index has decent forecasting ability
on changes in housing prices as suggested by the strong evidence of one-direction causal relations
running from the endurance index to housing prices. However, extreme volatility of housing stock
returns may impair the forecasting quality.
Practical implications – The endurance index of housing investor sentiment is easy to construct and
use for forecasting housing stock returns. The demonstrated predictability of the index on housing stock
returns in this study can have broad implications on housing-related business practices through providing
an effective forecasting tool to investors and analysts of housing stocks, as well as housing policy-makers.
Originality/value – Despite different investor sentiment proxies suggested in the previous studies,
few of them can effectively predict stock returns, due to some embedded limitations. Many increases
and decreases inn prices cancel out each other during the trading day, as many unreliable sentiments
cancel out each other. This dynamic process reveals not only investor sentiment but also resilience or
endurance of sentiment. It is only long-lasting resilient sentiment that can be built in the closing price.
It means that the only feasible way to use investor sentiment contained in stock prices to forecast future
stock prices is to detach resilient investor sentiment from stock prices and construct an index of
endurance of investor sentiment.
Keywords Forecasting and simulation, Financial forecasting, Real estate services
Paper type Research paper
JEL classifcation – E37, G17, L85
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1757-6385.htm
JFEP
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Received10 January2014
Revised5 March2014
16 June 2014
Accepted7 July2014
Journal of Financial Economic
Policy
Vol. 7 No. 2, 2015
pp. 90-103
©Emerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-01-2014-0004
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1. Introduction
Researchers have studied the predictability of housing market and housing stocks for
long time. In early studies, Case and Shiller (1989, 1990) argue that the housing market
is not effcient and that price changes display positive autocorrelation. Therefore, the
housing market may be predictable. The authors report that the ratio of construction to
price, changes in adult population and real per capita income have forecasting ability on
housing price changes. As then many researchers, including Dua et al. (1999), Goyal and
Welch (2003, 2008), Gallin (2008), Campbell et al. (2009), Rapach and Strauss (2009),
Cochrane (2011), Gupta et al. (2011) and Ghysels et al. (2012), use different variables, such
as the price-rent ratio, leading indicators and different regression models, to predict
changes in the housing prices and home sales. Furthermore, He (2000) reports causal
relationships between residential real estate and securitized real estate (stocks). Piazzesi
et al. (2007), with their consumption-based asset pricing model, fnd that the “housing
share can be used to forecast excess returns on stocks”.
The extension of housing research to including securitized real estate prompts
research interests on forecastability of securitized real estate, such as real estate
investment trusts (REIT) stocks. Many previous studies, based on different variables
and estimation models, fnd that returns of securitized real estate may be predictable
because they are signifcantly correlated with other assets and affected by investor
responses to important economic as well as frm-specifc information. Examples include
Liu and Mei (1992, 1994), Li and Wang (1995), Nelling and Gyourko (1998), Brooks and
Tsolacos (2003), He and Webb (2006), He (2007) and Cabrera et al. (2011). However,
results on predictability of REITstock returns are inconsistent. Ling et al. (2000) offer an
explanation claiming that predictability of REIT stock returns is time-varying, due to
the instability or dynamics of stock prices. It is consistent with Welch and Goyal’s (2008)
fnding that equity premium prediction models in the academic literature are unstable
and produce poor in-sample and out-of-sample forecasts for 30 years.
There is a consensus that the dynamics of stock returns are determined by investor
reactions to information. Creating accurate measurements of investor reactions to
important news is certainly a vital issue in forecasting stock returns. However, there is
no agreement on what kind of information that causes fuctuations in the stock prices.
For example, Fama and French (1993, 1996 and 1997) develop their three-factor model to
explain and predict factor betas and excess returns of stocks, while other researchers use
frm-specifc variables, instead of macro variables, to explain and forecast stock returns.
Daniel and Titman (1997) argue that information about frm characteristics can better
explain variations in cross-sectional stock returns. In fact, investors respond to all
pertinent information, not just frm-specifc information. To improve forecasting
quality, this study uses a comprehensive measure of investor reactions to all sorts of
relevant information, macro and frm-specifc, to predict changes in housing stock
returns.
According to Delong et al. (1990), the underlying issue of investor reaction to news or
investor sentiment essentially is about howinvestors interpret news to formtheir beliefs
about future cash fows and investment risks. However, this process is not linear.
Investors may underreact to news when stock prices slowly refect news; on the other
hand, investors might consistently overreact to news in the same direction over long
horizons and cause stocks overpriced (Barberis et al., 1998). Obviously, it is investor
sentiment that drives stock prices. There are many different kinds of investor sentiment
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indexes created and reported in the literature. For example, Baker and Wurgler (2007)
listed various widely used investor sentiment proxies, such as investor survey, investor
mood, retail investor trades, mutual fund fows, trading volume, dividend premium,
close-end fund discount, opinion implied volatility, initial public offering (IPO) frst-day
returns, IPO volume, equity issues over total new issues and insider trading. The
investor sentiment indexes and their lagged terms are often used as predictors for stock
market returns or portfolio returns (Baker and Wurgler, 2006).
Despite different investor sentiment proxies suggested in the previous studies, fewof
them can effectively predict stock returns, due to some embedded limitations. The
existing sentiment indexes are either event-based or opinion- and mood-based. Indexes
based on individual events cannot serve as a measure of a continuous process, because
different events have their own frequencies, regularly or irregularly. In contrast,
changes in stock prices follow a continuous process which refects the way investors to
react to news, i.e. continuously changing bid and ask prices. During a trading day,
investors have to constantly analyze and respond to different kinds of news, and their
reactions are instantaneously quantifed into stock prices, no matter the reactions are
rational or irrational, optimistic or pessimistic. Apparently, the event-based sentiment
indexes, as a non-continuous measure, cannot effectively forecast stock returns. In
addition, stock price dynamics essentially is a result of investor reactions to all relevant
important information, not just to a particular type of news. Investor reaction,
determined by its nature, is not constant but time-varying. The time-varying nature
makes some opinion- and mood-based sentiments short-lived and unreliable. That is,
these sentiments may not be refected into the closing price which is the only one that
can evaluate persistence of investor reactions to all signifcant events and news during
the entire trading day. Many other prices cancel out each other during the trading day,
as many unreliable sentiments cancel out each other.
Although many prices between the high and low prices are going to cancel out each
other during a trading day, He (2012) argues that some of them can form a lasting
momentumor force that drives stock prices more or less inclining to the high or lowprice
until the closure of the stock market. This dynamic process reveals not only
time-varying investor sentiments but also the resilience or endurance of sentiments,
which is built on signifcant pertinent information. The long-lasting resilient sentiment
cannot be offset and only refected in the closing price, the price at the end of a trading
day. Therefore, the probability of the high or lowprice being the closing price is used to
quantify the endurance of investor sentiment. It is an effective way to detach resilient
investor sentiment from stock price dynamics. He (2012) provides evidence that the
endurance index has decent forecasting power on returns of the stock market
represented by the S&P 500 Stock Index. Can the endurance index also effectively
predict stock returns in major industries or sectors? This study is to empirically examine
the issue.
Applying the endurance index of investor sentiment to forecast housing stock
returns and housing prices is an interesting and important endeavor. First, this
sentiment endurance-based forecasting approach is completely different from all
housing-related forecasting models reported in the literature. According to Welch and
Goyal’s (2008), equity premium prediction models in the academic literature are
unstable, and for long time, they produce poor in-sample and out-of-sample forecasts.
Given the fact that the endurance index model can produce decent forecasts on stock
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market returns (He, 2012), it is reasonable to expect the model that can demonstrate the
similar or even better forecasting ability on housing stock returns and housing prices.
Second, using endurance index model to enhance the forecasting ability on securitized
and unsecuritized housing market has valuable implications to many stakeholders in
the housing sector. The housing sector is one of major pillars of the US economy. The
sector covers several important industries, such as home building, fnancial services
(mortgage lending, home insurance, etc.) and building materials. The demonstrated
predictability of the index on housing stock returns and home prices in this study can
have broad infuences on housing-related business practices, including decisions on
hiring employees, as well as housing and fnancial policy-makers through providing a
near-termindicator of health of the housing market. Finally, additional beneft provided
by the endurance index of housing investor sentiment is that it is easy to construct and
can be used as an effective forecasting tool for investors and analysts of housing stocks,
as well as housing policy-makers.
The main purpose of this study is to create an endurance index of housing investor
sentiment and use it to forecast housing stock returns. This study performs not only
in-sample and out-of-sample forecasting, like many previous studies did, but also a true
forecasting by using all lag terms of independent variables. In addition, an evaluation
procedure is applied to quantify the quality of forecasts. Finally, causality tests are
conducted to verify if variations in the sentiment endurance (SE) index can
Grange-cause changes in housing prices.
The remainder of the paper is organized as the follow. Section 2 describes the
methods and data used in this study. Section 3 discusses empirical results, and Section
4 concludes major fndings.
2. Methods and data
The SE index essentially measures the probabilities of the most optimistic and
pessimistic sentiments, quantifed by the high and low prices, respectively, being the
closing price. The following is the binomial probability distribution model developed by
He (2012):
P
t
? H
t
? (1 ? P
t
) ? L
t
? C
t
, (1)
where P
t
represents the probability of the high price ( H
t
) being the closing price ( C
t
) and
takes a value between zero to one; and ( 1 ?P
t
) is the probability of the low price ( L
t
)
being the closing price. When P
t
? 0.5, the overall investor sentiment is neutral; if
P
t
? 0.5, the overall sentiment is considered optimistic, while P
t
? 0.5 indicates the
overall pessimistic sentiment. Therefore, the index of investor SEat time t is revealed in:
SE
t
? (P
t
? 0.5). (2)
A positive SE indicates a positive sentiment toward the closing price, while a negative
SErepresents a higher probability of the lowprice being the closing price. This SEindex
can effectively quantify investors’ continuous momentous reactions to all important
news. The persistence or endurance of these reactions, implied in closing prices, largely
shape the dynamics of stock market returns.
The primary data set used in this study is the Philadelphia Stock Exchange (PHLX)
Housing Sector Index (HGX) which comprises 19 companies that work directly in
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housing-related industries, such as construction of residential homes, mortgage
insurance and supply of building materials. The index has the potential to track the
strength of the housing market, such as home sales and residential real estate values.
Obviously, it is a better proxy for securitized residential real estate than equity REITs,
a widely used proxy, which essentially concentrates on commercial real estate. This is
the main reason why the HGX index, as a portfolio of housing stocks, can better serve
the purpose of predicting securitized residential real estate and home prices. The index
began in 2002. This study covers a period of November of 2002 through December of
2012. Data availability dictates the sample period. The index numbers include high, low
and closing prices. The daily indexes are averaged into monthly and quarterly series.
The monthly and quarterly SE indexes are constructed based on equations (1) and (2).
First, the high (H), low (L) and close (C) prices are plugged into equation (1) to solve the
probability (P), then, subtracting 0.5 from P to get SE index.
The monthly and quarterly endurance indexes of housing investor sentiment and the
lag terms of the indexes are then used to explain changes in monthly and quarterly
housing stock returns represented by percentage changes in the HGX, to examine the
explanatory power of each independent variable. Regression results indicate that only
the current term and one-period lagged term of SE (SEL) have signifcant infuence on
housing stock returns. The result is in line with fndings in previous studies. For
example, He (2012) reports that both the SE and lagged SE can explain a signifcant
portion of variation in the stock market which is represented by the S&P 500 Stock
Index and Baker and Wurgler (2006) fnd that their lagged sentiment index has a
negative impact on returns of some stock portfolios.
This study assesses the forecasting ability of SE to justify the relevancy or
importance of the endurance index to housing stock investing professionals. The
forecasting starts with applying different rolling periods to estimate coeffcients of the
following regression model:
R
t
? a
t
? b
t
SE
t
? c
t
SE
t?1
? e
t
, (3)
where R
t
represents housing stock returns at time t. The rolling coeffcient estimates of
SEand SEL, together with the rolling constant terms, are used to forecast housing stock
returns based on different forecasting methods. First, the in-sample forecasting which
uses rolling coeffcients at time t to predict housing stock returns at time t. There is no
time lag between predicting variables and the variable to be predicted. In fact, the
in-sample forecasting is simply a test for the goodness of ft. Second, the out-of-sample
forecasting that uses one-period lagged rolling coeffcients and constant terms to predict
changes in the housing stocks:
F
t
? a
t?1
? (b
t?1
? SE
t
) ? (c
t?1
? SE
t?1
). (4)
The out-of-sample forecasting demonstrates some forecasting ability of rolling
coeffcients, as it is widely used as a forecasting tool in previous studies, such as Fama
and French (1997). Nevertheless, there exists a potential problemthat SEat time t is still
used in predicting of housing stock returns at time t. A true feasible forecasting model
should use all lagged variables to forecast current changes in the housing stocks. That
leads to the third model which may be considered as a true forecasting model:
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F
t
? a
t?1
? (b
t?1
? SE
t?1
) ? (c
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? SE
t?1
). (5)
In equation (5), the SEL substitutes SE and multiplies with the one-period lagged
coeffcient of b. Equation (5) is not completely consistent with the rolling regression
model, equation (3), in which coeffcient of b represents sensitivity of housing stock
returns to the current term of SE, not the SEL. However, if SE is stable at times of t and
t?1, that may warrant the feasibility of equation (5).
A simple equality test can assess the quality of the above rolling forecasts. This
paper uses the t-test without the assumption of equal variances between the two series
in analysis of variance to examine if the averages of rolling forecasts are statistically
indifferent fromthe actual housing stock returns. An insignifcant test statistic indicates
that the forecasts, on average, are not considerably deviated from the actual housing
stock returns and, therefore, are statistically accurate. As He (2012) points out there is a
potential faw involved in this approach, that is extremely positive and negative
inaccurate forecasts may cancel out each other and result in an average of forecasts close
to the mean of actual housing stock returns. The procedure of calculating accuracy ratio
developed by He (2012) can effectively eliminate the conceivable unreliable and
misleading equality test results.
The procedure starts with sorting both series of stock return forecasts and actual
housing stock returns by forecast errors (forecasts – actual returns) in an ascending
order (smallest to largest). Forecasts with negative errors are known as under-forecasts
(UF), while those with positive errors are referred as over-forecasts. Then, all
observations associated with positive forecast errors (the bottompart of the sample) are
deleted. The remaining observations with negative forecast errors are in a sequence of
the smallest (most inaccurate) to the largest (most accurate). The equality test for the
forecasts and their corresponding real housing stock returns is performed repeatedly in
a loop that begins with all UFand their corresponding stock returns. If the statistic of the
frst test is signifcant, observation one of both variables goes out. If the second test
statistic remains signifcant, observation two is out. As more inaccurate forecasts are
thrown out, the signifcance level of the test statistic keeps going down, from the 1, 5 to
10 per cent. When the test statistic is not signifcant at the 10 per cent level, that is the
null hypothesis of equal means of the forecasts and their corresponding housing stock
returns cannot be rejected at the 10 per cent level, the loop stops. The remaining UF are
statistically considered accurate.
The above process is repeated one more time with variables sorted by positive
forecast errors from the largest to the smallest to identify accurate over-forecasts. The
number of accurate over-forecasts (OF) plus the number of accurate UF from the
previous process equals the total number of accurate forecasts. The total number of
accurate forecasts is then divided by the total number of forecasts to get the accuracy
ratio which effectively removes the problemof cancellation between extreme under- and
over-forecasts. Compared with the traditional forecast quality measure, the absolute
forecast error, the above forecast quality assessment reports not only the overall
forecast accuracy which is also refected in the absolute forecast error but also the
unique distribution of accurate forecasts by showing the numbers of accurate over- and
under-forecasts.
This study performs the Granger-causality test to examine the causal relations
between the endurance index of housing invest sentiment and housing prices. Three
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housing price indexes compiled by the Federal Housing Finance Agency (FHFA) are
used in the test, the Purchase-only Housing Price Index (SALES), the Expanded-data
Housing Price Index (EXPANDED) and the All-transaction Housing Price Index
(ALLTRANSAC). Due to the unavailability of the high and low housing prices, it is
impossible to build an endurance index derived from housing prices. This is the
reason why the causality test is used to replace a true forecasting on housing prices.
3. Results
3.1 Correlations between the SE index and housing stock returns
The descriptive statistics for the period of November 2002 through December 2012
(Table I) suggest optimistic sentiment of housing investors as evidenced with positive
monthly and quarterly average SE, the investor SE index and the SEL index. If
the investor SE index can effectively capture the overall investor reactions to news, the
positive investor sentiment should be refected in high stock returns. The average
monthly housing stock returns of 0.64 per cent and quarterly returns of 1.85 per cent
over the sample period provide supportive evidence. The fact that both monthly and
quarterly series of SE and SEL share sizable positive coeffcients of correlation (ranged
from 43 to 61 per cent) with housing stock returns indicates the relevance and
importance of SE index in driving housing stock prices. Nonetheless, the correlation
between SE and SEL is low, 6.45 per cent in the monthly series and 7.29 per cent in the
quarterly data set. It means that SE and SEL may have independent explanatory power
on variations in housing stock prices. Results of regression equation (3) confrm that
Table I.
Descriptive statistics
and regression
coeffcients of SE
index
Monthly data (2002.11-2012.12) Quarterly data (2003.Q1-2012.Q4)
N Mean SD N Mean SD
Return 121 0.0064 0.0773 39 0.0185 0.1282
SE 121 0.0225 0.0795 39 0.0239 0.0483
SEL 121 0.0223 0.0794 39 0.0237 0.0484
Coeffcients of correlation
Return 1.0000 1.0000
SE 0.5240 1.0000 0.6139 1.0000
SEL 0.4260 0.0645 1.0000 0.4531 0.0729 1.0000
SE SEL Constant R
2
Coeffcient estimates of model (3) with the dependent variable of return
Monthly regression 0.4852 0.3834 ?0.0130 0.4290
(7.152)*** (5.650)*** (?2.268)**
Quarterly regression 1.5491 1.0884 ?0.0443 0.5444
(5.177)*** (3.639)*** (?2.573)**
Notes: Return ? percentage changes of the Nasdaq Housing Indexes; SE ? sentiment endurance
index from equations (1) and (2); SEL ? one-term lagged SE; N ? number of observations used in
calculations, the frst observationis excludedfromcalculations because of the use of SEL, the laggedSE;
t-values are inparentheses andall of themare signifcant at the 1 %level; **, ***represent the 5%and
1% signifcance levels, respectively
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both the current termof the SEindex and SELindex have signifcant explanatory power
on the housing stock returns based on either monthly or quarterly data. The two
variables can explain about 43 per cent of variation in the monthly housing stock returns
and 54 per cent in quarterly returns (Table I).
The descriptive statistics indicate some differences between the monthly and quarterly
series of SE. For instance, the standard deviation is about 4.8 per cent for the quarterly SE
andSELand8.0per cent for monthlySEandSEL. It suggests that the quarterlySEandSEL
are much less volatile than the monthly SEand SEL. Furthermore, the correlations between
housing stock returns and quarterly SEand SEL (61 and 45 per cent) seemhigher than that
between the monthly SE and SEL and housing stock returns (52 and 43 per cent). Those
differences canaffect forecastingqualityandmake the quarterlySEandSELmore accurate
predictors of future housing stock returns.
3.2 Rolling forecasts of housing stock returns
The forecasting ability of SE is the most crucial factor in verifying its importance to the
housing stock investors. To generate forecasts, equation (3) is frst estimated on a rolling
basis to get a set of coeffcient estimates of SE and SEL, and then, the coeffcients are
multipliedwithSEandSEL, combinedwiththe constant terms, to formin-sample forecasts.
All in-sample forecasts, 6- and 12-month and 4-, 6- and 8-quarter rolling forecasts, are
statistically indifferent from the actual housing stock returns (Table II). The results are
expected because the in-sample forecasting is merely about testing the goodness of ft for
data. To examine forecasting power of estimated rolling coeffcients of SEand SEL, lagged
coeffcients andconstant terms must replace the current ones. Table II reports out-of-sample
forecasts that are basedonone-periodlaggedcoeffcients. Althoughthe averages of absolute
errors for different kinds of out-of-sample forecasts are larger than that for the in-sample
forecasts, t-statistics of the equalitytest without anassumptionof equal variance once again
fail to reject the null hypothesis of equal means of Forecast and Return for all rolling
out-of-sample forecasts. The same results are obtained for the true forecasts that use only
one-period lagged coeffcients and intercepts as well as the one-period lagged independent
variable, SE. Overall, results reported in Table II suggest the decent forecasting ability for
SE. Nevertheless, the equality test perhaps exaggerate the accuracy of forecasting because
the test simply compares the mean of rolling forecasts with the mean of actual returns;
therefore, the test result may be skewed by the potential cancelations of extreme under- and
over-forecasts. The overstated accuracy is evidenced with high average absolute forecast
errors (over 10 per cent) for all quarterly rolling out-of-sample and true forecasts (Table II).
3.3 Quality of forecasts of housing stock returns
To eliminate the cancellation bias in assessing the forecasting ability of SE, this study
calculates accuracy ratios, the number of accurate forecasts versus the number of total
forecasts, for various kinds of rolling true forecasts. The accurate forecasts are defned as
those with an average value close to that of actual returns as suggested by the equality test.
There are two kinds of forecasts, UF with negative forecast errors and OF with positive
forecast errors. For example, the total number of 6-month rolling true forecasts is 116 in
which57 are UFand59 OF(Table III). After large under- andOFare rejectedbythe equality
test at the 10per cent signifcance level inseparate testingloops, the retainedUFare 32while
retained OF 27. Those retained UF and OF are statistically indifferent from the actual
housing stock returns. Therefore, the accuracy ratio for UF is 0.5614 (32/57) and for OF is
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0.4576 (27/59). The overall accuracy ratio for the combination of UF and OF is 0.5086 (59/
116). In contrast, the 12-month rolling true forecasts generate higher OF accuracy (0.5577)
and lower UF accuracy (0.4655); however, the overall accuracy remains the same (0.5091).
The quality of 6-month rolling forecast is better if the mean absolute forecast error (MAFE)
is considered. Fama and French (1997) report about 2.98 per cent and 2.77 per cent for the
average monthly rolling forecast errors for 48 industries based on the capital asset pricing
model (CAPM) and their 3-factor model, respectively. MAFE (2.31 per cent) for 6-month
rolling forecasts in Table III is much lower, about17%-22 per cent, than that. But MAFE is
about 2.73 per cent for 12-month rolling forecasts.
All 4-, 6- and 8-quarter rolling forecasts exhibit high accuracy. They have overall
accuracy ratios of 0.6944, 0.7941 and 0.8438, respectively (Table III). In fact, all three
quarterly forecasts enjoy considerable higher accuracy ratios in almost all aspects than
that for the monthly forecasts. The quarterly MAFE, range from 6.65 - 7.02 per cent, is
equivalent to a monthly MAFE of 2.31 per cent. The better forecasting ability of the
quarterly forecasts is consistent with the lower standard deviation of quarterly SE,
higher correlations between housing stock returns and quarterly SE and SEL, and
higher explanatory power of regression model, compared with monthly SE (Table I). It
Table II.
Results of equality
test for forecast and
return based on
different rolling
regressions in
equation (3)
Forecast Return t-stat P-value AbsError N
6-month rolling regressions
In-sample 0.0091 0.0069 0.2246 0.8225 0.0310 117
Out-of-sample 0.0163 0.0062 0.9450 0.3457 0.0604 116
True forecasting 0.0142 0.0062 0.7234 0.4702 0.0679 116
12-month rolling regressions
In-sample 0.0057 0.0039 0.1893 0.8500 0.0364 111
Out-of-sample 0.0065 0.0031 0.3468 0.7291 0.0478 110
True forecasting 0.0063 0.0031 0.2950 0.7683 0.0659 110
4-quarter rolling regressions
In-sample 0.0087 0.0111 ?0.0846 0.9328 0.0340 37
Out-of-sample 0.0050 0.0061 ?0.0309 0.9755 0.1473 36
True forecasting 0.0235 0.0061 0.5080 0.6131 0.1268 36
6-quarter rolling regressions
In-sample ?0.0042 0.0044 ?0.3018 0.7637 0.0578 35
Out-of-sample ?0.0092 0.0047 ?0.4580 0.6484 0.1075 34
True forecasting ?0.0085 0.0047 ?0.3914 0.6968 0.1154 34
8-quarter rolling regressions
In-sample ?0.0032 0.0042 ?0.2538 0.8005 0.0621 33
Out-of-sample ?0.0009 0.0011 ?0.0670 0.9468 0.1051 32
True forecasting 0.0042 0.0011 0.0931 0.9254 0.1092 32
Notes: In-sample forecasting ?constant
t
?[(coeffcient of SE)
t
*SE)] ?[(coeffcient of SEL)
t
*SEL)];
out-of-sample forecasting ?constant
t-1
?[(coeffcient of SE)
t-1
*SE] ?[(coeffcient of SEL)
t-1
*SEL]; true
forecasting ?constant
t-1
?[(coeffcient of SE)
t-1
*SEL] ?[(coeffcient of SEL)
t-1
*SEL]; SE ?sentiment
endurance index from equations (1) and (2); SEL ?one-term lagged SE; AbsError ?absolute value of
(Forecast and Return); N?number of observations used in calculations; t-stat ?statistic of the test for
equal means (Forecast and Return) without an assumption of equal variance
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is interesting to point out that the quarterly forecasts tend to generate higher accuracy
for under-forecasts (Table III).
In contrast to Fama and French’s (1997) fnding that length of the rolling estimation
period has no impact on forecasting accuracy, accuracy ratios for both OF and UF of
quarterly rolling forecasts in this study indicate that the length of the rolling estimation
period can affect the accuracy of forecasting. Results in Table III suggest that the
8-quarter rolling estimation period is more appropriate to predict future changes in
housing stock prices because it produces higher accuracy for UF, OF, and total forecasts
than for 4- and 6-quarter rolling forecasts.
Results in Table III validate the overall decent forecasting ability of the endurance
index. However, persistent extreme changes in housing stock market may severely
thwart the accuracy of rolling forecasts in tremendous volatile periods. Results in
Table IV indicate that most inaccurate forecasts are generated in the extraordinarily
volatile period of 2008 through 2009. For example, three out of fve most inaccurate
8-quarter rolling forecasts appear in the period which also contains most inaccurate 4-
and 6-quarter rolling forecasts. Clearly, the endurance index fails to predict the collapse
of the housing market in 2008. All three rolling forecasts for the fourth quarter 2008
greatly overestimate housing stock returns, as evidenced by the gigantic forecast errors
ranging from 44.78 to 65.70 per cent.
3.4 Forecasting housing prices
The overall decent forecasting ability of the endurance index may also be demonstrated
in the housing market. Past empirical evidence suggests that changes in housing prices
can signifcantly infuence corporate earnings and stock prices in the housing sector; if
the endurance index of housing investor sentiment can predict housing stock returns,
Table III.
Accuracy ratios for
different kinds of
rolling true forecasts
6-month 12-month 4-quarter 6-quarter 8-quarter
UF 57 58 20 21 18
Retained UF 32 27 17 17 16
Accuracy ratio 0.5614 0.4655 0.8500 0.8095 0.8889
Average error ?0.0233 ?0.0229 ?0.0715 ?0.0661 ?0.0722
OF 59 52 16 13 14
Retained OF 27 29 8 10 11
Accuracy ratio 0.4576 0.5577 0.5000 0.7692 0.7857
Average error 0.0229 0.0313 0.0559 0.0773 0.0646
Retained UF and OF 59 56 25 27 27
Total forecasts 116 110 36 34 32
Accuracy ratio 0.5086 0.5091 0.6944 0.7941 0.8438
MAFE 0.0231 0.02725 0.0665 0.0702 0.0691
Notes: UF ?number of forecasts that are smaller than actual returns; OF ?number of forecasts that
are greater than actual returns; retained UF?number of UFthat are statistically indifferent fromactual
returns, after excluding large UF at the 10 % signifcance level; retained OF ?number of OF that are
statistically indifferent from actual returns, after excluding large OF at the 10% signifcance level; UF
retain ratio ?retained UF/UF; OF retain ratio ?retained OF/OF; accuracy ratio ?ratio of retained UF
or OF to the number of forecasts; average error ?average of (Forecast and Return) for retained UF or
retained OF; MAFE ?mean absolute forecast error
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the index should be able to validate its forecasting ability on housing prices as well.
However, technically, it is impossible to construct the endurance index based on housing
prices because of the unavailability of the high and low housing prices. Therefore, this
study examines the causal relations between the endurance index of housing investor
sentiment and housing prices instead of conducting the true forecasting (equation [5])
that requires an endurance index based on housing prices.
Three housing price indexes compiled by the FHFA are used in the Granger-
causality test, the SALES, the EXPANDEDand the ALLTRANSAC. Results in Table V
show that SE and four lagged terms of SE have substantial explanatory power on all
three housing price indexes, supported by highly signifcant F-statistics and above
35 per cent R-squares. Results of the Granger-causality test based on 2- and 4-quarter lag
lengths indicate signifcant one-direction causal relations running from the endurance
index of housing investor sentiment to all three housing price indexes, except for
ALLTRANSAC which might Granger-cause changes in the endurance index up to four
quarters; nonetheless, the relation is signifcant only at the ten per cent level. The strong
evidence of one-direction causal relations reinforces that the endurance index of housing
investor sentiment has the decent forecasting ability on housing prices.
4. Concluding comments
Based on the PHLX HGX, this study creates a binomial probability distribution-based
endurance indexof housinginvestor sentiment to measure the probabilityof the highor low
housing stock price being the closing price. This housing investor SE index directly uses
housing stock price differentials to measure housing investor reactions to all relevant news.
Empirical results in this study suggest that the index not only plays a signifcant role in
explaining variations in housing stock returns but also has decent forecasting abilities.
To eliminate potential limitations in conventional forecasting assessment approach, this
study adopts forecasting and forecast-quality assessing methods developed by He (2012),
which use all lagged independent variables to forecast housing stock returns and a rigorous
procedure that excludes bias of offsets between extreme over- and under-forecasts to assess
the quality of forecasting. Results of the assessment indicate the following:
Table IV.
Distribution of
rejected inaccurate
quarterly rolling
forecasts
4-quarter 6-quarter 8-quarter
2004 Q1 (0.1147)
2005 Q4 (0.2075)
2006 Q3 (0.3356) Q2 (0.2182) Q2 (0.2148)
2007 Q3 (0.1769)
2008 Q4 (0.4478) Q4 (0.5185) Q4 (0.6570)
2009 Q1 (0.1315)
Q2 (?0.2379) Q2 (?0.2861) Q2 (?0.2899)
Q3 (?0.2954) Q3 (?0.3090) Q3 (?0.2495)
2010 Q4 (0.4513) Q1 (?0.2345)
2011 Q4 (?0.2206) Q4 (?0.2309)
2012 Q2 (0.2824) Q2 (0.2288) Q2 (0.2151)
Total number of rejected forecasts 11 7 5
Note: Forecast errors (Forecast and Return) are in parentheses
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• The 8-quarter rolling forecasts have the highest quality with an overall accuracy
ratio of 84.38 per cent, while the ratio (69.44 per cent) is the lowest for the 4-quarter
rolling forecasts.
• Quarterly forecasts are more accurate than monthly forecasts which have
accuracy ratios around 51 per cent.
• Extreme volatility of housing stock returns may impair the quality of forecasting
as suggested by the result that most inaccurate quarterly forecasts are
concentrated in the extraordinarily volatile years, 2008 and 2009.
• The decent forecasting ability of the endurance index of housing investor
sentiment on housing prices is refected in the signifcant one-direction causal
relations running from the index to all three housing price indexes.
Table V.
Quarterly OLS
coeffcients of SE and
its lag terms (2002.4-
2012.4)
Dependent variables
SALES EXPANDED ALLTRANSAC
SE ?0.0200 ?0.0005 0.0077
(?0.318) (?0.007) (0.144)
SE-1 0.0997 0.1266 0.0070
(1.624) (1.889)* (0.033)
SE-2 0.1621 0.1486 0.1204
(2.651)** (2.227)** (2.298)**
SE-3 0.1297 0.1696 0.1291
(2.114)** (2.534)** (2.457)**
SE-4 0.0332 0.0569 0.1375
(0.528) (0.828) (2.549)**
Constant term ?0.0066 ?0.0105 ?0.0055
(?1.667) (?2.455)** (?1.648)
SUM (COEFS) 0.4048 0.5012 0.4017
(3.27)*** (3.71)*** (3.78)***
F-statistic 3.34*** 3.69*** 3.99***
R
2
(%) 35.02 37.34 39.15
Granger causality tests Lag length ?2 Lag length ?4
Null hypothesis F-statistic P-value F-statistic P-value
SE does not Granger-cause SALES 4.0098 0.0273 2.4782 0.0669
SALES does not Granger-cause SE 1.6952 0.1987 2.1271 0.1039
SE dose not Granger-cause EXPANDED 3.0565 0.0602 3.1286 0.0302
EXPANDED does not Granger-cause SE 1.7470 0.1869 1.5287 0.2209
SE does not Granger-cause ALLTRANSAC 3.8754 0.0305 3.1835 0.0283
ALLTRANSAC does not Granger-cause SE 1.3569 0.2710 2.3072 0.0828
Notes: SE?sentiment endurance index fromequations (1) and (2); SALES ?Purchase-only Housing
Price Index by FHFA; EXPANDED ?Expanded-data Housing Price Index by FHFA; ALLTRANSAC ?
All-transaction Housing Price Index by FHFA; t-values are in parentheses; OLS ? ordinary least
squares; *, **, ***represent the 10%, 5% and 1% signifcance levels, respectively
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Findings of this study evidently suggest that, except for some extremely volatile
periods, the housing investor SE index can be used to predict, with decent accuracy,
future changes in the housing stock prices on a monthly or quarterly basis as well as
quarterly changes in the housing prices. Those projections are valuable to housing stock
investors and housing policy-makers.
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Corresponding author
Ling T. He can be contacted at: [email protected]
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