Description
This study aims to adapt a neural network based fuzzy time series model to improve Taiwan’s
tourism demand forecasting
International Journal of Culture, Tourism and Hospitality Research
Forecasting tourism demand by fuzzy time series models
Kun-Huang Huarng Tiffany Hui-Kuang Yu Luiz Moutinho Yu-Chun Wang
Article information:
To cite this document:
Kun-Huang Huarng Tiffany Hui-Kuang Yu Luiz Moutinho Yu-Chun Wang, (2012),"Forecasting tourism demand by fuzzy time series models",
International J ournal of Culture, Tourism and Hospitality Research, Vol. 6 Iss 4 pp. 377 - 388
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Forecasting tourism demand by fuzzy time
series models
Kun-Huang Huarng, Tiffany Hui-Kuang Yu, Luiz Moutinho and Yu-Chun Wang
Abstract
Purpose – This study aims to adapt a neural network based fuzzy time series model to improve Taiwan’s
tourism demand forecasting.
Design/methodology/approach – Fuzzy sets are for modeling imprecise data and neural networks are
for establishing non-linear relationships among fuzzy sets. A neural network based fuzzy time series
model is adapted as the forecasting model. Both in-sample estimation and out-of-sample forecasting
are performed.
Findings – This study outperforms previous studies undertaken during the SARS events of 2002-2003.
Research limitations/implications – The forecasting model only takes the observation of one previous
time period into consideration. Subsequent studies can extend the model to consider previous time
periods by establishing fuzzy relationships.
Originality/value – Non-linear data is complicated to forecast, and it is even more dif?cult to forecast
nonlinear data with shocks. The forecasting model in this study outperforms other studies in forecasting
the nonlinear tourism demands during the SARS event of November 2002 to June 2003.
Keywords Degrees of memberships, Fuzzy time series models, Neural networks,
Severe Acute Respiratory Syndrome (SARS), Tourism management, Modelling
Paper type Research paper
1. Introduction
International tourism has become a fairly large industry (Tisdell, 2000) and a very
competitive business. Tourism also plays a signi?cant role in national economies both
directly and indirectly by providing employment and earning much foreign exchange,
explaining why so many small countries rely heavily on tourism. Forecasting arrivals of
tourists is meaningful in that forecasts can help public or private sectors to avoid shortages
or surpluses of goods and services. Hence, the need for accurate forecasts of the demand
for tourism is widely recognized (Witt and Witt, 1995).
Researchers, practitioners, and policy makers have long recognized the necessity of
accurate forecasts for tourism demand (Sheldon and Var, 1985). Accurate forecasts would
help managers and investors make operational tactical and strategic decisions. Similarly,
governments need accurate forecasts about tourism demand to plan for tourism
infrastructure such as accommodation site planning, and transportation development.
In spite of consensus on the need for accurate forecasting, and an understanding of the
bene?ts of accurate forecasts, no standard supplier of tourism forecasts exists (Witt and
Witt, 1995). Also, no single forecasting model can outweigh all other forecasting models in
terms of forecasting accuracy. Previous studies of forecasting demand for tourism have
been primarily time-series models and regression models (Wong, 1997). Time-series
models are often able to achieve good forecasting results (Andrew et al., 1990; Martin and
Witt, 1989).
DOI 10.1108/17506181211265095 VOL. 6 NO. 4 2012, pp. 377-388, Q Emerald Group Publishing Limited, ISSN 1750-6182
j
INTERNATIONAL JOURNAL OF CULTURE, TOURISM AND HOSPITALITY RESEARCH
j
PAGE 377
Kun-Huang Huarng and
Tiffany Hui-Kuang Yu are
Professors at Feng Chia
University, Taichung,
Taiwan. Luiz Moutinho is a
Professor at the University
of Glasgow, Glasgow, UK.
Yu-Chun Wang is a
Graduate Student at Feng
Chia University, Taichung,
Taiwan.
Received September 2010
Revised January 2011
Accepted September 2011
This work was supported in part
by the National Science
Council, Taiwan, ROC, under
grant NSC 97-2410-H-035-021.
Special thanks to the Guest
Editor of this Special Issue,
Professor Andreas Zins, and
the two reviewers’ invaluable
comments to help the authors to
improve this paper. The authors
also thank Ms Yi-Chia Li of
Kreative Commons, University
Library of Feng Chia University,
Taiwan, for helping to organize
this paper.
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The na? ¨ve model, moving average model, and exponent smoothing model, are time-series
based, make no assumptions about the dependence relationship, and are relatively easy to
implement. Athiyaman and Robertson (1992) ?nd that these time-series models generate
relatively accurate forecasts for international tourism demand when annual data are used.
Many studies apply the conventional time series approaches to forecast tourism demand
(Cho, 2003). These conventional time series models, such as ARIMA, suffer from some
limitations, such as assumptions and number of observations (Tseng et al., 2001). Fuzzy time
series models forecast true values such as university enrollment (e.g. Chen, 1996), stock
index (e.g. Huarng, 2001a), temperature (e.g. Wang and Chen, 2009), etc. Many studies
show that fuzzy time series models outperform the conventional alternatives, making them
suitable for modeling imprecise observations. In addition, neural networks are used to model
nonlinear relationships between data (Huarng and Yu, 2006b). Hence, this study adapts a
neural network based fuzzy time series model (Yu and Huarng, 2010) to model and forecast
tourism demand in Taiwan, including the period November 2002 to June 2003 when the
Severe Acute Respiratory Syndrome (SARS) outbreak threatened tourism demand,
particularly in Asia.
Tourism forecasting can help predict three factors: the number of tourists expected to visit a
destination, the tourism opportunities provided by a destination, and the factors that affect
tourist visitation (Uysal and Crompton, 1985). This study intends to forecast tourism to
Taiwan. To that end, this paper is organized as follows. Section 2 shows some related
literature. Section 3 describes the data. Section 4 explains the forecasting model. Section 5
compares the forecasting results. Section 6 concludes this paper.
2. Literature review
2.1 Tourism demand forecasting
Many studies work on forecasting tourism demand. Burger et al. (2001) compare a variety of
time-series forecasting methods to forecast the US demand for travel to Durban in South
Africa. Herna´ ndez-Lo´ pez and Ca´ ceres-Herna´ ndez (2007) forecast the characteristics of
tourists by means of a genetic algorithm with a transition matrix. Witt et al. (1995) develop an
econometric model to explain tourism demand for an international conference and estimate
such demand using maximum likelihood techniques. Song and Witt (2006) forecast the
numbers of international tourists ?owing to Macau. Chu (1998a) employs a combined
seasonal/non-seasonal auto-regression integrated moving average (ARIMA) and sine wave
nonlinear regression forecasting model to predict international tourism arrivals. Chu (1998b)
scrutinizes issues relating to the forecasting of international tourist arrivals by examining six
different forecasting techniques in the Asia-Paci?c region. The results show that the
accuracy of forecasts differs depending on the country being forecast, but that overall, the
seasonal/non-seasonal ARIMA model is the most accurate method for forecasting
international tourist arrivals.
Previous studies have suggested that the exogenous variables in econometric forecasting
models for international tourism demand comprise mainly the population and income of the
origin country, the cost of living in the destination country, currency foreign exchange rate,
and marketing expenditure on promotional activities in the destination country (Lim, 1997).
Garcia-Ferrer and Queralt (1997) consider the extent to which price and income proxy
variables help in forecasting tourismdemand. Contrary to some recent studies, they ?nd that
the inputs’ contribution in terms of ?tting and forecasting is nil when compared with
alternative univariate models. Whether these ?ndings are the result of the restrictions
embedded in building the proxy inputs or the result of a poor speci?cation of the dynamics of
these models remains to be seen. The authors also contend that when dealing with medium
long-term forecasting comparisons, the use of the traditional aggregate accuracy measures
like root mean squared error (RMSE), and mean absolute percentage error (MAPE), help
very little in discriminating among competing models. In these situations, predicted annual
growth rates may be a better alternative.
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Yu et al. (2007) develop an innovative method to identify and categorize typical tourism
demand patterns, and assess the impact of the identi?ed patterns on the accuracy of
various tourism forecasting methods. Four distinct patterns are identi?ed:
1. a stable linear trend;
2. a nonlinear trend;
3. a wave-shaped trend; and
4. an abrupt change pattern.
These four arrival data patterns affect the accuracy of forecasting models in a speci?c and
systematic manner. Within the tourismindustry, data can be feasibly categorized based on a
small number of typical, easily observable features.
2.2 Advanced techniques for forecasting
A neural network model is computer software that simulates human intelligence in deducing
or learning from data. The model consists of an input layer, an output layer, and one or more
hidden layers. Each of the layers contains nodes, and these nodes are connected with each
other. For example, the neural network in Figure 1 consists of ten input and ten output nodes.
The hidden nodes connect all of these input and output nodes. The neural network trains the
relationships of input and output nodes via the hidden nodes. The trained neural networks
can serve to forecast afterwards.
Neural networks have recently attracted more attention in forecasting than in past years
(Indro et al., 1999; Law and Au, 1999; Law, 2000; Tugba and Casey, 2005; Ma and
Khorasani, 2004; Palmer et al., 2006; Tugba and Casey, 2005). Unlike linear regression
analysis, which is limited to mapping linear functions, neural networks are useful forecasting
tools that can solve complex problems and discover complex non-linear relationships in
data (Indro et al., 1999). In addition, the neural network model is convenient for forecasting
without understanding the characteristics of the time series (Huarng et al., 2007). Law(2000)
uses the neural network model to forecast Japanese arrivals and the results outperform the
Figure 1 The neural network structure
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multiple regression, moving average, and exponential smoothing approaches. Moutinho
et al. (2008) also apply neural networks to forecast the tourism demand from mainland China
to Taiwan.
Many other studies apply neural networks for forecasting. Law and Au (1999) use a
supervised feed-forward neural network model to forecast Japanese tourist arrivals in Hong
Kong. The input layer of the neural network contained six nodes:
1. service price;
2. average hotel rate;
3. foreign exchange rate;
4. population;
5. marketing expenses; and
6. gross domestic expenditure.
The single node in the output layer of the neural network represents the Japanese demand
for travel to Hong Kong. Experimental results show that using the neural network model to
forecast Japanese arrivals outperforms multiple regression, na? ¨ve, moving average, and
exponent smoothing. These four models are some of the most common models utilized in
tourism demand forecasting (Carey, 1991; Lim, 1997; Witt and Witt, 1995; Wong, 1997).
A neural network is expected to be superior to traditional statistical methods in forecasting
because a neural network is better able to recognize any high-level features, such as serial
correlation, of a training set. A neural network was shown to outperform standard statistical
models in forecasting with a small-sized training set and a high level of white noise (Pattie
and Snyder, 1996). An additional advantage of applying a neural network to forecasting is
that a neural network can capture the non-linearity of samples in the training set (Wang and
Sun, 1996). The non-linear factor handling capability makes a neural network different from
time-series models. Pattie and Snyder (1996) claim, with substantiation, that using a neural
network to forecast non-linear tourist behavior achieves a lower mean absolute percentage
error, lower cumulative relative absolute error, lower cumulative relative absolute error, and
lower root mean square error than linear trend, exponential smoothing, Box-Jenkins, or the
na? ¨ve extrapolation models. Similarly, Mazanec (1992) demonstrates that a neural network is
superior to the discriminant analysis function in classifying tourists into market segments
based on a set of non-linear demographic, socio-economic, and behavioral variables.
Meanwhile, fuzzy time series models have also been widely applied in forecasting (Huarng
et al., 2007b). They have been good at modeling and forecasting imprecise observations.
Neural network based fuzzy time series models have shown that they outperform fuzzy time
series models as well as conventional models (Yu et al., 2009; Yu and Huarng, 2010). Hence,
this study adapts a neural network based fuzzy time series model to forecast tourism
demand.
3. Data
The forecasting target is the number of tourists arriving in Taiwan each month. The data
extend from January 1984 to August 2005. To demonstrate the performance, this study
conducts both in-sample estimation and out-of-sample forecasting (Martin and Witt, 1989).
The data are divided into in-sample data, covering the period from 1984/01 to 2000/03, and
out-of-sample data, for the period from 2000/04 to 2005/08. The in-sample and
out-of-sample ratio is about 3:1. The in-sample data are for establishing the fuzzy
relationships and the out-of-sample data are for testing the performance.
The period of out-of-sample covers the outbreak of SARS, which had a large impact on the
tourism demand in most Asian countries, including Taiwan. Of critical interest to this study is
how well the model forecasts the time series for unplanned events such as the SARS
outbreak.
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4. The forecasting model
This study adapts a neural network based fuzzy time series model to forecast tourism
demand, consisting of fuzzi?cation, neural network training, forecasting, and de-fuzzi?cation
(Yu and Huarng, 2010). Rather than employing adjustment of universe of discourse, this
study applies different thresholds based on estimation results.
4.1 Step 1: Fuzzi?cation
Obtaining the difference between year t and t 21, all differences are fuzzi?ed into fuzzy
numbers. The minimum and maximum of all differences, D
min
and D
max
, are de?ned. D
min
¼
2147; 488 and D
max
¼ 97; 043 are deduced from the data. The universe of discourse
de?nition covers both D
min
and D
max
; hence, U ¼ ½2150; 000; 100; 000?.
Some studies show different ways to set the length of interval (Huarng, 2001b; Huarng and
Yu, 2006a). Many studies set the length of interval according to particular study domains. In
this study, the length of interval is set to 25,000. Uis separated into ten equal intervals named
u
1
, u
2
, u
3
, u
4
, u
5
, u
6
, u
7
, u
8
, u
9
and u
10
, where u
1
¼ ½2150; 000; 2125; 000?,
u
2
¼ ½2125; 000; 2100; 000?, u
3
¼ ½2100; 000; 275; 000?, u
4
¼ ½275; 000; 250; 000?,
u
5
¼ ½250; 000; 225; 000?, u
6
¼ ½225; 000; 0?, u
7
¼ ½0; 25; 000?, u
8
¼ ½25; 000; 50; 000?,
u
9
¼ ½50; 000; 75; 000?, and u
10
¼ ½75; 000; 100; 000?.
The linguistic values of the fuzzy sets are de?ned as A
1
, A
2
, A
3
, A
4
, A
5
, A
6
, A
7
, A
8
, A
9
and A
10
,
and all fuzzy sets are labeled by possible linguistic values, u
1
, u
2
, u
3
, u
4
, u
5
, u
6
, u
7
, u
8
, u
9
and
u
10
. If u
k
completely belongs to A
i
, the degree of membership is set to 1.0; if u
k
does not
belong to A
i
at all, the degree of membership is set to 0.0; if some part of u
k
belongs to A
i
, the
degree of membership is set to some number between 1.0 and 0.0.
Chen (1996) considers only the fuzzy numbers with the maximum degrees of membership
in the establishment of fuzzy relationships. He suggests that if the maximum degree of
membership belongs to A
i
, the fuzzi?ed data is regarded as A
i
. Instead, this study
intends to take other degrees of membership into consideration. The data for 1984/08
and 1984/07 are taken as an illustration. The difference between 1984/08 and 1984/07 is
equal to 5,839. The corresponding fuzzy numbers and degrees of memberships are
depicted in Figure 2.
In Figure 2, the value 5,839 completely belongs to A
7
, and the degree of membership is set
to 1.0. Meanwhile, the degree of membership for A
8
is equal to ð5; 839 20Þ=25; 000 ¼ 0:23,
that for A
6
is equal to 1 20:23 ¼ 0:77, and the rest degrees of membership are equal to 0.0.
The corresponding degrees of memberships are calculated similarly.
Figure 2 Membership functions
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4.2 Step 2: Neural network training
Using the degrees of memberships in the previous step to establish fuzzy relationships, this
study applies back-propagation neural networks for training and forecasting. In the neural
network structure in Figure 1, the input and output layers contain ten input and output nodes
for A
1
to A
10
linguistic values. The number of hidden node is set to the sum of the input and
output nodes.
The ten nodes in the input layer are for the degrees of membership for ten intervals for the
fuzzi?ed data at t 21, and the ten nodes of the output layer are for the fuzzi?ed data at t. The
data from 1984/01 to 2000/03 are used for training. For example, using the degrees of
membership for 1984/01 (t 21) as the inputs in the neural network: 0.00, 0.00, 0.00, 0.00,
0.00, 0.44, 1.00, 0.56, 0.00, 0.00. And those for 1984/02 (t) as the outputs: 0.00, 0.00, 0.00,
0.00, 0.07, 1.00, 0.93, 0.00, 0.00, 0.00.
Repeatedly, all of the in-sample data are used to train the neural network.
4.3 Step 3: Forecasting
After the neural network training, the trained neural network can forecast the out-of-sample
data. The degrees of membership for ten intervals can be used for the fuzzi?ed data at t to
forecast the ten nodes of the output layer, which are the forecasted degrees of membership
at t þ 1. For example, using the degrees of membership for 2004/03 as the inputs: 0.00,
0.00, 0.00, 0.00, 0.42, 1.00, 0.58, 0.00, 0.00, 0.00. The trained neural network outputs (or
forecasts) the degrees of membership for 2004/04 as m
~
1
m
10
¼ 0:01, 0.00, 0.02, 0.03, 0.17,
0.54, 0.77, 0.44, 0.05, 0.02. All the forecasted degrees of membership are calculated
similarly.
4.4 Step 4: Defuzzi?cation
Defuzzi?cation serves many purposes. Interpreting forecast results (degrees of
memberships with corresponding fuzzy sets) is rather dif?cult to do directly. Comparing
forecasting performance between different models is also dif?cult. The previous fuzzy time
series models all apply defuzzi?cation to get the crisp values as forecasts. This study
applies the widely used method of weighted averages. First, the midpoints of u
1
, u
10
are
m
1
, m
10
¼ 213; 7500, 2112,500, 287,500, 262,500, 237,500, 212,500, 12,500,
37,500, 62,500 and 87,500, respectively:
Forecast
tþ1
¼
P
10
g¼1
m
g
£ m
g
P
10
g¼1
m
g
:
4.5 Step 5: Performance evaluation
To facilitate the comparison, the RMSE is used to compare the performance as in many other
studies (Yu, 2005; Huarng and Yu, 2006b; Yu and Huarng, 2008):
RMSE ¼
????????????????????????????????????????????????????????????????????
P
n21
t¼kþ1
ðforecast
tþ1
2actual
tþ1
Þ
n 2k 21
s
;
where t represents the time slot, n is the total number of data, k is the total number of
in-sample data, and n 2k 21 is the number of forecasts for out-of-sample data. Meanwhile,
forecast
t þ1
is the forecast at t þ 1 from any model and actual
tþ1
is the actual number of
tourists at t þ 1.
4.6 Step 6: Determining thresholds
To screen out insigni?cant degrees of membership, thresholds are tested. The thresholds of
0.4, 0.5, and 0.6 are set for two reasons:
1. to ignore those insigni?cant degrees of membership; and
2. because most degrees of membership are located between 0.4 and 0.6.
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Estimated RMSEs are used to choose proper thresholds. The estimated RMSEs of the
thresholds 0.4, 0.5 and 0.6 are 23,311, 22,441, and 23,890, respectively; 0.5 is chosen as
the threshold for out-of-sample forecasting. For example, to forecast 2000/04 with threshold
0.5, A
6
and A
7
are utilized, with degrees of memberships 0.5788 and 0.7441, respectively.
A
6
and A
7
are at intervals u
6
¼ ½225; 000; 0? and u
7
¼ ½0; 25; 000?, respectively, whose
midpoints are 212,500 and 12,500. Then the midpoints are weighted by the corresponding
degrees of membership 0.5788 and 0.7441. Consequently, the forecast for the number of
tourists is equal to:
0:5788 £ ð212; 500Þ þ 0:7441 £ 12; 500
0:5788 þ 0:7441
¼ 1; 562:
5. Empirical analysis
According to the estimation results, the threshold is set at 0.5. Forecasting is conducted and
the forecasting results based on various thresholds are shown in Table I. The RMSEs for
out-of-sample forecasting of the thresholds 0.4, 0.5 and 0.6 are 30,943, 30,789, and 30,867,
respectively; the RMSE for the 0.5 threshold is the smallest of all.
Meanwhile, results are compared with those of the previous fuzzy time series studies: Chen
(1996) and Huarng et al. (2007a), as shown in Table II. Chen (1996) give a typical fuzzy time
series model to consider only the maximum degrees of memberships. Meanwhile, Huarng
et al. (2007a) also conducted neural network based fuzzy time series forecasting but with only
the maximum degrees of memberships for tourism demand. Models with more degrees of
memberships perform better than the ones with only the maximum degrees of memberships.
The RMSEs obtained by Chen (1996) and Huarng et al. (2007a) are 32,759 and 30,939,
respectively. The RMSE obtained in this study, depicted in Figure 3, is smaller than those of
the previous studies under comparison.
Considering the SARS period only, November 2002 to June 2003, the RMSEs for Chen
(1996), Huarng et al. (2007a), and this study are 63,445, 62,124, and 61,863, respectively.
These RMSEs are more than twice of the corresponding RMSEs for the entire period,
indicating the dif?culty of forecasting demands during this period of time. However, the
Table I The comparison of forecasts based on thresholds
Threshold
Month 0.4 0.5 0.6
2000/04 9,872 1,562 12,500
2000/05 827 827 827
2000/06 2523 2523 2523
2000/07 10,386 1,820 12,500
2000/08 226 226 226
2000/09 491 491 491
2000/10 211,038 22,053 212,500
2000/11 2,902 2,902 2,902
2000/12 1,264 1,264 1,264
2001/01 13,342 22,344 12,500
. . . . . . . . . . . .
2004/12 2233 2233 2233
2005/01 13,126 22,276 12,500
2005/02 21,035 21,035 21,035
2005/03 211,171 22,130 212,500
2005/04 13,356 22,349 12,500
2005/05 21,188 21,188 21,188
2005/06 2584 2584 2584
2005/07 13,531 22,404 12,500
2005/08 210,87 21,087 21,087
RMSE 30,943 30,789 30,867
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Table II Comparison of forecasts
Month
Actual tourist
numbers
Forecasted numbers
by Chen (1996)
Forecasted numbers by
Huarng et al. (2007a)
Forecasted numbers
by this study
2000/05 216,692 217,500 217,500 219,138
2000/06 225,069 216,500 216,500 217,519
2000/07 217,302 225,500 225,500 224,546
2000/08 220,227 217,500 217,500 219,122
2000/09 221,504 179,500 217,607 220,453
2000/10 249,352 219,500 218,545 221,995
2000/11 232,810 249,500 249,500 247,299
2000/12 228,821 232,500 232,500 235,712
2001/01 199,800 202,500 225,105 230,085
2001/02 234,386 180,500 197,927 222,144
2001/03 251,111 234,500 234,500 232,287
2001/04 235,251 251,500 251,500 249,710
2001/05 227,021 235,500 235,500 238,079
2001/06 239,878 204,500 224,167 228,914
2001/07 218,673 239,500 239,500 238,869
2001/08 224,208 218,500 218,500 240,966
2001/09 193,254 224,500 224,500 224,076
2001/10 192,452 193,500 193,500 215,560
2001/11 190,500 213,000 191,367 193,244
2001/12 210,603 194,833.3 189,493 191,470
2002/01 217,600 194,500 208,236 208,926
2002/02 233,896 217,500 217,500 217,268
2002/03 281,522 233,500 233,500 232,541
2002/04 245,759 281,500 281,500 279,376
2002/05 243,941 245,500 245,500 267,961
2002/06 241,378 243,500 243,500 244,875
2002/07 234,596 241,500 241,500 242,421
2002/08 246,079 234,500 234,500 236,270
2002/09 233,613 246,500 246,500 245,205
2002/10 258,360 233,500 233,500 236,077
2002/11 255,645 258,500 258,500 256,345
2002/12 285,303 255,500 255,500 256,724
2003/01 238,031 285,500 285,500 283,235
2003/02 259,966 215,500 234,476 240,587
2003/03 258,128 259,500 259,500 258,138
2003/04 110,640 258,500 258,500 259,062
2003/05 40,256 110,500 110,500 111,762
2003/06 57,131 40,500 40,500 41,693
2003/07 154,174 57,500 57,500 55,717
2003/08 200,614 155,500 155,755 155,234
2003/09 218,594 174,166.7 198,864 198,470
2003/10 223,552 218,500 218,500 217,083
2003/11 241,349 217,500 223,500 223,489
2003/12 245,682 241,500 241,500 239,859
2004/01 212,854 245,500 245,500 245,725
2004/02 221,020 212,500 212,500 235,124
2004/03 239,575 219,500 218,545 220,528
2004/04 229,061 239,500 239,500 238,021
2004/05 232,293 229,500 229,500 231,267
2004/06 258,861 232,500 232,500 232,482
2004/07 243,396 258,500 258,500 256,818
2004/08 253,544 243,500 243,500 246,198
2004/09 245,915 253,500 253,500 252,812
2004/10 266,590 245,500 245,500 247,735
2004/11 270,553 266,500 266,500 264,855
2004/12 276,680 270,500 270,500 270,632
2005/01 244,252 276,500 276,500 276,447
2005/02 257,340 244,500 244,500 266,528
2005/03 298,282 257,500 257,500 256,305
2005/04 269,513 298,500 298,500 296,152
2005/05 284,049 269,500 269,500 291,862
2005/06 293,044 284,500 284,500 282,861
(continued)
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RMSE of this study is smaller than those of Chen (1996) and Huarng et al. (2007a),
demonstrating that the forecasting model can be applied to forecast the time series with
events as well as with regular time series. The RMSEs for the entire period, including the
SARS period, are compared in Table III.
6. Conclusion
This study adapts a neural network based fuzzy time series model (Yu and Huarng, 2010) to
forecast Taiwan’s tourism demand. Fuzzy sets are for modeling imprecise data and neural
networks are for establishing the nonlinear relationships among the fuzzy sets. This study
takes other degrees of membership into consideration, and forecasts the numbers of tourists
with the corresponding degrees of membership by means of neural networks. The different
approach to this study explains why the results produce smaller RMSEs than the previous
studies under comparison.
Table II
Month
Actual tourist
numbers
Forecasted numbers
by Chen (1996)
Forecasted numbers by
Huarng et al. (2007a)
Forecasted numbers
by this study
2005/07 268,269 293,500 293,500 292,460
2005/08 281,693 268,500 268,500 290,673
2005/09 270,700 281,500 281,500 280,606
RMSE 32,759 30,939 30,789
Table III Comparisons of RMSEs
Chen (1996) Huarng et al. (2007a) This study
Entire period 32,759 30,939 30,867
SARS period 63,445 62,124 61,863
Figure 3 Performance comparison with other studies
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The out-of-sample data covers the period of SARS, which caused a dramatic impact to
tourism demand in Asia. Taiwan was one of the countries that suffered from the drastic drop
in tourism demand. However, the forecasting model also outperforms the other two fuzzy
time series models when considering the period of SARS, November 2002 to June 2003.
This indicates that the forecasting model not only can forecast nonlinear data but also can
forecast the time series with events.
The model applied is an autoregressive model of order 1, or AR(1). In this model, only the
observation of one previous time period can be considered. Subsequent studies can extend
the model into an AR( p) model, which considers more observations in the previous time
periods by establishing fuzzy relationships.
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About the authors
Kun-Huang Huarng is based in the Department of International Trade, Feng Chia University,
Taiwan. Professor Huarng is also the University Librarian of the same institute and the Chair
of the Taiwan E-Books Supply Cooperative. Kun-Huang Huarng is the corresponding author
and can be contacted at: [email protected]
Tiffany Hui-Kuang Yu is based in the Department of Public Finance, Feng Chia University,
Taiwan. Professor Yu is also the Dean of the Of?ce of International Affairs of the same
institution.
Luiz Moutinho is based at the Business School, University of Glasgow, UK. Professor
Moutinho is also the Foundation Chair of Marketing and the Founding Editor of Journal of
Modelling in Management.
Yu-Chun Wang is a graduate of the Department of International Trade, Feng Chia University,
Taiwan.
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This article has been cited by:
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doc_207442459.pdf
This study aims to adapt a neural network based fuzzy time series model to improve Taiwan’s
tourism demand forecasting
International Journal of Culture, Tourism and Hospitality Research
Forecasting tourism demand by fuzzy time series models
Kun-Huang Huarng Tiffany Hui-Kuang Yu Luiz Moutinho Yu-Chun Wang
Article information:
To cite this document:
Kun-Huang Huarng Tiffany Hui-Kuang Yu Luiz Moutinho Yu-Chun Wang, (2012),"Forecasting tourism demand by fuzzy time series models",
International J ournal of Culture, Tourism and Hospitality Research, Vol. 6 Iss 4 pp. 377 - 388
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Forecasting tourism demand by fuzzy time
series models
Kun-Huang Huarng, Tiffany Hui-Kuang Yu, Luiz Moutinho and Yu-Chun Wang
Abstract
Purpose – This study aims to adapt a neural network based fuzzy time series model to improve Taiwan’s
tourism demand forecasting.
Design/methodology/approach – Fuzzy sets are for modeling imprecise data and neural networks are
for establishing non-linear relationships among fuzzy sets. A neural network based fuzzy time series
model is adapted as the forecasting model. Both in-sample estimation and out-of-sample forecasting
are performed.
Findings – This study outperforms previous studies undertaken during the SARS events of 2002-2003.
Research limitations/implications – The forecasting model only takes the observation of one previous
time period into consideration. Subsequent studies can extend the model to consider previous time
periods by establishing fuzzy relationships.
Originality/value – Non-linear data is complicated to forecast, and it is even more dif?cult to forecast
nonlinear data with shocks. The forecasting model in this study outperforms other studies in forecasting
the nonlinear tourism demands during the SARS event of November 2002 to June 2003.
Keywords Degrees of memberships, Fuzzy time series models, Neural networks,
Severe Acute Respiratory Syndrome (SARS), Tourism management, Modelling
Paper type Research paper
1. Introduction
International tourism has become a fairly large industry (Tisdell, 2000) and a very
competitive business. Tourism also plays a signi?cant role in national economies both
directly and indirectly by providing employment and earning much foreign exchange,
explaining why so many small countries rely heavily on tourism. Forecasting arrivals of
tourists is meaningful in that forecasts can help public or private sectors to avoid shortages
or surpluses of goods and services. Hence, the need for accurate forecasts of the demand
for tourism is widely recognized (Witt and Witt, 1995).
Researchers, practitioners, and policy makers have long recognized the necessity of
accurate forecasts for tourism demand (Sheldon and Var, 1985). Accurate forecasts would
help managers and investors make operational tactical and strategic decisions. Similarly,
governments need accurate forecasts about tourism demand to plan for tourism
infrastructure such as accommodation site planning, and transportation development.
In spite of consensus on the need for accurate forecasting, and an understanding of the
bene?ts of accurate forecasts, no standard supplier of tourism forecasts exists (Witt and
Witt, 1995). Also, no single forecasting model can outweigh all other forecasting models in
terms of forecasting accuracy. Previous studies of forecasting demand for tourism have
been primarily time-series models and regression models (Wong, 1997). Time-series
models are often able to achieve good forecasting results (Andrew et al., 1990; Martin and
Witt, 1989).
DOI 10.1108/17506181211265095 VOL. 6 NO. 4 2012, pp. 377-388, Q Emerald Group Publishing Limited, ISSN 1750-6182
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INTERNATIONAL JOURNAL OF CULTURE, TOURISM AND HOSPITALITY RESEARCH
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PAGE 377
Kun-Huang Huarng and
Tiffany Hui-Kuang Yu are
Professors at Feng Chia
University, Taichung,
Taiwan. Luiz Moutinho is a
Professor at the University
of Glasgow, Glasgow, UK.
Yu-Chun Wang is a
Graduate Student at Feng
Chia University, Taichung,
Taiwan.
Received September 2010
Revised January 2011
Accepted September 2011
This work was supported in part
by the National Science
Council, Taiwan, ROC, under
grant NSC 97-2410-H-035-021.
Special thanks to the Guest
Editor of this Special Issue,
Professor Andreas Zins, and
the two reviewers’ invaluable
comments to help the authors to
improve this paper. The authors
also thank Ms Yi-Chia Li of
Kreative Commons, University
Library of Feng Chia University,
Taiwan, for helping to organize
this paper.
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The na? ¨ve model, moving average model, and exponent smoothing model, are time-series
based, make no assumptions about the dependence relationship, and are relatively easy to
implement. Athiyaman and Robertson (1992) ?nd that these time-series models generate
relatively accurate forecasts for international tourism demand when annual data are used.
Many studies apply the conventional time series approaches to forecast tourism demand
(Cho, 2003). These conventional time series models, such as ARIMA, suffer from some
limitations, such as assumptions and number of observations (Tseng et al., 2001). Fuzzy time
series models forecast true values such as university enrollment (e.g. Chen, 1996), stock
index (e.g. Huarng, 2001a), temperature (e.g. Wang and Chen, 2009), etc. Many studies
show that fuzzy time series models outperform the conventional alternatives, making them
suitable for modeling imprecise observations. In addition, neural networks are used to model
nonlinear relationships between data (Huarng and Yu, 2006b). Hence, this study adapts a
neural network based fuzzy time series model (Yu and Huarng, 2010) to model and forecast
tourism demand in Taiwan, including the period November 2002 to June 2003 when the
Severe Acute Respiratory Syndrome (SARS) outbreak threatened tourism demand,
particularly in Asia.
Tourism forecasting can help predict three factors: the number of tourists expected to visit a
destination, the tourism opportunities provided by a destination, and the factors that affect
tourist visitation (Uysal and Crompton, 1985). This study intends to forecast tourism to
Taiwan. To that end, this paper is organized as follows. Section 2 shows some related
literature. Section 3 describes the data. Section 4 explains the forecasting model. Section 5
compares the forecasting results. Section 6 concludes this paper.
2. Literature review
2.1 Tourism demand forecasting
Many studies work on forecasting tourism demand. Burger et al. (2001) compare a variety of
time-series forecasting methods to forecast the US demand for travel to Durban in South
Africa. Herna´ ndez-Lo´ pez and Ca´ ceres-Herna´ ndez (2007) forecast the characteristics of
tourists by means of a genetic algorithm with a transition matrix. Witt et al. (1995) develop an
econometric model to explain tourism demand for an international conference and estimate
such demand using maximum likelihood techniques. Song and Witt (2006) forecast the
numbers of international tourists ?owing to Macau. Chu (1998a) employs a combined
seasonal/non-seasonal auto-regression integrated moving average (ARIMA) and sine wave
nonlinear regression forecasting model to predict international tourism arrivals. Chu (1998b)
scrutinizes issues relating to the forecasting of international tourist arrivals by examining six
different forecasting techniques in the Asia-Paci?c region. The results show that the
accuracy of forecasts differs depending on the country being forecast, but that overall, the
seasonal/non-seasonal ARIMA model is the most accurate method for forecasting
international tourist arrivals.
Previous studies have suggested that the exogenous variables in econometric forecasting
models for international tourism demand comprise mainly the population and income of the
origin country, the cost of living in the destination country, currency foreign exchange rate,
and marketing expenditure on promotional activities in the destination country (Lim, 1997).
Garcia-Ferrer and Queralt (1997) consider the extent to which price and income proxy
variables help in forecasting tourismdemand. Contrary to some recent studies, they ?nd that
the inputs’ contribution in terms of ?tting and forecasting is nil when compared with
alternative univariate models. Whether these ?ndings are the result of the restrictions
embedded in building the proxy inputs or the result of a poor speci?cation of the dynamics of
these models remains to be seen. The authors also contend that when dealing with medium
long-term forecasting comparisons, the use of the traditional aggregate accuracy measures
like root mean squared error (RMSE), and mean absolute percentage error (MAPE), help
very little in discriminating among competing models. In these situations, predicted annual
growth rates may be a better alternative.
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Yu et al. (2007) develop an innovative method to identify and categorize typical tourism
demand patterns, and assess the impact of the identi?ed patterns on the accuracy of
various tourism forecasting methods. Four distinct patterns are identi?ed:
1. a stable linear trend;
2. a nonlinear trend;
3. a wave-shaped trend; and
4. an abrupt change pattern.
These four arrival data patterns affect the accuracy of forecasting models in a speci?c and
systematic manner. Within the tourismindustry, data can be feasibly categorized based on a
small number of typical, easily observable features.
2.2 Advanced techniques for forecasting
A neural network model is computer software that simulates human intelligence in deducing
or learning from data. The model consists of an input layer, an output layer, and one or more
hidden layers. Each of the layers contains nodes, and these nodes are connected with each
other. For example, the neural network in Figure 1 consists of ten input and ten output nodes.
The hidden nodes connect all of these input and output nodes. The neural network trains the
relationships of input and output nodes via the hidden nodes. The trained neural networks
can serve to forecast afterwards.
Neural networks have recently attracted more attention in forecasting than in past years
(Indro et al., 1999; Law and Au, 1999; Law, 2000; Tugba and Casey, 2005; Ma and
Khorasani, 2004; Palmer et al., 2006; Tugba and Casey, 2005). Unlike linear regression
analysis, which is limited to mapping linear functions, neural networks are useful forecasting
tools that can solve complex problems and discover complex non-linear relationships in
data (Indro et al., 1999). In addition, the neural network model is convenient for forecasting
without understanding the characteristics of the time series (Huarng et al., 2007). Law(2000)
uses the neural network model to forecast Japanese arrivals and the results outperform the
Figure 1 The neural network structure
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multiple regression, moving average, and exponential smoothing approaches. Moutinho
et al. (2008) also apply neural networks to forecast the tourism demand from mainland China
to Taiwan.
Many other studies apply neural networks for forecasting. Law and Au (1999) use a
supervised feed-forward neural network model to forecast Japanese tourist arrivals in Hong
Kong. The input layer of the neural network contained six nodes:
1. service price;
2. average hotel rate;
3. foreign exchange rate;
4. population;
5. marketing expenses; and
6. gross domestic expenditure.
The single node in the output layer of the neural network represents the Japanese demand
for travel to Hong Kong. Experimental results show that using the neural network model to
forecast Japanese arrivals outperforms multiple regression, na? ¨ve, moving average, and
exponent smoothing. These four models are some of the most common models utilized in
tourism demand forecasting (Carey, 1991; Lim, 1997; Witt and Witt, 1995; Wong, 1997).
A neural network is expected to be superior to traditional statistical methods in forecasting
because a neural network is better able to recognize any high-level features, such as serial
correlation, of a training set. A neural network was shown to outperform standard statistical
models in forecasting with a small-sized training set and a high level of white noise (Pattie
and Snyder, 1996). An additional advantage of applying a neural network to forecasting is
that a neural network can capture the non-linearity of samples in the training set (Wang and
Sun, 1996). The non-linear factor handling capability makes a neural network different from
time-series models. Pattie and Snyder (1996) claim, with substantiation, that using a neural
network to forecast non-linear tourist behavior achieves a lower mean absolute percentage
error, lower cumulative relative absolute error, lower cumulative relative absolute error, and
lower root mean square error than linear trend, exponential smoothing, Box-Jenkins, or the
na? ¨ve extrapolation models. Similarly, Mazanec (1992) demonstrates that a neural network is
superior to the discriminant analysis function in classifying tourists into market segments
based on a set of non-linear demographic, socio-economic, and behavioral variables.
Meanwhile, fuzzy time series models have also been widely applied in forecasting (Huarng
et al., 2007b). They have been good at modeling and forecasting imprecise observations.
Neural network based fuzzy time series models have shown that they outperform fuzzy time
series models as well as conventional models (Yu et al., 2009; Yu and Huarng, 2010). Hence,
this study adapts a neural network based fuzzy time series model to forecast tourism
demand.
3. Data
The forecasting target is the number of tourists arriving in Taiwan each month. The data
extend from January 1984 to August 2005. To demonstrate the performance, this study
conducts both in-sample estimation and out-of-sample forecasting (Martin and Witt, 1989).
The data are divided into in-sample data, covering the period from 1984/01 to 2000/03, and
out-of-sample data, for the period from 2000/04 to 2005/08. The in-sample and
out-of-sample ratio is about 3:1. The in-sample data are for establishing the fuzzy
relationships and the out-of-sample data are for testing the performance.
The period of out-of-sample covers the outbreak of SARS, which had a large impact on the
tourism demand in most Asian countries, including Taiwan. Of critical interest to this study is
how well the model forecasts the time series for unplanned events such as the SARS
outbreak.
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4. The forecasting model
This study adapts a neural network based fuzzy time series model to forecast tourism
demand, consisting of fuzzi?cation, neural network training, forecasting, and de-fuzzi?cation
(Yu and Huarng, 2010). Rather than employing adjustment of universe of discourse, this
study applies different thresholds based on estimation results.
4.1 Step 1: Fuzzi?cation
Obtaining the difference between year t and t 21, all differences are fuzzi?ed into fuzzy
numbers. The minimum and maximum of all differences, D
min
and D
max
, are de?ned. D
min
¼
2147; 488 and D
max
¼ 97; 043 are deduced from the data. The universe of discourse
de?nition covers both D
min
and D
max
; hence, U ¼ ½2150; 000; 100; 000?.
Some studies show different ways to set the length of interval (Huarng, 2001b; Huarng and
Yu, 2006a). Many studies set the length of interval according to particular study domains. In
this study, the length of interval is set to 25,000. Uis separated into ten equal intervals named
u
1
, u
2
, u
3
, u
4
, u
5
, u
6
, u
7
, u
8
, u
9
and u
10
, where u
1
¼ ½2150; 000; 2125; 000?,
u
2
¼ ½2125; 000; 2100; 000?, u
3
¼ ½2100; 000; 275; 000?, u
4
¼ ½275; 000; 250; 000?,
u
5
¼ ½250; 000; 225; 000?, u
6
¼ ½225; 000; 0?, u
7
¼ ½0; 25; 000?, u
8
¼ ½25; 000; 50; 000?,
u
9
¼ ½50; 000; 75; 000?, and u
10
¼ ½75; 000; 100; 000?.
The linguistic values of the fuzzy sets are de?ned as A
1
, A
2
, A
3
, A
4
, A
5
, A
6
, A
7
, A
8
, A
9
and A
10
,
and all fuzzy sets are labeled by possible linguistic values, u
1
, u
2
, u
3
, u
4
, u
5
, u
6
, u
7
, u
8
, u
9
and
u
10
. If u
k
completely belongs to A
i
, the degree of membership is set to 1.0; if u
k
does not
belong to A
i
at all, the degree of membership is set to 0.0; if some part of u
k
belongs to A
i
, the
degree of membership is set to some number between 1.0 and 0.0.
Chen (1996) considers only the fuzzy numbers with the maximum degrees of membership
in the establishment of fuzzy relationships. He suggests that if the maximum degree of
membership belongs to A
i
, the fuzzi?ed data is regarded as A
i
. Instead, this study
intends to take other degrees of membership into consideration. The data for 1984/08
and 1984/07 are taken as an illustration. The difference between 1984/08 and 1984/07 is
equal to 5,839. The corresponding fuzzy numbers and degrees of memberships are
depicted in Figure 2.
In Figure 2, the value 5,839 completely belongs to A
7
, and the degree of membership is set
to 1.0. Meanwhile, the degree of membership for A
8
is equal to ð5; 839 20Þ=25; 000 ¼ 0:23,
that for A
6
is equal to 1 20:23 ¼ 0:77, and the rest degrees of membership are equal to 0.0.
The corresponding degrees of memberships are calculated similarly.
Figure 2 Membership functions
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4.2 Step 2: Neural network training
Using the degrees of memberships in the previous step to establish fuzzy relationships, this
study applies back-propagation neural networks for training and forecasting. In the neural
network structure in Figure 1, the input and output layers contain ten input and output nodes
for A
1
to A
10
linguistic values. The number of hidden node is set to the sum of the input and
output nodes.
The ten nodes in the input layer are for the degrees of membership for ten intervals for the
fuzzi?ed data at t 21, and the ten nodes of the output layer are for the fuzzi?ed data at t. The
data from 1984/01 to 2000/03 are used for training. For example, using the degrees of
membership for 1984/01 (t 21) as the inputs in the neural network: 0.00, 0.00, 0.00, 0.00,
0.00, 0.44, 1.00, 0.56, 0.00, 0.00. And those for 1984/02 (t) as the outputs: 0.00, 0.00, 0.00,
0.00, 0.07, 1.00, 0.93, 0.00, 0.00, 0.00.
Repeatedly, all of the in-sample data are used to train the neural network.
4.3 Step 3: Forecasting
After the neural network training, the trained neural network can forecast the out-of-sample
data. The degrees of membership for ten intervals can be used for the fuzzi?ed data at t to
forecast the ten nodes of the output layer, which are the forecasted degrees of membership
at t þ 1. For example, using the degrees of membership for 2004/03 as the inputs: 0.00,
0.00, 0.00, 0.00, 0.42, 1.00, 0.58, 0.00, 0.00, 0.00. The trained neural network outputs (or
forecasts) the degrees of membership for 2004/04 as m
~
1
m
10
¼ 0:01, 0.00, 0.02, 0.03, 0.17,
0.54, 0.77, 0.44, 0.05, 0.02. All the forecasted degrees of membership are calculated
similarly.
4.4 Step 4: Defuzzi?cation
Defuzzi?cation serves many purposes. Interpreting forecast results (degrees of
memberships with corresponding fuzzy sets) is rather dif?cult to do directly. Comparing
forecasting performance between different models is also dif?cult. The previous fuzzy time
series models all apply defuzzi?cation to get the crisp values as forecasts. This study
applies the widely used method of weighted averages. First, the midpoints of u
1
, u
10
are
m
1
, m
10
¼ 213; 7500, 2112,500, 287,500, 262,500, 237,500, 212,500, 12,500,
37,500, 62,500 and 87,500, respectively:
Forecast
tþ1
¼
P
10
g¼1
m
g
£ m
g
P
10
g¼1
m
g
:
4.5 Step 5: Performance evaluation
To facilitate the comparison, the RMSE is used to compare the performance as in many other
studies (Yu, 2005; Huarng and Yu, 2006b; Yu and Huarng, 2008):
RMSE ¼
????????????????????????????????????????????????????????????????????
P
n21
t¼kþ1
ðforecast
tþ1
2actual
tþ1
Þ
n 2k 21
s
;
where t represents the time slot, n is the total number of data, k is the total number of
in-sample data, and n 2k 21 is the number of forecasts for out-of-sample data. Meanwhile,
forecast
t þ1
is the forecast at t þ 1 from any model and actual
tþ1
is the actual number of
tourists at t þ 1.
4.6 Step 6: Determining thresholds
To screen out insigni?cant degrees of membership, thresholds are tested. The thresholds of
0.4, 0.5, and 0.6 are set for two reasons:
1. to ignore those insigni?cant degrees of membership; and
2. because most degrees of membership are located between 0.4 and 0.6.
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Estimated RMSEs are used to choose proper thresholds. The estimated RMSEs of the
thresholds 0.4, 0.5 and 0.6 are 23,311, 22,441, and 23,890, respectively; 0.5 is chosen as
the threshold for out-of-sample forecasting. For example, to forecast 2000/04 with threshold
0.5, A
6
and A
7
are utilized, with degrees of memberships 0.5788 and 0.7441, respectively.
A
6
and A
7
are at intervals u
6
¼ ½225; 000; 0? and u
7
¼ ½0; 25; 000?, respectively, whose
midpoints are 212,500 and 12,500. Then the midpoints are weighted by the corresponding
degrees of membership 0.5788 and 0.7441. Consequently, the forecast for the number of
tourists is equal to:
0:5788 £ ð212; 500Þ þ 0:7441 £ 12; 500
0:5788 þ 0:7441
¼ 1; 562:
5. Empirical analysis
According to the estimation results, the threshold is set at 0.5. Forecasting is conducted and
the forecasting results based on various thresholds are shown in Table I. The RMSEs for
out-of-sample forecasting of the thresholds 0.4, 0.5 and 0.6 are 30,943, 30,789, and 30,867,
respectively; the RMSE for the 0.5 threshold is the smallest of all.
Meanwhile, results are compared with those of the previous fuzzy time series studies: Chen
(1996) and Huarng et al. (2007a), as shown in Table II. Chen (1996) give a typical fuzzy time
series model to consider only the maximum degrees of memberships. Meanwhile, Huarng
et al. (2007a) also conducted neural network based fuzzy time series forecasting but with only
the maximum degrees of memberships for tourism demand. Models with more degrees of
memberships perform better than the ones with only the maximum degrees of memberships.
The RMSEs obtained by Chen (1996) and Huarng et al. (2007a) are 32,759 and 30,939,
respectively. The RMSE obtained in this study, depicted in Figure 3, is smaller than those of
the previous studies under comparison.
Considering the SARS period only, November 2002 to June 2003, the RMSEs for Chen
(1996), Huarng et al. (2007a), and this study are 63,445, 62,124, and 61,863, respectively.
These RMSEs are more than twice of the corresponding RMSEs for the entire period,
indicating the dif?culty of forecasting demands during this period of time. However, the
Table I The comparison of forecasts based on thresholds
Threshold
Month 0.4 0.5 0.6
2000/04 9,872 1,562 12,500
2000/05 827 827 827
2000/06 2523 2523 2523
2000/07 10,386 1,820 12,500
2000/08 226 226 226
2000/09 491 491 491
2000/10 211,038 22,053 212,500
2000/11 2,902 2,902 2,902
2000/12 1,264 1,264 1,264
2001/01 13,342 22,344 12,500
. . . . . . . . . . . .
2004/12 2233 2233 2233
2005/01 13,126 22,276 12,500
2005/02 21,035 21,035 21,035
2005/03 211,171 22,130 212,500
2005/04 13,356 22,349 12,500
2005/05 21,188 21,188 21,188
2005/06 2584 2584 2584
2005/07 13,531 22,404 12,500
2005/08 210,87 21,087 21,087
RMSE 30,943 30,789 30,867
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Table II Comparison of forecasts
Month
Actual tourist
numbers
Forecasted numbers
by Chen (1996)
Forecasted numbers by
Huarng et al. (2007a)
Forecasted numbers
by this study
2000/05 216,692 217,500 217,500 219,138
2000/06 225,069 216,500 216,500 217,519
2000/07 217,302 225,500 225,500 224,546
2000/08 220,227 217,500 217,500 219,122
2000/09 221,504 179,500 217,607 220,453
2000/10 249,352 219,500 218,545 221,995
2000/11 232,810 249,500 249,500 247,299
2000/12 228,821 232,500 232,500 235,712
2001/01 199,800 202,500 225,105 230,085
2001/02 234,386 180,500 197,927 222,144
2001/03 251,111 234,500 234,500 232,287
2001/04 235,251 251,500 251,500 249,710
2001/05 227,021 235,500 235,500 238,079
2001/06 239,878 204,500 224,167 228,914
2001/07 218,673 239,500 239,500 238,869
2001/08 224,208 218,500 218,500 240,966
2001/09 193,254 224,500 224,500 224,076
2001/10 192,452 193,500 193,500 215,560
2001/11 190,500 213,000 191,367 193,244
2001/12 210,603 194,833.3 189,493 191,470
2002/01 217,600 194,500 208,236 208,926
2002/02 233,896 217,500 217,500 217,268
2002/03 281,522 233,500 233,500 232,541
2002/04 245,759 281,500 281,500 279,376
2002/05 243,941 245,500 245,500 267,961
2002/06 241,378 243,500 243,500 244,875
2002/07 234,596 241,500 241,500 242,421
2002/08 246,079 234,500 234,500 236,270
2002/09 233,613 246,500 246,500 245,205
2002/10 258,360 233,500 233,500 236,077
2002/11 255,645 258,500 258,500 256,345
2002/12 285,303 255,500 255,500 256,724
2003/01 238,031 285,500 285,500 283,235
2003/02 259,966 215,500 234,476 240,587
2003/03 258,128 259,500 259,500 258,138
2003/04 110,640 258,500 258,500 259,062
2003/05 40,256 110,500 110,500 111,762
2003/06 57,131 40,500 40,500 41,693
2003/07 154,174 57,500 57,500 55,717
2003/08 200,614 155,500 155,755 155,234
2003/09 218,594 174,166.7 198,864 198,470
2003/10 223,552 218,500 218,500 217,083
2003/11 241,349 217,500 223,500 223,489
2003/12 245,682 241,500 241,500 239,859
2004/01 212,854 245,500 245,500 245,725
2004/02 221,020 212,500 212,500 235,124
2004/03 239,575 219,500 218,545 220,528
2004/04 229,061 239,500 239,500 238,021
2004/05 232,293 229,500 229,500 231,267
2004/06 258,861 232,500 232,500 232,482
2004/07 243,396 258,500 258,500 256,818
2004/08 253,544 243,500 243,500 246,198
2004/09 245,915 253,500 253,500 252,812
2004/10 266,590 245,500 245,500 247,735
2004/11 270,553 266,500 266,500 264,855
2004/12 276,680 270,500 270,500 270,632
2005/01 244,252 276,500 276,500 276,447
2005/02 257,340 244,500 244,500 266,528
2005/03 298,282 257,500 257,500 256,305
2005/04 269,513 298,500 298,500 296,152
2005/05 284,049 269,500 269,500 291,862
2005/06 293,044 284,500 284,500 282,861
(continued)
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RMSE of this study is smaller than those of Chen (1996) and Huarng et al. (2007a),
demonstrating that the forecasting model can be applied to forecast the time series with
events as well as with regular time series. The RMSEs for the entire period, including the
SARS period, are compared in Table III.
6. Conclusion
This study adapts a neural network based fuzzy time series model (Yu and Huarng, 2010) to
forecast Taiwan’s tourism demand. Fuzzy sets are for modeling imprecise data and neural
networks are for establishing the nonlinear relationships among the fuzzy sets. This study
takes other degrees of membership into consideration, and forecasts the numbers of tourists
with the corresponding degrees of membership by means of neural networks. The different
approach to this study explains why the results produce smaller RMSEs than the previous
studies under comparison.
Table II
Month
Actual tourist
numbers
Forecasted numbers
by Chen (1996)
Forecasted numbers by
Huarng et al. (2007a)
Forecasted numbers
by this study
2005/07 268,269 293,500 293,500 292,460
2005/08 281,693 268,500 268,500 290,673
2005/09 270,700 281,500 281,500 280,606
RMSE 32,759 30,939 30,789
Table III Comparisons of RMSEs
Chen (1996) Huarng et al. (2007a) This study
Entire period 32,759 30,939 30,867
SARS period 63,445 62,124 61,863
Figure 3 Performance comparison with other studies
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The out-of-sample data covers the period of SARS, which caused a dramatic impact to
tourism demand in Asia. Taiwan was one of the countries that suffered from the drastic drop
in tourism demand. However, the forecasting model also outperforms the other two fuzzy
time series models when considering the period of SARS, November 2002 to June 2003.
This indicates that the forecasting model not only can forecast nonlinear data but also can
forecast the time series with events.
The model applied is an autoregressive model of order 1, or AR(1). In this model, only the
observation of one previous time period can be considered. Subsequent studies can extend
the model into an AR( p) model, which considers more observations in the previous time
periods by establishing fuzzy relationships.
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About the authors
Kun-Huang Huarng is based in the Department of International Trade, Feng Chia University,
Taiwan. Professor Huarng is also the University Librarian of the same institute and the Chair
of the Taiwan E-Books Supply Cooperative. Kun-Huang Huarng is the corresponding author
and can be contacted at: [email protected]
Tiffany Hui-Kuang Yu is based in the Department of Public Finance, Feng Chia University,
Taiwan. Professor Yu is also the Dean of the Of?ce of International Affairs of the same
institution.
Luiz Moutinho is based at the Business School, University of Glasgow, UK. Professor
Moutinho is also the Foundation Chair of Marketing and the Founding Editor of Journal of
Modelling in Management.
Yu-Chun Wang is a graduate of the Department of International Trade, Feng Chia University,
Taiwan.
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