Description
A statement about the future value of a variable of interest such as demand, Forecasting is used to make informed decisions.
Quantitative Analysis for Management
Forecasting
By
Wichian Srichaipanya
Contents
• Measure of Forecast Accuracy
• Monitoring and Controlling Forecast
• Moving Average
• Exponential Smoothing
2
• Introduction
FORECAST:
• A statement about the future value of a variable of
interest such as demand.
• Forecasting is used to make informed decisions.
Introduction
Uses of Forecasts
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
3-4
Features of Forecasts
• Assumes causal system past ==> future
• Forecasts rarely perfect because of
randomness
• Forecasts more accurate for groups vs.
individuals
• Forecast accuracy decreases as time horizon
increases
3-5
Steps in the Forecasting Process
3-6
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”
Types of Forecasts
• Judgmental - uses subjective inputs
• Time series - uses historical data
assuming the future will be like the past
• Associative models - uses explanatory
variables to predict the future
3-7
Judgmental Forecasts
• Executive opinions
• Sales force opinions
• Consumer surveys
• Outside opinion
• Delphi method
– Opinions of managers and staff
– Achieves a consensus forecast
3-8
Time Series Forecasts
• Trend - long-term movement in data
• Seasonality - short-term regular variations in
data
• Cycle – wavelike variations of more than one
year’s duration
• Irregular variations - caused by unusual
circumstances
• Random variations - caused by chance
3-9
Forecast Variations
3-10
Trend
Irregular
variatio
n
Seasonal variations
90
89
88
Cycles
Moving average – A technique that averages a
number of recent actual values, updated as new
values become available.
where F
t+1
= Forecast for time period t+1
Y
t
= actual value in time period t
n = number of periods to average
3-11
F
t+1
=
n
Y
t
+Y
t-1
+ …+Y
t-n+1
Moving Average
• Weighted moving average – More recent values in
a series are given more weight in computing the
forecast.
3-12
F
t+1
=
n
w
1
Y
t
+w
2
Y
t-1
+ …+w
n
Y
t-n+1
where w
i
= weight for i
th
observation
Simple Moving Average
3-13
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
3-14
Example : Moving Average
A 3-month moving average for some company according to
actual sales volume and estimated sales volume.
3-15
Example : Weighted Moving Average
Forecast with weights of 3 for the most recent observation, 2 for
the next observation, and 1 for the most distant observation.
• Premise--The most recent observations might
have the highest predictive value.
– Therefore, we should give more weight to the more
recent time periods when forecasting.
3-16
F
t+1
= F
t
+ ?(Y
t
- F
t
)
Exponential Smoothing
• Weighted averaging method based on previous
forecast plus a percentage of the forecast error
• Y-F is the error term, ? is the % feedback
3-17
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error
1 42
2 40 42 -2.00 42 -2
3 43 41.8 1.20 41.2 1.8
4 40 41.92 -1.92 41.92 -1.92
5 41 41.73 -0.73 41.15 -0.15
6 39 41.66 -2.66 41.09 -2.09
7 46 41.39 4.61 40.25 5.75
8 44 41.85 2.15 42.55 1.45
9 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.88
11 40 41.92 -1.92 41.53 -1.53
12 41.73 40.92
Example - Exponential Smoothing
Example : Exponential Smoothing graph
3-18
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
D
e
m
a
n
d
? ? .1
? ? .4
Actual
3-19
Measure of Forecast Accuracy
• Error - difference between actual value and
predicted value
• Mean Absolute Deviation (MAD)
– Average absolute error
• Mean Squared Error (MSE)
– Average of squared error
• Mean Absolute Percent Error (MAPE)
– Average absolute percent error
MAD, MSE and MAPE
• MAD
– Easy to compute
– Weights errors linearly
• MSE
– Squares error
– More weight to large errors
• MAPE
– Puts errors in perspective
3-20
MAD, MSE, and MAPE
3-21
MAD =
Actual forecast ? ?
n
MSE =
Actual forecast)
- 1
2
? ?
n
(
MAPE =
Actual forecast ?
n
/ Actual*100) ?(
Example : MAD, MSE, MAPE
3-22
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100
1 217 215 2 2 4 0.92
2 213 216 -3 3 9 1.41
3 216 215 1 1 1 0.46
4 210 214 -4 4 16 1.90
5 213 211 2 2 4 0.94
6 219 214 5 5 25 2.28
7 216 217 -1 1 1 0.46
8 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75
MSE= 10.86
MAPE= 1.28
3-23
Monitoring and Controlling Forecast
After a forecast has been completed, it is important
that it is not be forgotten.
No manager wants to be reminded when his or her
forecast is horribly in accurate,
but the firm needs to determine why the actual
demand differed from that projected.
Tracking Signal
3-24
Tracking signal =
(Actual - forecast)
MAD
?
• Running sum of the forecast error(RSFE)
divided by the mean absolute deviation (MAD)
Upper and Lower limit– Persistent tendency for
forecasts to be Greater or less than actual values.
One way to monitor forecasts to ensure that they are
performing well
Upper and Lower Limit
3-25
There is no single answer, but they try to find
reasonable values.
Example : Tracking signals
3-26
The objective is to compute the tracking signal and
determine whether forecasts are performing
adequately.
In period 6, this tracking signal is within acceptable
limits from -2.0 MADs to +2.5 MADs.
Any Question?
Thank You
doc_462817680.ppt
A statement about the future value of a variable of interest such as demand, Forecasting is used to make informed decisions.
Quantitative Analysis for Management
Forecasting
By
Wichian Srichaipanya
Contents
• Measure of Forecast Accuracy
• Monitoring and Controlling Forecast
• Moving Average
• Exponential Smoothing
2
• Introduction
FORECAST:
• A statement about the future value of a variable of
interest such as demand.
• Forecasting is used to make informed decisions.
Introduction
Uses of Forecasts
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
3-4
Features of Forecasts
• Assumes causal system past ==> future
• Forecasts rarely perfect because of
randomness
• Forecasts more accurate for groups vs.
individuals
• Forecast accuracy decreases as time horizon
increases
3-5
Steps in the Forecasting Process
3-6
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”
Types of Forecasts
• Judgmental - uses subjective inputs
• Time series - uses historical data
assuming the future will be like the past
• Associative models - uses explanatory
variables to predict the future
3-7
Judgmental Forecasts
• Executive opinions
• Sales force opinions
• Consumer surveys
• Outside opinion
• Delphi method
– Opinions of managers and staff
– Achieves a consensus forecast
3-8
Time Series Forecasts
• Trend - long-term movement in data
• Seasonality - short-term regular variations in
data
• Cycle – wavelike variations of more than one
year’s duration
• Irregular variations - caused by unusual
circumstances
• Random variations - caused by chance
3-9
Forecast Variations
3-10
Trend
Irregular
variatio
n
Seasonal variations
90
89
88
Cycles
Moving average – A technique that averages a
number of recent actual values, updated as new
values become available.
where F
t+1
= Forecast for time period t+1
Y
t
= actual value in time period t
n = number of periods to average
3-11
F
t+1
=
n
Y
t
+Y
t-1
+ …+Y
t-n+1
Moving Average
• Weighted moving average – More recent values in
a series are given more weight in computing the
forecast.
3-12
F
t+1
=
n
w
1
Y
t
+w
2
Y
t-1
+ …+w
n
Y
t-n+1
where w
i
= weight for i
th
observation
Simple Moving Average
3-13
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
3-14
Example : Moving Average
A 3-month moving average for some company according to
actual sales volume and estimated sales volume.
3-15
Example : Weighted Moving Average
Forecast with weights of 3 for the most recent observation, 2 for
the next observation, and 1 for the most distant observation.
• Premise--The most recent observations might
have the highest predictive value.
– Therefore, we should give more weight to the more
recent time periods when forecasting.
3-16
F
t+1
= F
t
+ ?(Y
t
- F
t
)
Exponential Smoothing
• Weighted averaging method based on previous
forecast plus a percentage of the forecast error
• Y-F is the error term, ? is the % feedback
3-17
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error
1 42
2 40 42 -2.00 42 -2
3 43 41.8 1.20 41.2 1.8
4 40 41.92 -1.92 41.92 -1.92
5 41 41.73 -0.73 41.15 -0.15
6 39 41.66 -2.66 41.09 -2.09
7 46 41.39 4.61 40.25 5.75
8 44 41.85 2.15 42.55 1.45
9 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.88
11 40 41.92 -1.92 41.53 -1.53
12 41.73 40.92
Example - Exponential Smoothing
Example : Exponential Smoothing graph
3-18
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
D
e
m
a
n
d
? ? .1
? ? .4
Actual
3-19
Measure of Forecast Accuracy
• Error - difference between actual value and
predicted value
• Mean Absolute Deviation (MAD)
– Average absolute error
• Mean Squared Error (MSE)
– Average of squared error
• Mean Absolute Percent Error (MAPE)
– Average absolute percent error
MAD, MSE and MAPE
• MAD
– Easy to compute
– Weights errors linearly
• MSE
– Squares error
– More weight to large errors
• MAPE
– Puts errors in perspective
3-20
MAD, MSE, and MAPE
3-21
MAD =
Actual forecast ? ?
n
MSE =
Actual forecast)
- 1
2
? ?
n
(
MAPE =
Actual forecast ?
n
/ Actual*100) ?(
Example : MAD, MSE, MAPE
3-22
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100
1 217 215 2 2 4 0.92
2 213 216 -3 3 9 1.41
3 216 215 1 1 1 0.46
4 210 214 -4 4 16 1.90
5 213 211 2 2 4 0.94
6 219 214 5 5 25 2.28
7 216 217 -1 1 1 0.46
8 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75
MSE= 10.86
MAPE= 1.28
3-23
Monitoring and Controlling Forecast
After a forecast has been completed, it is important
that it is not be forgotten.
No manager wants to be reminded when his or her
forecast is horribly in accurate,
but the firm needs to determine why the actual
demand differed from that projected.
Tracking Signal
3-24
Tracking signal =
(Actual - forecast)
MAD
?
• Running sum of the forecast error(RSFE)
divided by the mean absolute deviation (MAD)
Upper and Lower limit– Persistent tendency for
forecasts to be Greater or less than actual values.
One way to monitor forecasts to ensure that they are
performing well
Upper and Lower Limit
3-25
There is no single answer, but they try to find
reasonable values.
Example : Tracking signals
3-26
The objective is to compute the tracking signal and
determine whether forecasts are performing
adequately.
In period 6, this tracking signal is within acceptable
limits from -2.0 MADs to +2.5 MADs.
Any Question?
Thank You
doc_462817680.ppt