Measuring Forecasting Error MBA,
A Time Series is a set of observations on a
quantitative variable collected over time.
Time Series Data
Most businesses keep track of a number of time series variables. Examples might
include:
Daily
Weekly
Monthly
Quarterly figures on
- Sales
- Costs
- Profits
- Inventory
- Back orders
- Customer counts
- and so on.
- Time Series Methods
- if we can discover some sort of systematic variation in the past behavior of the time
- series variable, we can attempt to construct a model of this behavior to help us
- forecast its future behavior.
- For example, we might find a long-term upward (or downward) trend in the time
- series that might be expected to continue in the future.
- Or, we might discover some predictable seasonal fluctuations in the data that could
- help us make estimates about the future. As you may have surmised, time series
- forecasting is based largely on the maxim that history tends to repeat itself.
- Techniques that analyze the past behavior of a time series variable
- to predict the future are sometimes referred to as
- Extrapolation models.
- Measuring Forecasting Errors
- MUHAMMAD IDREES ASGHAR
- A Time Series is a set of observations on a
- quantitative variable collected over time.
- Time Series Data
- Most businesses keep track of a number of time series variables. Examples might
- include:
- Daily
- Weekly
- Monthly
- Quarterly figures on
- Sales
- Costs
- Profits
- Inventory
- Back orders
- Customer counts
- and so on.
Time Series Methods
if we can discover some sort of systematic variation in the past behavior of the time
series variable, we can attempt to construct a model of this behavior to help us
forecast its future behavior.
For example, we might find a long-term upward (or downward) trend in the time
series that might be expected to continue in the future.
Or, we might discover some predictable seasonal fluctuations in the data that could
help us make estimates about the future. As you may have surmised, time series
forecasting is based largely on the maxim that history tends to repeat itself.
Techniques that analyze the past behavior of a time series variable
to predict the future are sometimes referred to as
Extrapolation models.
Time Series Methods
The general form of an Extrapolation model is:
Time Series Methods
The general form of an Extrapolation model is:
6/11/2022
4 - Ft = At – 1 + (1-)At – 2 + (1- )2·At – 3
- (1- )3At – 4 + … + (1- )t-1·A0
– Ft = Forecast value
– At = Actual value
– = Smoothing constant - Ft = Ft-1 + (At-1 – Ft-1)
– Use for computing forecast
Exponential Smoothing Equations
PowerPoint presentation to accompany Heizer/Render –
Principles of Operations Management, 5e, and Operations
Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-8
During the past 8 quarters, the Port of Baltimore has unloaded large
quantities of grain. ( = .10). The first quarter forecast was 175..
Quarter Actual
1 180
2 168
3 159
4 175
5 190
6 205
7 180
8 182
9 ?
Exponential Smoothing Example
Find the forecast
for the 9th quarter.
6/11/2022
5
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168
3 159
4 175
5 190
6 205
175.00 +
Exponential Smoothing Solution
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(
3 159
4 175
5 190
6 205
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
6/11/2022
6
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 –
3 159
4 175
5 190
6 205
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 – 175.00)
3 159
4 175
5 190
6 205
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
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7
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 – 175.00) = 175.50
3 159
4 175
5 190
6 205
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
PowerPoint presentation to accompany Heizer/Render –
Principles of Operations Management, 5e, and Operations
Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-14
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 – 175.00) = 175.50
3 159 175.50 + .10(168 – 175.50) = 174.75
4 175
5 190
6 205
Exponential Smoothing Solution
8
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1995 180 175.00 (Given)
1996 168 175.00 + .10(180 – 175.00) = 175.50
1997 159 175.50 + .10(168 – 175.50) = 174.75
1998 175
1999 190
2000 205
174.75 + .10(159 – 174.75)= 173.18
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 – 175.00) = 175.50
3 159 175.50 + .10(168 – 175.50) = 174.75
4 175 174.75 + .10(159 – 174.75) = 173.18
5 190 173.18 + .10(175 – 173.18) = 173.36
6 205
Exponential Smoothing Solution
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Quarter Actual Forecast, Ft
(α = .10)
1 180 175.00 (Given)
2 168 175.00 + .10(180 – 175.00) = 175.50
3 159 175.50 + .10(168 – 175.50) = 174.75
4 175 174.75 + .10(159 – 174.75) = 173.18
5 190 173.18 + .10(175 – 173.18) = 173.36
6 205 173.36 + .10(190 – 173.36) = 175.02
Exponential Smoothing Solution
PowerPoint presentation to accompany Heizer/Render –
Principles of Operations Management, 5e, and Operations
Management, 7e
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-18
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Time Actual Forecast, Ft
(α = .10)
4 175 174.75 + .10(159 – 174.75) = 173.18
5 190 173.18 + .10(175 – 173.18) = 173.36
6 205 173.36 + .10(190 – 173.36) = 175.02
Exponential Smoothing Solution
7 180
8
175.02 + .10(205 – 175.02) = 178.02
9
10
Ft = Ft-1 + 0.1(At-1 – Ft-1)
Time Actual Forecast, Ft
(α = .10)
4 175 174.75 + .10(159 – 174.75) = 173.18
5 190 173.18 + .10(175 – 173.18) = 173.36
6 205 173.36 + .10(190 – 173.36) = 175.02
Exponential Smoothing Solution
7 180
8
175.02 + .10(205 – 175.02) = 178.02
9 178.22 + .10(182 – 178.22) = 178.58
182 178.02 + .10(180 – 178.02) = 178.22
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