1. SLR w SI = Simple Linear Regression with Seasonality Indices
MGTSC 352
Lecture 5: Forecasting
Choosing LS, TS, and SS
SLR w SI = Simple Linear Regression with Seasonality Indices
Range estimates

2. Choosing Weights
Find the values for LS, TS and SS that minimize* some performance measure.
* Exception?
Two methods:
Table – If you want to use more than one performance measure
Solver – If you want to ‘optimize’ against one performance measure only

3. What’s This Solver Thing?
In Excel: Tools  Solver, to bring up:
Optimize something (maximize profit, minimize cost, etc.)
By varying some decision variables (“changing cells”)
Keeping in mind any restrictions (“constraints”) on the decision variables

4. Using Solver to Choose LS, TS, SS
Pg. 33
Using Solver to Choose LS, TS, SS
What to optimize: minimize SE
Could minimize MAD or MAPE, but solver works more reliably with SE
For the geeks: because SE is a smooth function
Decision variables: LS, TS, SS
Constraints: LS TS SS
Something a bit bigger than zero
(f. ex.: 0.01, 0.05)
Something a bit smaller than one
(f. ex.: 0.99, 0.95) ≤ ≤
Let’s try it out …

5. Why Solver Doesn’t Always Give the Same Solution
Everywhere I look is uphill! I must have reached the lowest point.
local optimum
global optimum

6. SLR w SI = Simple Linear Regression with Seasonality Indices
Pg. 34
SLR w SI = Simple Linear Regression with Seasonality Indices
Captures level, trend, seasonality, like TES
Details are different
SLR Forecast
Ft+k = (intercept + [(t + k)  slope])  SI
Excel

7. multiplicative seasonality
TES vs SLRwSI
TES
Ft+k = (Lt + k  Tt)  St+k-p
SLRwSI
Ft+k = (intercept + (t + k)  slope)  SI
additive trend
multiplicative seasonality

8. TES vs SLRwSI Both estimate Level, Trend, Seasonality
Data points are weighted differently
TES: weights decline as data age
SLR w SI: same weight for all points
TES adapts, SLR w SI does not

9. Which Method Would Work Well for This Data?

10. Patterns in the Data? Trend: Seasonality? Yes, but it is not constant
Zero, then positive, then zero again
Seasonality?
Yes, cycle of length four

11. Comparison TES: SE = 24.7 SLRwSI: SE = 32.6 TES trend is adaptive
SLR uses constant trend

12. How Good are the Forecasts?
Pg. 38
How Good are the Forecasts?
TES (optimized): Year 5, Quarter 1 sales =
Are you willing to bet on it?
Forecasts are always wrong
How wrong will it be?
Put limits around a “point forecast”
“Prediction interval”
95%* sure sales will be between low and high
How do we compute low and high?
* (give or take)

13. Forecast Error Distribution

14. Approximate with Normal Distribution
“Standard Error” of the forecast errors
Average Error = .3
Standard
Error = 127

15. 95% Prediction Interval 1-step Point forecast + bias  2  StdError
9 Jan TSX =  2  127 =  254 =[12400, 12908] =[low, high]
Actual 12,467.99

16. Are TES and SLR w SI it? Certainly not Additive seasonality models
TES’ or SLR w SD
Multiplicative trend models
TES’’ or Nonlinear Regression (Dt+1 = 1.1Dt)

17. Steps in a Forecasting Project
Pg. 39
Steps in a Forecasting Project
-1: Collect data
0: Plot the data (helps detect patterns)
1: Decide which models to use
level – SA, SMA, WMA, ES
level + trend – SLR, DES
level + trend + seas. – TES, SLR w SI, ...
2: Use models
3: Compare and select (one or more)
4: Generate forecast and range (prediction interval)
More on selection

18. How to select a model? Look at performance measures
Pg. 41
How to select a model?
Look at performance measures
BIAS, MAD, MAPE, MSE
Use holdout strategy
Example: 4 years of data
Use first 3 years to fit model(s)
Forecast for Year 4 and check the fit(s)
Select model(s)
Refit model(s) adding Year 4 data
If you have more than one good model...
COMBINE FORECASTS

19. Appropriate model... Nonlinear (ex. power) linear
S-curve (ex. any CDF)

20. DATA

21. Which method would you choose?
TES vs. SLR w/ SI
Which method would you choose?

22. Holdout Strategy Ignore part of the data (the “holdout data”)
Build models using the rest of the data
Optimize parameters
Forecast for the holdout data
Calculate perf. measures for holdout data
Choose model that performs best on holdout data
Refit parameters of best model, using all data

23. TES vs. SLR w/ SI …in holdout period

24. TES vs. SLR w/ SI …in holdout period
Now which method would you choose?

25. Calgary EMS Data
Number of calls / month
Trend?
Seasonality?

26. Checking for (Yearly) Seasonality
Number of calls / month

27. Weekly Seasonality
Avg. # of calls / hr., 2004