1. Deseasonalizing Forecasts
The following presentation is meant to familiarize individuals with methods of deseasonalizing forecasts. The most simple method of dealing with seasonality is discussed, and an example is provided.
Prior knowledge of basic linear regression is assumed.
If you have questions, you may contact the creator:
Aaron Hirst

2. Agenda: Seasonality defined & seasonal adjustment methods
Brainstorming Exercise
Nuts and Bolts
How It Works
Seasonal adjustment example
Exercise
Summary
Appendix A: Solution to Exercise
The solution to the exercise is included in Appendix A.

3. Seasonality
A repeated pattern of spikes or drops in the variable of interest associated with a period of time
Examples-
Consumer buying habits
Price of gasoline
This definition comes from Bozarth, Cecil C. and Robert B. Handfield. Introduction To Operations And Supply Chain Management. New Jersey: Prentice Hall, 2006, p.251.
Dr. Tom Foster modified the definition by replacing “certain times of the year” with “a period of time.”
Consumer buying habits experience seasonal swings. For example, people spend more money around Christmas.
Gasoline prices typically peak during the summer months.

4. Seasonality Causes of seasonal movement by class:
1. Weather (temperature, precipitation)
2. Calendar Events (religious or secular festivals)
3. Timing decisions (vacations, accounting periods)
Hylleberg, Svend. Modeling Seasonality. New York: Oxford Press, 1992, p. 3
Hylleberg suggests that these three basic causes may have indirect effects through the decisions of economic agents. Hylleberg proposes the following definition of seasonality in Economics: “Seasonality is the systematic, although not necessarily regular, intra-year movement caused by the changes of the weather, the calendar, and timing of decisions, directly or indirectly through the production and consumption decisions made by the agents of the economy. These decisions are influenced by endowments, the expectations and preferences of the agents, and the production techniques available in the economy.”

5. Seasonal Adjustment Methods
Seasonal index
Hylleberg, Svend. Seasonality in Regression. Orlando, FL: Academic Press Inc., 1986, p. 89.
The first five methods (X-12 ARIMA, X-11 ARIMA, EEC Method, Burman Method, TRAMO) are not discussed at any length. For more information about these seasonal adjustment methods, please refer to the sources on the reading list.
The most basic method to adjust a forecast when there is seasonality is by using the seasonal index. This will be the focus of this presentation.

6. Nuts and Bolts Why make seasonal adjustments?
Reduces errors in time-series forecasting
Improves quality of judgmental forecasts
Gives good insight into the factors influencing demand
The purpose of finding seasonal indexes is to remove the seasonal effects from the time series
Armstrong, J. Scott. Principles of Forecasting: A Handbook for Researchers and Practitioners. Norwell, MA: Kluwer Academic Publishers, 2001, p.224.
DeLurgio, Stephen and Carl Bhame. Forecasting Systems For Operations Management. Homewood: Irwin, 1991.

7. How It Works: Deseasonalizing Forecasts
Four-step procedure for seasonal adjustments:
1. Calculate forecast for each demand values in the time series
2. For each demand value, calculate Demand/Forecast
3. Average the Demand/Forecast for months or quarters to get the seasonal index
4. Multiply the unadjusted forecast by the seasonal index to find adjusted forecast value
Cecil C. Bozarth, Cecil C. and Robert B. Handfield. Introduction To Operations And Supply Chain Management. New Jersey: Prentice Hall, 2006, p.265
This is an easy way to work with linear regression with seasonal adjustments.
Demand/Forecast ratio
-less than 1  forecast model overforecasted
-greater than 1  underforecasted

8. Season Adjustment Example
Foster Company makes widgets. The quarterly demand for its widget is given in Exhibit 1
Using linear regression forecasting, develop a seasonal index for each quarter and reforecast each quarter
The following is a comprehensive example of how to develop a seasonal index.

9. Seasonal Adjustments Example Step 1
Calculate forecast for each demand values in the time series
Use the unadjusted regression forecast model
Y= a + bx
This can be easily calculated in Microsoft Excel. Go to ToolsData AnalysisRegression

10. Seasonal Adjustments Example – Step 1
Forecasted demand
Y= *period
Year 1 Quarter 1:
Y= (1)
=99.9
Using the regression tools in Microsoft Excel, the forecasted demand equation is found to be Y= *period. From this equation the unadjusted regression forecast can be calculated.

11. Seasonal Adjustments Example – Step 2
For each demand value, calculate Demand/Forecast
Year 1 Quarter 1:
72/99.9= 0.72
This simple step requires you to divide the demand by the forecast.

12. Seasonal Adjustments Example - Step 3
Average the Demand/Forecast for the quarters to get the seasonal index
Quarterly Seasonal Index for Quarter 1:
( )/4 = 0.63
Since the time series covers multiple years, we need to average the demand/forecast ratios for each quarter (1st, 2nd, 3rd, 4th) to find the seasonal index.
Quarter 2: ( )/4 = 0.94
Quarter 3: ( )/4 = 0.99
Quarter 4: ( )/4 = 1.45

13. Seasonal Adjustments Example - Step 4
Multiply the unadjusted forecast by the seasonal index to find the adjusted forecast values
Year 1 Quarter 1:
99.9 * 0.63 = 62.7 (adjusted forecast)
This step helps you calculate the seasonally adjusted forecast values. The next slide includes a table with the solution.

14. Seasonal Adjustments Example - Step 4

15. Seasonal Adjustments Example
The plot on the left compares the actual demand to the unadjusted forecast demand (y= t). The plot on the right compares the demand with the seasonally adjusted forecast. We can see how well the adjusted forecast fits the past data.

16. Exercise
Smith Company makes widgets. The quarterly demand for its widget is given in Exhibit A
You have been asked to develop a seasonal index for each quarter and reforecast each quarter
The next slide provided a table to complete the problem. The solution can be found in Appendix A.

17. Exercise Table
For your convenience, I have provided this table to complete the exercise. The unadjusted regression forecast can be calculated using the regression tool in Excel.

18. Summary Deseasonalizing forecasts is effective for
Short-term forecasting
Comparability
Detecting trend changes early
The Seasonal Index is the most simple method for making seasonal adjustments
Summary

19. Appendix A: Solution to Exercise
This is the output from the regression tool in Microsoft Excel. Notice the Intercept and the X Variable. These values are used to develop the forecasted demand equation: Y= t
Now that you have the forecasted demand equation, you can calculate the unadjusted regression forecast.

20. Appendix A: Solution to Exercise