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 aaronjhirst@yahoo.com

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.

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.

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.”

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.

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.

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

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.

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

Seasonal Adjustments Example – Step 1 Forecasted demand Y=95.85+4.03*period Year 1 Quarter 1: Y=95.85+4.03(1) =99.9 Using the regression tools in Microsoft Excel, the forecasted demand equation is found to be Y=95.85+4.03*period. From this equation the unadjusted regression forecast can be calculated.

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.

Seasonal Adjustments Example - Step 3 Average the Demand/Forecast for the quarters to get the seasonal index Quarterly Seasonal Index for Quarter 1: (0.72+0.66+0.59+0.55)/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: (1.06+0.93+0.87+0.88)/4 = 0.94 Quarter 3: (1.08+1.05+0.91+0.90)/4 = 0.99 Quarter 4: (1.54+1.51+1.39+1.35)/4 = 1.45

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.

Seasonal Adjustments Example - Step 4

Seasonal Adjustments Example The plot on the left compares the actual demand to the unadjusted forecast demand (y=95.85+4.03t). 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.

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.

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.

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

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= 11.77+4.60t Now that you have the forecasted demand equation, you can calculate the unadjusted regression forecast.

Appendix A: Solution to Exercise