1. Economics 173 Business Statistics Lecture 27 © Fall 2001, Professor J. Petry http://www.cba.uiuc.edu/jpetry/Econ_173_fa01/

2. 2 20.7 Introduction to Forecasting * * * * * * * * o o o o o o o o Model 1Model 2 Which model performs better? There are many forecasting models available ?

3. 3 To choose a forecasting method, we can evaluate forecast accuracy using the actual time series. The two most commonly used measures of forecast accuracy are: –Mean Absolute Deviation –Sum of Squares for Forecast Error

4. 4 Choose SSE if it is important to avoid (even a few) large errors. Otherwise, use MAD. A useful procedure for model selection. –Use some of the observations to develop several competing forecasting models. –Run the models on the rest of the observations. –Calculate the accuracy of each model. –Select the model with the best accuracy measure.

5. 5 Example 20.7 –Annual data from 1963 to 1990 were used to develop three forecasting models. –Use MAD and SSE to determine which model performed best for 1991, 1992, 1993, and 1994.

6. 6 Solution –For model 1 –Summary of results Actual y in 1991 Forecast for y in 1991

7. 7 Example –For the actual values and the forecast values of a time series shown in the following table, calculate MAD and SSE. Forecast Value F t Actual Value y t 173166 186179 192195 211214 223220

8. 8 The exponential smoothing model can be used to produce forecasts when the time series –exhibits gradual(not a sharp) trend, –no cyclical effects, –no seasonal effects. Forecast for period t+k is computed by F t+k = S t t is the current period; S t =  y t + (1-  )S t-1 20.8 Time-Series Forecasting with Exponential Smoothing

9. 9 Example 20.8 –Forecast the consumption of distilled spirit in the US for 1994, based on the data of annual consumption for the years 1963 to 1993. Use exponential smoothing. –Data

10. 10 1960 1993 There is a gradual increase from 1960 through 1980, then a gradual decrease. There is no evidence for the presence of cyclical effects. Exponential smoothing can be used. Not much smoothing is needed. We select  =.8

11. 11 S 1 = y 1 = 99 F 2 = 99 S 2 =.8(102) + (.2)(99) = 101.4 F 3 = 101.4 S 3 =.8(106) +.2(101.4) = 105.08 F 4 = 105.08 S 33 =.8(144) + (.2)(147.197) = 144.639 F 34 = 144.639 101.4 2 3 4 1 99 102 106 105.08 Exponential smoothing: The forecasting process

12. 12 Example –Use exponential smoothing, with w=.6, to forecast the next value of the time series that follows. t y t 123 218 326 427 524 622