1. Quantitative Business Forecasting Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

2. Quantitative Forecasting Regression Models Time Series Models Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

3. Procedure for Forecasting with Time Series Model Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

4. Time Series Trend and Seasonsality Calculate the deseasonalized data from the original time series Construct a least squares line through the deseasonalized data. Calculate the forecast for the time period T+1 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

5. Exponential Smoothing This technique uses all the preceding observations to determine a smoothed value for a particular time period. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

6. Exponential Smoothing S t = Smoothed value for time period t t = 2, 3, 4,..... Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

7. Simple Exponential Smoothing Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

8. Simple Exponential Smoothing Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

9. Linear Exponential Smoothing Procedures for Summarizing the Results Procedure 1: –b 1 = 0 Provided you have a large number of years, this procedure provides an adequate initial estimate for the trend. Procedure 2: –use the first five years to estimate the initial trend. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

10. Linear Exponential Smoothing Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

11. Forecasting Using Linear and Seasonal Exponential Smoothing Procedure 1: –Set the initial seasonal factors equal to 1. –Set the initial trend estimate equal to 0. –Set the initial smoothed value for quarter 4 (t) equal to the actual value for quarter 4 (t+1). Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

12. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

13. Forecasting Using Linear and Seasonal Exponential Smoothing Procedure 2: –Use the first two years of data to determine the seasonal indexes. –Deseasonalize the datat for the first two years and calculate the least squares line through these deseasonalized values. –The initial smoothed value for quarter 4 (t). S o is the forecast value for each of the 4 quarters in year t+1. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

14. Forecasting Using Linear and Seasonal Exponential Smoothing Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

15. Comparison of the Procedures Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

16. Time as a Factor for Choosing the Appropriate Forecasting Procedure Length of the forecast –short term forecast: one to three months –Medium-range forecast: four months to two years –Long-range forecast: two or more years Exponential smoothing procedures are excellent for short-term forcasts, whereas the component decomposition is useful for medium- and long-range forecasting Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

18. “Fit” as a Factor for Choosing the Appropriate Forecasting Procedure MAD - mean absolute deviation MAPE - mean absolute percentage error MSE - mean square error There is no consensus among statisticians as to which measure is preferable. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

19. “Fit” as a Factor for Choosing the Appropriate Forecasting Procedure Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

20. Autoregressive Forecasting Used when the time series variable is related to past values of itself. We can expect the autoregressive technique to perform well for a time series that (1) is not extremely volatile and (2) requires a short-term or medium-range forecast. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

21. Autocorrelation Durbin-Watson Statistic Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

22. Autocorrelation H o : no autocorrelation exists H a : positive autocorrelation exists Reject H o if DW < d L Fail to Reject H o if DW < d U The test is inconclusive if d L  DW  d U Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

23. Procedures for Correcting Autocorrelated Errors 1. Replace y t by the first difference y t = y t - y t-1 2. Replace y t by the percentage change during year t Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

24. Procedures for Correcting Autocorrelated Errors 3. Include the lagged dependent variables as predictors of y. 4. Attempt to discover other significant predictor variables. 5. Model the error term in much the same way we handled the situation of autocorrelated observations. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing