1 1 Chapter 6 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods in Forecasting n Using Trend Projection in Forecasting n Using Trend and Seasonal Components in Forecasting n Using Regression Analysis in Forecasting n Qualitative Approaches to Forecasting Quantitative Approaches to Forecasting n Quantitative methods are based on an analysis of historical data concerning one or more time series. n A time series is a set of observations measured at successive points in time or over successive periods of time. n If the historical data used are restricted to past values of the series that we are trying to forecast, the procedure is called a time series method. n If the historical data used involve other time series that are believed to be related to the time series that we are trying to forecast, the procedure is called a causal method.

2 2 Time Series Methods n Three time series methods are: smoothing trend projection trend projection adjusted for seasonal influence n The trend component accounts for the gradual shifting of the time series over a long period of time. n Any regular pattern of sequences of values above and below the trend line is attributable to the cyclical component of the series. n The seasonal component of the series accounts for regular patterns of variability within certain time periods, such as over a year. n The irregular component of the series is caused by short-term, unanticipated and non-recurring factors that affect the values of the time series. One cannot attempt to predict its impact on the time series in advance. Components of a Time Series

3 3 Measures of Forecast Accuracy n Mean Squared Error The average of the squared forecast errors for the historical data is calculated. The forecasting method or parameter(s) which minimize this mean squared error is then selected. n Mean Absolute Deviation The mean of the absolute values of all forecast errors is calculated, and the forecasting method or parameter(s) which minimize this measure is selected. The mean absolute deviation measure is less sensitive to individual large forecast errors than the mean squared error measure. Smoothing Methods n In cases in which the time series is fairly stable and has no significant trend, seasonal, or cyclical effects, one can use smoothing methods to average out the irregular components of the time series. n Four common smoothing methods are: Moving averages Centered moving averages Weighted moving averages Exponential smoothing

4 4 Example: Gasoline Sales n Excel Spreadsheet Showing Input Data Smoothing Methods n Moving Average Method The moving average method consists of computing an average of the most recent n data values for the series and using this average for forecasting the value of the time series for the next period.t GasolineSales.xls Error=Actual-Forecast

5 5 Plot of Actual Gasoline Sales vs. Simulated Forecast with Moving Average Base set at 3 periods (n=3).

6 6 Smoothing Methods Exponential Smoothing Using exponential smoothing, the forecast for the next period is equal to the forecast for the current period plus a proportion (  ) of the forecast error in the current period. Using exponential smoothing, the forecast is calculated by:  [the actual value for the current period] + (1-   )[the forecasted value for the current period], where the smoothing constant, , is a number between 0 and 1. F t+1 = forecast for the next time period, t+1 Y t = actual value as the time period t F t = forecast that was calculated for the time period t  = value of the smoothing constant is an approximation of the equivalent smoothing constant for a moving average using "n" periods as the base of the average. For example, n=3 periods, then  = Therefore, using a smoothing constant of 0.50 has roughly the same effect as a moving average of three time periods. or

7 7 Exponential Smoothing Forecast,  = 0.2

8 8

9 9 Smoothing Methods: Evaluating the Smoothing Constant Suppose we have the following actual demands and we want to figure out the best smoothing constant, , to use for future forecasts. The MSE will be used to evaluate the worth of the chosen smoothing constant. ExpSmoNotes.xls

10 Smoothing Methods: Evaluating the Smoothing Constant The Solver screen in Excel 2010 set up to minimize the MSE by varying the Smoothing Constant from 0.01 to ExpSmoNotes.xls