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Error Forecasting

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MEASURING FORECASTING ERROR
(The students are advised to refer to the book under reference for details.)

Because quantitative forecasting techniques frequently involve time series data, a mathematical notation is developed to refer to each specific time period. The letter Y will be used to denote a time series variable unless there is more than one variable involved. The time period associated with an observation is shown as a subscript. Thus Y1 refers to the value of the time series at time period t. The quarterly data for the Outboard Marine Corporation presented in Example 3.5 (see p. 73) would be denoted Y1 = 147.6,Y2 = 251.8, Y3 = 273.1, ... , Y52 = 281.4.

Mathematical notation must also be developed for distinguishing between an actual value of time series and the forecast value. A^ (hat) will be placed above a value to indicate that it is being forecast. The forecast value for Yt is Yt^. The accuracy of a forecasting technique is frequently judged by comparing the original series Y1, Y2, ... with the series of forecast values Y^1, Y^ 2, ....
Basic Forecasting Notation

Basic forecasting notation is summarized as follows. Yt = value of time series at period t t = forecast value of Yt et = Yt - Yt^ = residual, or forecast error Several methods have been devised to summarize the errors generated by a particular forecasting technique. Most of these measures involve averaging some function of the difference between an actual value and its forecast value. These differences between observed values and forecast values are ofteri referred to as residuals.
A residual is difference between an actual value and its forecaste Equation 3.6 is used to compute the error, or residual, for each forecast period. et = Yt - Yt^

et = forecast error in time

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