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# Solve and see what happens via ma3 and ma6 happens

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Unformatted text preview: lve and see what happens via MA(3) and MA(6). happens Exponential Smoothing It is a type of moving average forecasting technique which weighs past data in an exponential manner so that the most recent data carries more weight in the moving average. average. 1. New Forecast = α (most recent observation) + (1 - α) (last forecast) (1 α) (last or 2. New Forecast = last forecast - α (last forecast error) 2. where 0 < α < 1 is the smoothing constant and generally where is small for stability of forecasts (around .1 to .2). is 10 Exponential Smoothing Ft+1 = α Dt + (1 - α ) Ft (1 = α Dt + (1 - α ) (α Dt-1 + (1 - α ) Ft-1) (1 = α Dt + (1 - α )(α )Dt-1 + (1 - α)2 (α )Dt - 2 +... (1 )( Hence the method applies a set of exponentially Hence declining weights to past data. It is easy to show that the sum of the weights is exactly one. sum Simply; Ft + 1 = Ft - α (Ft - Dt) Example Example α = 0.1 and from assumption we know that the forecast for week 1 is 200. forecast Week 1 2 3 4 5 6 7 8 Failures Forecast 200 200(assumption) 250 175 186 225 285 305 190 11 Example Week 1 2 3 4 5 6 7 8 Failures 200 250 175 186 225 285 305 190 ES 200(assumption) error MA(3) error Comparison of ES and MA Similarities Similarities Both methods are appropriate for stationary series Both Both methods depend on a single parameter Both Both methods lag behind a trend Both One can achieve the same distribution of forecast error by setting α = 2/ ( N + 1). 2/ Differences Differences...
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