ForecastingGeneral

ForecastingGeneral - Chapter 7 My interest is in the future...

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1 Chapter 7 My interest is in the future because I am going to spend the rest of my life there.— Charles F. Kettering Forecasting
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2 Time-Series Analysis A time series is numerical sequence of values generated over regular time intervals. The classical time-series model involves four components: Secular trend ( T t ). Cyclical movement ( C t ). Seasonal fluctuation ( S t ). Irregular variation ( I t ). The multiplicative model determine the level of the forecast variable Y t : Y t = T t × C t × S t × I t
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3 Classical Time-Series Model
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4 Exponential Smoothing Finding the components is difficult. A direct approach averages past Y t values by exponential smoothing . The forecast value is computed from F t +1 = α Y t + (1 - α ) F t The above involves a single parameter , the smoothing constant (α29 alpha. All previous time periods are reflected in the F s, and greater weight is given to the more recent.
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5 Forecasts with Single-Parameter Exponential Smoothing
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6 Single-Parameter Forecasts The preceding slide shows single-parameter forecasts of Blitz Beer sales. These were generated by computer. The level for α was .20. A greater will assign more weight to the present. Quality of forecasts may be measured. Most common is the mean squared error : which averages errors over all forecasts made. Other measures are the mean absolute deviation ( MAD ) and mean absolute percent error ( MAPE ). MSE = ( Y t F t ) 2 n
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7 Two-Parameter Exponential Smoothing The smoothing constant can be tuned to the past, possibly providing better forecasts. But single-parameter forecasts may still lead or lag actuals , as seen for Blitz Beer, because the impact of trends is delayed. Trend T t can be incorporated with a second trend smoothing constant γ (gamma): T t = α Y t + (1 – )( T t –1 + b t –1 ) b t = ( T t T t –1 ) + (1 – ) b t –1 F t+ 1 = T t + b t
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8 Forecasts with Two-Parameters
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9 Seasonal Exponential Smoothing with Three Parameters Many time series have regular seasonal patterns to be incorporated into forecasts. The three-parameter model incorporates a seasonal smoothing constant β (beta): T t = α( Y t / S t p ) + (1 – α )( T t –1 + b t –1 ) b t = γ ( T t T t –1 ) + (1 – ) b t –1 S t = β( Y t / T t ) + (1 – ) S t p F t+ 1 = ( T t + b t ) S t p +1
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10 Forecasting with Three Parameters
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11 Forecasting with Three Parameters The above works for p = 4 quarters or p = 12 months . The preceding slide needs 6 quarters to generate the first (very bad) forecast. The process settles quickly , providing good forecasts p periods into the future.
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12 Forecasting Trend Using Regression To forecast years in advance, regression analysis provides a trend line . Ŷ
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This note was uploaded on 12/02/2011 for the course QM 670 taught by Professor Dr.keeney during the Fall '11 term at Jefferson College.

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ForecastingGeneral - Chapter 7 My interest is in the future...

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