NTop-4 - Ec 178 ECONOMIC & BUSINESS FORECASTING L...

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Ec 178 – ECONOMIC & BUSINESS FORECASTING LECTURE NOTES Foster, UCSD February 25, 2010 TOPIC 4 – FORECAST ACCURACY A. Two Approaches to Evaluating Model Accuracy 1. Goodness of Fit: a) The model is estimated or run in over all historical data y t , t = 1. ..n. Estimated or forecasted values ŷ t are computed. b) Goodness of fit measures are based on forecast errors or regression residuals û t = y t - ŷ t . Trend, curve fitting, and econometric regression: the ŷ t are the fitted values on the line or curve, and the û t are the regression residuals. Decomposition: ŷ t = T ̃ t + A ̃ t + C ̃ t or T ̃ t × A ̃ t × C ̃ t . Smoothing and ARIMA: ŷ t is the 1-step forecast ŷ t-1,1 . (About the first 20% of the u ̃ t observations should be dropped for smoothing models, allowing the smoothing equations to “run in” to the data pattern.) c) Every forecast model should first be evaluated on goodness of fit. 1) Models with poor fit are discarded at this point without further analysis. 2) Good models should be further evaluated on their ability to forecast ex post . y t τ n Fig. 1 Ex post Estimation Period (t = 1. ..τ) Ex post Forecast Period (t = τ+1. ..n) In-Sample Period (t = 1. ..n) Ex ante Forecast period (t = n+1…)
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Ec 178 FORECAST ACCURACY p. 2 2. Ex post Forecast Evaluation: a) The model parameters are re-estimated using only data y t , t = 1. .. < n. The model τ is then used to produce an ex post trace forecast ŷ +1 τ , ŷ +2 τ ... ŷ n . b) Measures of ex post forecast accuracy are also based on forecast errors û t = y t - ŷ t . 1) The ex post ŷ +h τ are produced using the same equations as ex ante forecasts ŷ n+h . 2) The ex post forecast period length should be n/10 or 1 full seasonal cycle.
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Ec 178 FORECAST ACCURACY p. 3 B. Measures of Accuracy 1. Three Desirable Characteristics of All Forecasts: a) Unbiased. 1) We want E( ŷ t ) = y t , which implies E(û t ) = 0. 2) Therefore, models with small average errors are preferred. b) Efficient. We want small forecast error variance E(y t −ŷ t ) 2 = E(û t 2 ). Therefore, we prefer models with small sums of squared errors (and which use all infor-mation in Ω n ). c) No pattern in û t series. The error term holds all of the pattern in y t which was not captured in the model. A good model gets most of this pattern, so we prefer models whose errors plot out as ZMWN (purely random series). d) For the summary accuracy measures below, T n is the number of û t terms used in the cal-culation, perhaps after dropping observations at the beginning or end of the period t = 1. ..n. 2. Measures of Absolute Forecast Accuracy: a) Mean Error (ME). Measures average forecast bias. For a good model, one wants ME 0. For OLS regression residuals, ME 0, and is not helpful. Mean Absolute Error (MAE). Smaller is better. c) Measures based on sum of squared errors.
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NTop-4 - Ec 178 ECONOMIC &amp; BUSINESS FORECASTING L...

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