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Abstract Details
Activity Number:
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248
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Type:
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Contributed
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Date/Time:
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Monday, August 1, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Business and Economic Statistics Section
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Abstract - #301288 |
Title:
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Multi-Step Forecast Model Selection and Combination
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Author(s):
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Bruce E. Hansen*+
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Companies:
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University of Wisconsin
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Address:
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Department of Economics, Madison, WI, 53706,
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Keywords:
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MSFE ;
cross-validation ;
forecast combination ;
model averaging ;
information criterion ;
multi-step forecasting
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Abstract:
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This paper examines model selection and combination in the context of multi-step linear forecasting. We start by investigating multi-step mean squared forecast error (MSFE). We derive the bias of the in-sample sum of squared residuals as an estimator of the MSFE. We find that the bias is not generically a scale of the number of parameters, in contrast to the one-step-ahead forecasting case. Instead, the bias depends on the long-run variance of the forecast model. In consequence, standard information criterion (Akaike, FPE, Mallows and leave-one-out cross-validation) are biased estimators of the MSFE in multi-step forecast models. These criteria are generally under-penalizing for over-parameterization and this discrepancy is increasing in the forecast horizon. In contrast, we show that the leave-h-out cross validation criterion is an approximately unbiased estimator of the MSFE and is thus a suitable criterion for model selection. Leave-h-out is also suitable for selection of model weights for forecast combination. We provide strong simulation and empirical evidence in favor of weight selection by leave-h-out cross validation.
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