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New In-Sample Prediction Errors In Time Series With Applications

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  • Daniel Peña

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  • Ismael Sánchez

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    Abstract

    This article introduces two new types of prediction errors in time series: the filtered prediction errors and the deletion prediction errors. These two prediction errors are obtained in the same sample used for estimation, but in such a way that they share some common properties with out of sample prediction errors. It is proved that the filtered prediction errors are uncorrelated, up to terms of magnitude order O(T-2), with the in sample innovations, a property that share with the out-of-sample prediction errors. On the other hand, deletion prediction errors assume that the values to be predicted are unobserved, a property that they also share with out-of-sample prediction errors. It is shown that these prediction errors can be computed with parameters estimated by assuming innovative or additive outliers, respectively, at the points to be predicted. Then the prediction errors are obtained by running the procedure for all the points in the sample of data. Two applications of these new prediction errors are presented. The first is the estimation and comparison of the prediction mean squared errors of competing predictors. The second is the determination of the order of an ARMA model. In the two applications the proposed filtered prediction errors have some advantages over alternative existing methods..

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    File URL: http://docubib.uc3m.es/WORKINGPAPERS/WS/ws011107.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws011107.

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    Date of creation: Jan 2001
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    Handle: RePEc:cte:wsrepe:ws011107

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    1. Todd E. Clark & Michael W. McCracken, 1999. "Tests of equal forecast accuracy and encompassing for nested models," Research Working Paper 99-11, Federal Reserve Bank of Kansas City.
    2. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
    3. Koreisha, Sergio G & Pukkila, Tarmo, 1995. "A Comparison between Different Order-Determination Criteria for Identification of ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 127-31, January.
    4. Ashley, Richard, 1998. "A new technique for postsample model selection and validation," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 647-665, May.
    5. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
    6. Chong, Yock Y & Hendry, David F, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 671-90, August.
    7. John Haslett, 1999. "A Simple Derivation of Deletion Diagnostic Results for the General Linear Model with Correlated Errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 603-609.
    8. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    9. Kenneth D. West & Michael W. McCracken, 1998. "Regression-Based Tests of Predictive Ability," NBER Technical Working Papers 0226, National Bureau of Economic Research, Inc.
    10. Ashley, R & Granger, C W J & Schmalensee, R, 1980. "Advertising and Aggregate Consumption: An Analysis of Causality," Econometrica, Econometric Society, vol. 48(5), pages 1149-67, July.
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