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A Predictive Approach for Selection of Diffusion Index Models

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  • Tomohiro Ando
  • Ruey S. Tsay

Abstract

In this article, we propose a predictive mean squared error criterion for selecting diffusion index models, which are useful in forecasting when many predictors are available. A special feature of the proposed criterion is that it takes into account the uncertainty in estimated common factors. The new criterion is based on estimating the predictive mean squared error in forecasting with correction for asymptotic bias. The resulting estimate of bias-corrected forecast-error is shown to be consistent. The proposed criterion is a natural extension of the traditional Akaike information criterion (AIC), but it does not require the distributional assumptions for the likelihood. Results of real data analysis and Monte Carlo simulations demonstrate that the proposed criterion works well in comparison with the commonly used AIC and Bayesian information criteria.

Suggested Citation

  • Tomohiro Ando & Ruey S. Tsay, 2014. "A Predictive Approach for Selection of Diffusion Index Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 68-99, June.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:1-4:p:68-99
    DOI: 10.1080/07474938.2013.807105
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    1. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    2. Tatsuya Kubokawa, 2009. "Conditional and Unconditional Methods for Selecting Variables in Linear Mixed Models," CIRJE F-Series CIRJE-F-688, CIRJE, Faculty of Economics, University of Tokyo.
    3. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    4. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    5. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," International Journal of Central Banking, International Journal of Central Banking, vol. 1(3), December.
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    1. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    2. Maldonado, Javier & Ruiz Ortega, Esther, 2017. "Accurate Subsampling Intervals of Principal Components Factors," DES - Working Papers. Statistics and Econometrics. WS 23974, Universidad Carlos III de Madrid. Departamento de Estadística.

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