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Model selection in the presence of nonstationarity

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  • Kim, Jae-Young

Abstract

This paper studies model selection methods in the presence of nonstationarity. We focus on the Bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice. First, we derive each of these criteria in the presence of nonstationarity. In particular, we study the Bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity. One important feature of the Bayesian model selection criterion (BMSC) is that BMSC gives different weights to the stationary and nonstationary components of a model while the other criteria do not. This feature of BMSC is a desirable property for a model selection rule in the presence of possible nonstationarity. Second, we compare these criteria with regard to parsimony and power. We have found that BMSC shows the highest parsimony, AIC is the second, and Cp and R̄2, having the same level of parsimony, are the third. With regard to power, the order is not clearly established. However, for the size adjusted power BMSC becomes dominant as the sample size increases. Without size adjustment the order in the power is exactly the opposite to that in parsimony. Also, we find that BMSC is a consistent selection rule while the other criteria are not. Third, we consider four different cases of practical interest for which BMSC with some of the other criteria is applicable. We discuss how our BMSC can be used in these cases of practical interest. Results of an extensive Monte Carlo simulation for models in these four cases show that overall the BMSC outperforms other criteria.

Suggested Citation

  • Kim, Jae-Young, 2012. "Model selection in the presence of nonstationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 247-257.
    • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:247-257
    DOI: 10.1016/j.jeconom.2012.01.029
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    1. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    2. Geweke, John & Meese, Richard, 1981. "Estimating regression models of finite but unknown order," Journal of Econometrics, Elsevier, vol. 16(1), pages 162-162, May.
    3. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
    4. Martin Crowder, 1988. "Asymptotic expansions of posterior expectations, distributions and densities for stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 297-309, June.
    5. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    6. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    7. Han Hong & Bruce Preston & Matthew Shum, 2001. "Empirical Likelihood-Based Selection Criteria for Moment Condition Models," Economics Working Paper Archive 459, The Johns Hopkins University,Department of Economics.
    8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    9. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
    10. Cavanaugh, Joseph E., 1999. "A large-sample model selection criterion based on Kullback's symmetric divergence," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 333-343, May.
    11. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    12. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    13. Hong, Han & Preston, Bruce & Shum, Matthew, 2003. "Generalized Empirical Likelihood–Based Model Selection Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 923-943, December.
    14. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
    15. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    16. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    17. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    18. Amemiya, Takeshi, 1980. "Selection of Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 331-354, June.
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    2. Harris, David & Kew, Hsein & Taylor, A.M. Robert, 2020. "Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem," Journal of Econometrics, Elsevier, vol. 219(2), pages 354-388.

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    More about this item

    Keywords

    Model selection; Nonstationarity; Bayesian rule; Parsimony; Power;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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