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Model Selection Criteria for the Leads-and-Lags Cointegrating Regression

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  • Choi, In
  • Kurozumi, Eiji
  • 黒住, 英司

Abstract

In this paper, Mallows’ (1973)Cp criterion, Akaike’s (1973) AIC, Hurvich and Tsai’s (1989) corrected AIC and the BIC of Akaike (1978) and Schwarz (1978) are derived for the leads-and-lags cointegrating regression. Deriving model selection criteria for the leads-and-lags regression is a nontrivial task since the true model is of infinite dimension. This paper justifies using the conventional formulas of those model selection criteria for the leads-and-lags cointegrating regression. The numbers of leads and lags can be selected in scientific ways using the model selection criteria. Simulation results regarding the bias and mean squared error of the long-run coefficient estimates are reported. It is found that the model selection criteria are successful in reducing bias and mean squared error relative to the conventional, fixed selection rules. Among the model selection criteria, the BIC appears to be most successful in reducing MSE, and Cp in reducing bias. We also observe that, in most cases, the selection rules without the restriction that the numbers of the leads and lags be the same have an advantage over those with it.
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Suggested Citation

  • Choi, In & Kurozumi, Eiji & 黒住, 英司, 2008. "Model Selection Criteria for the Leads-and-Lags Cointegrating Regression," CCES Discussion Paper Series 6, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:ccesdp:6
    Note: First Draft: April, 2008; Revised: August, 2008
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    2. Schweikert, Karsten, 2018. "Are gold and silver cointegrated? New evidence from quantile cointegrating regressions," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 44-51.
    3. Alloza, Mario & Sanz, Carlos, 2019. "Dynamic Effects of Persistent Shocks," UC3M Working papers. Economics 29187, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    5. Daniel Ordonez Callamand & Luis Fernando Melo-Velandia & Daniel Parra-Amado, 2018. "Una exploración reciente a la demanda por dinero en Colombia bajo un enfoque no lineal," Revista de Economía del Rosario, Universidad del Rosario, vol. 21(1), pages 5-37, June.
    6. Skrobotov, Anton, 2021. "Structural breaks in cointegration models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 63, pages 117-141.
    7. Martin Wagner & Dominik Wied, 2017. "Consistent Monitoring of Cointegrating Relationships: The US Housing Market and the Subprime Crisis," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 960-980, November.
    8. Jack R. Rogers, 2013. "Monetary Transmission to UK Retail Mortgage Rates before and after August 2007," Discussion Papers 1307, University of Exeter, Department of Economics.
    9. Eiji Kurozumi & Anton Skrobotov, 2018. "Confidence Sets for the Break Date in Cointegrating Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(3), pages 514-535, June.
    10. Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
    11. David Tennant & Marlon Tracey, 2013. "Explaining related party transactions in commercial banking: looted lending and information-based investments," Applied Financial Economics, Taylor & Francis Journals, vol. 23(19), pages 1509-1530, October.
    12. Karsten Reichold & Carsten Jentsch, 2022. "A Bootstrap-Assisted Self-Normalization Approach to Inference in Cointegrating Regressions," Papers 2204.01373, arXiv.org.
    13. David Neto, 2023. "Penalized leads-and-lags cointegrating regression: a simulation study and two empirical applications," Empirical Economics, Springer, vol. 65(2), pages 949-971, August.

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    Keywords

    Cointegration; Leads-and-lags regression; AIC; Corrected AIC; BIC; Cp;
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