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Cointegrating rank selection in models with time-varying variance

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  • Cheng, Xu
  • Phillips, Peter C.B.

Abstract

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient Cn→∞ and Cn/n→0 as n→∞. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2009a) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application to exchange rate data is provided.

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  • Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:155-165
    DOI: 10.1016/j.jeconom.2012.01.022
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    References listed on IDEAS

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    Cited by:

    1. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    2. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    3. Liao, Zhipeng & Phillips, Peter C. B., 2015. "Automated Estimation Of Vector Error Correction Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 581-646, June.
    4. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    5. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    6. Onatski, Alexei & Wang, Chen, 2019. "Extreme canonical correlations and high-dimensional cointegration analysis," Journal of Econometrics, Elsevier, vol. 212(1), pages 307-322.
    7. Sabzikar, Farzad & Wang, Qiying & Phillips, Peter C.B., 2020. "Asymptotic theory for near integrated processes driven by tempered linear processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 192-202.
    8. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    9. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.
    10. Mathias Drton & Martyn Plummer, 2017. "A Bayesian information criterion for singular models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 323-380, March.
    11. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised Oct 2019.

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    More about this item

    Keywords

    Cointegrating rank; Heterogeneity; Information criteria; Model selection; Time varying variances;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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