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Adaptive estimation of AR∞ models with time-varying variances

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  • Zhang, Erhua
  • Wu, Jilin

Abstract

This paper considers adaptive estimation of AR∞ models under time-varying variances of unknown forms. We utilize the sieve method to approximate the autoregressive model of infinite order, and then develop kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. We prove the ALS estimator has the same efficiency as its infeasible counterpart. Simulation results show the adaptive procedure can help achieve efficiency gains in finite samples.

Suggested Citation

  • Zhang, Erhua & Wu, Jilin, 2020. "Adaptive estimation of AR∞ models with time-varying variances," Economics Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:ecolet:v:197:y:2020:i:c:s0165176520304018
    DOI: 10.1016/j.econlet.2020.109641
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    1. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    2. Harris, David & Kew, Hsein, 2017. "Adaptive Long Memory Testing Under Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 33(3), pages 755-778, June.
    3. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    4. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    5. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    6. Peter C. B. Phillips & Ke‐Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 289-308, March.
    7. David I. Harvey & Stephen J. Leybourne & Yang Zu, 2019. "Testing explosive bubbles with time-varying volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1131-1151, November.
    8. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    9. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    10. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, University Library of Munich, Germany.
    11. H. Peter Boswijk & Yang Zu, 2018. "Adaptive wild bootstrap tests for a unit root with non‐stationary volatility," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 87-113, June.
    12. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-1132, September.
    13. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    14. A. C. Harvey & P. M. Robinson, 1988. "Efficient Estimation Of Nonstationary Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 201-214, May.
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    Cited by:

    1. Hwang, Eunju & Hong, Won-Tak, 2021. "A multivariate HAR-RV model with heteroscedastic errors and its WLS estimation," Economics Letters, Elsevier, vol. 203(C).

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    More about this item

    Keywords

    Time-varying variances; Sieve approximation; Adaptive estimation; Lag selection;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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