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Adaptive parametric change point inference under covariance structure changes

Author

Listed:
  • Stergios B. Fotopoulos

    (Washington State University)

  • Abhishek Kaul

    (Washington State University)

  • Vasileios Pavlopoulos

    (University of Alabama in Huntsville)

  • Venkata K. Jandhyala

    (Washington State University)

Abstract

The article offers a method for estimating the volatility covariance matrix of vectors of financial time series data using a change point approach. The proposed method supersedes general varying-coefficient parametric models, such as GARCH, whose coefficients may vary with time, by a change point model. In this study, an adaptive pointwise selection of homogeneous segments with a given right-end point by a local change point analysis is introduced. Sufficient conditions are obtained under which the maximum likelihood process is adaptive against the covariance estimate to yield an optimal rate of convergence with respect to the change size. This rate is preserved while allowing the jump size to diminish. Under these circumstances, argmax results of a two-sided negative Brownian motion or a two-sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively, provide inference for the change point parameter. Theoretical results are supported by the Monte–Carlo simulation study. A bivariate data on daily log returns of two US stock market indices as well as tri-variate data on daily log returns of three banks are analyzed by constructing confidence interval estimates for multiple change points that have been identified previously for each of the two data sets.

Suggested Citation

  • Stergios B. Fotopoulos & Abhishek Kaul & Vasileios Pavlopoulos & Venkata K. Jandhyala, 2024. "Adaptive parametric change point inference under covariance structure changes," Statistical Papers, Springer, vol. 65(5), pages 2887-2913, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01495-0
    DOI: 10.1007/s00362-023-01495-0
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    References listed on IDEAS

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    1. Olimjon Sh. Sharipov & Martin Wendler, 2020. "Bootstrapping covariance operators of functional time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 648-666, July.
    2. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    3. Wolfgang Hardle & Helmut Herwartz & Vladimir Spokoiny, 2003. "Time Inhomogeneous Multiple Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 55-95.
    4. Harchaoui, Z. & Lévy-Leduc, C., 2010. "Multiple Change-Point Estimation With a Total Variation Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1480-1493.
    5. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Stoehr, Christina & Aston, John A D & Kirch, Claudia, 2021. "Detecting changes in the covariance structure of functional time series with application to fMRI data," Econometrics and Statistics, Elsevier, vol. 18(C), pages 44-62.
    8. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. Stryhn, Henrik, 1996. "The location of the maximum of asymmetric two-sided Brownian motion with triangular drift," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 279-284, September.
    10. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    11. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    12. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    13. 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.
    14. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    15. Wied, Dominik & Krämer, Walter & Dehling, Herold, 2012. "Testing For A Change In Correlation At An Unknown Point In Time Using An Extended Functional Delta Method," Econometric Theory, Cambridge University Press, vol. 28(3), pages 570-589, June.
    16. Bai, Jushan, 2010. "Common breaks in means and variances for panel data," Journal of Econometrics, Elsevier, vol. 157(1), pages 78-92, July.
    17. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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