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On score vector- and residual-based CUSUM tests in ARMA–GARCH models

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  • Haejune Oh

    (Seoul National University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

In this study, we consider the problem of testing for a parameter change in ARMA–GARCH models. We suggest two types of cumulative sum (CUSUM) tests, namely, score vector- and residual-based CUSUM tests. It is shown that under regularity conditions, their limiting null distributions are the sup of Brownian bridges. A simulation study and real data analysis are conducted for illustration.

Suggested Citation

  • Haejune Oh & Sangyeol Lee, 2018. "On score vector- and residual-based CUSUM tests in ARMA–GARCH models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 385-406, August.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0408-9
    DOI: 10.1007/s10260-017-0408-9
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    References listed on IDEAS

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    1. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    2. Sangyeol Lee & Siyun Park, 2001. "The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 625-644, December.
    3. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    4. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    5. Berkes, Istvan & Horváth, Lajos & Kokoszka, Piotr, 2004. "Testing for parameter constancy in GARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 263-273, December.
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    Cited by:

    1. Minyoung Jo & Sangyeol Lee, 2021. "On CUSUM test for dynamic panel models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 515-542, June.
    2. Lee, Youngmi & Kim, Sungdon & Oh, Haejune, 2024. "Sequential change-point detection in time series models with conditional heteroscedasticity," Economics Letters, Elsevier, vol. 236(C).
    3. Hsu, Shu-Han & Cheng, Po-Keng & Yang, Yiwen, 2024. "Diversification, hedging, and safe-haven characteristics of cryptocurrencies: A structural change approach," International Review of Financial Analysis, Elsevier, vol. 93(C).

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