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Modified residual CUSUM test for location-scale time series models with heteroscedasticity

Author

Listed:
  • Haejune Oh

    (Seoul National University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

This study considers the residual-based CUSUM test for location-scale time series models with heteroscedasticity. The estimates- and score vector-based CUSUM tests are widely used for detecting abrupt changes in time series models. However, their performance is often unsatisfactory with severe size distortions when the underlying model is complicated and the sample size is small. To circumvent this defect, the residual-based CUSUM test is suggested as an alternative. However, this test can only detect scale parameter changes and suffers severe power loss against location parameter changes. To remedy this, we introduce a modified residual-based CUSUM test and demonstrate its validity for both location and scale parameter changes. We conduct a simulation study and data analysis for illustration.

Suggested Citation

  • Haejune Oh & Sangyeol Lee, 2019. "Modified residual CUSUM test for location-scale time series models with heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1059-1091, October.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0679-4
    DOI: 10.1007/s10463-018-0679-4
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    References listed on IDEAS

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    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.
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    7. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    8. 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.
    9. de Pooter, M.D. & van Dijk, D.J.C., 2004. "Testing for changes in volatility in heteroskedastic time series - a further examination," Econometric Institute Research Papers EI 2004-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    1. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.

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