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Strong approximation for RCA(1) time series with applications

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  • Aue, Alexander

Abstract

In this paper, we derive a strong invariance principle for the partial sums of RCA(1) random variables. An application yields asymptotic tests for a change in the mean of the observations both for sequential and a posteriori procedures based on CUSUMs.

Suggested Citation

  • Aue, Alexander, 2004. "Strong approximation for RCA(1) time series with applications," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 369-382, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:369-382
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    References listed on IDEAS

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    1. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    2. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    3. Lajos Horváth, 1997. "Detection of Changes in Linear Sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 271-283, June.
    4. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
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    Cited by:

    1. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    2. Joanna Górka, 2008. "Description of the Kurtosis of Distributions by Selected Models with Sign Function," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 119-128.
    3. Joanna Górka, 2009. "Application of the Family of Sign RCA Models for Obtaining the Selected Risk Measures," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 9, pages 39-50.
    4. Mihalache, Stefan, 2012. "Strong approximations and sequential change-point analysis for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 464-472.

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