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Modified tests for variance changes in autoregressive regression

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  • Jin, Hao
  • Zhang, Jinsuo

Abstract

In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR(p) processes meanwhile autoregressive parameters shifts occur. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the bootstrap method introduced to eliminate the influence caused by the autoregressive parameters shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. Simulation results as to AR(1) processes and an example of real data analysis are provided for illustration.

Suggested Citation

  • Jin, Hao & Zhang, Jinsuo, 2011. "Modified tests for variance changes in autoregressive regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1099-1109.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:6:p:1099-1109
    DOI: 10.1016/j.matcom.2010.02.011
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    References listed on IDEAS

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    1. 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.
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    5. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    6. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Subsampling tests for the mean change point with heavy-tailed innovations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2157-2166.
    7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
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    Cited by:

    1. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.

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