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A bootstrap test for the comparison of nonlinear time series

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  • Dette, Holger
  • Weißbach, Rafael

Abstract

The difference between the regression functions of two stationary conditional heteroskedastic autoregressive time series is tested. The functions can be equal, or shifted, under the null hypothesis. Local linear estimation of the regression function results in observable residuals. Bootstrap residuals lead to a marked empirical process as test statistic and a Kolmogorov-Smirnov version is applied. The simulation study for linear, exponential or trigonometric regression functions with homoskedastic or heteroskedastic errors finds the rejection probability under the null hypothesis to be near the level. Comparing series with different combinations of linear, exponential and trigonometric functions, the rejection probability under the alternative yields mixed results.

Suggested Citation

  • Dette, Holger & Weißbach, Rafael, 2009. "A bootstrap test for the comparison of nonlinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1339-1349, February.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1339-1349
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    References listed on IDEAS

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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.

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