Testing for threshold autoregression with conditional heteroscedasticity

C. S. WONG, Wai Keung LI

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33 Citations (Scopus)

Abstract

This paper addresses the null distribution of the Lagrange-multiplier statistic for the threshold autoregression with conditional heteroscedasticity. The problem is nonstandard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis. We generalise the results of Chan (1990) and Chan & Tong (1990) to show that the asymptotic null distribution of the Lagrange-multiplier statistic is a functional of a zero-mean Gaussian process. The generalisation is not direct as the conditional variance is changing and the unconditional distribution of the process variable is no longer normal. In some special cases, we can reduce the problem to the asymptotic distribution of certain functions of Brownian bridges and the upper percentage points can be tabulated as in Chan (1991). Monte Carlo experiments show that the approximation and the power of the test are quite good. We also demonstrate the importance of using our test if the true model has conditional heteroscedasticity. Copyright © 1997 Oxford University Press.
Original languageEnglish
Pages (from-to)407-418
JournalBiometrika
Volume84
Issue number2
DOIs
Publication statusPublished - Jun 1997

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Conditional Heteroscedasticity
heteroskedasticity
multipliers
Autoregression
Lagrange multipliers
Null Distribution
Asymptotic distribution
Statistic
statistics
Statistics
Brownian Bridge
Threshold Parameter
Percentage Points
Conditional Variance
Testing
Monte Carlo Experiment
Nuisance Parameter
Gaussian Process
Null hypothesis
testing

Citation

Wong, C. S., & Li, W. K. (1997). Testing for threshold autoregression with conditional heteroscedasticity. Biometrika, 84(2), 407-418. doi: 10.1093/biomet/84.2.407

Keywords

  • Conditional heteroscedasticity
  • Gaussian process
  • Lagrange-multiplier test
  • Threshold time series model