Testing for double threshold autoregressive conditional heteroscedastic model

Abstract: The testing problem for the hypothesis of linearity against the double threshold autoregressive conditional heteroscedastic model is addressed. The prob-lem is nonstandard as the threshold parameter is a nuisance parameter which is absent under the null hypothesis. We will show that the asymptotic null distribu-tion of the Lagrange-multiplier test statistic is a functional of a zero-mean Gaussian process. In some cases, we give the upper percentage points of the test statistic. The performance of the test statistic is illustrated by extensive simulation experi-ments and an example. Key words and phrases: Conditional heteroscedasticity, Gaussian process, Lag-range-multiplier test, threshold time series model. 1