On Likelihood Ratio Tests for Threshold Autoregression
研究了正态噪声下阈值自回归模型似然比统计量的零分布，将问题转化为高斯过程的首达概率，发现某些情况下渐近零分布仅依赖于自由度。
SUMMARY This paper addresses the null distribution of the likelihood ratio statistic for threshold autoregression with normally distributed noise. The problem is non-standard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis. We reduce the problem to the first-passage probability associated with a Gaussian process which, in some special cases, turns out to be a Brownian bridge. It is also shown that, in some specific cases, the asymptotic null distribution of the test statistic depends only on the ‘degrees of freedom' and not on the exact null joint distribution of the time series.