R. Moeanaddin, Howell Tong, A Comparison of Likelihood Ratio Test and CUSUM Test for Threshold Autoregression, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 37, No. 2, Special Issue: Statistical Forecasting and Decision-Making (1988), pp. 213-225
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Moeanaddin et al. (1988) studied this question.