An autoregressive model with Markov regime‐switching is analyzed that reflects on the properties of the quasi‐likelihood ratio test developed by Cho and White (2007). For such a model, we show that consistency of the quasi‐maximum likelihood estimator for the population parameter values, on which consistency of the test is based, does not hold. We describe a condition that ensures consistency of the estimator and discuss the consistency of the test in the absence of consistency of the estimator.