The random coefficient autoregressive model has been utilized for modeling financial time series because it possesses features that are often observed in financial time series. When the mean of the random coefficient is one, it is called the stochastic unit root model. This paper proposes two Lagrange multiplier tests for the null hypotheses of random coefficient autoregressive and stochastic unit root models against a more general model. We apply our Lagrange multiplier tests to several stock index data, and find that the stochastic unit root model is rejected, whereas the random coefficient autoregressive model is not. This result indicates that it is important to check the validity of the stochastic unit root model prior to applying it to financial time series data, which may be better modeled by the random coefficient autoregressive model with the mean being not equal to one.
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