In this paper, we show a two-stage estimation method to discuss the parameter estimation problem of the first-order generalized random coefficient autoregressive model (GRCA(1)). Firstly, we obtain the consistency and asymptotic normality of the covariance estimators by Hellinger minimum distance estimation methods and moment estimation methods respectively. Secondly, we obtain the estimators of parameters for the model by the weighted least squares method and prove the asymptotic properties of parameter estimators. Numerical simulations show that the two-stage estimation method in this paper has a smaller mean square error compared to the least squares method. Thus, Hellinger minimum distance method is better than the moment estimation method.
A kind of integer autoregressive model of random coefficients in random environment based on Signed thinning operator of signed generalized power series thinning operator is studied statistically. Conditional maximum likelihood estimators of model parameters are presented. The simulation results show that the model is effective in solving the parameter estimation problem of negative integer-valued time series in random environment.
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