Semiparametric Estimation of the Modified Random Coefficient Autoregressive Model and it's Properties

In this paper, we introduce a modified version of a random coefficient autoregressive model (MRCA) and discuss the estimation of its mean parameter of interest by estimating function (EF) approach. We derive the implications of the optimal EF estimate in terms of various symmetric and asymmetric GARCH models. On the light of the interpretation, we also consider a MRCA model with variables having non-zero means. We derive several complementary asymptotic properties such as consistency, asymptotic normality, and asymptotic bound, for the EF estimate. We also show how the methods can be extended to the multivariate settings, and perform some simulation experiments. The results support the finite sample optimality property of EF estimator as we take into account the simultaneous presence of autocorrelation and conditional heteroscedasticity in the underlying data generating scheme.