Kybernetika 38 no. 4, 405-424, 2002

Estimation of variances in a heteroscedastic RCA(1) model

Hana Janečková


The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form $X_t=b_tX_{t-1}+Y_t$. Two different procedures for estimating $\sigma_t^2=EY_t^2, \sigma_b^2=Eb_t^2$ or $\sigma_B^2=E(b_t-Eb_t)^2$, respectively, are described under the special seasonal behaviour of $\sigma_t^2$. For both types of estimators strong consistency and asymptotic normality are proved.