Minimum distance estimation of k-factors GARMA processes

We consider minimum distance estimation of k-factors Gegenbauer Autoregressive Moving Average (k-GARMA) processes. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through k-GARMA parameters. We establish the consistency of the estimator. When the k frequencies are unknown, asymptotic distribution theory for parameters estimators including the long memory parameters is significantly harder. We discuss the (non-standard) limiting distributional behavior of the estimators of k. And for the remaining parameter estimator, we establish asymptotic normality.