Optimal Instrumental Variable Estimates of the AR Parameters of an ARMA Process

In this thesis we compare the performances of instrumental variable (IV) methods for estimating AR parameters of an ARMA process. The IV method, also called modified Yule Walker method, is based on the minimization of a weighted quadratic loss function with an appropriate choice of weighting matrix. In this thesis we study the performance of two optimally weighted IV algorithms and compare them with other commonly used methods. As both algorithms require a prior estimate for the calculation of the weighting matrix, multistep estimation approaches are implemented. We use the Yule-Walker and a sub-optimally weighted Yule-Walker method to get the prior estimate. The estimators are compared with respect to accuracy, efficiency, and effects of the prior estimate (robustness). As a benchmark, we use the prediction error method ARMAX from Matlab’s system identification toolbox, which ideally achieves the Cramèr-Rao bound. After comparison, one of the optimally weighted IV algorithms is proved to b