Fixed Size Confidence Regions for Parameters of Stationary Processes Based on a Minimum Contrast Estimator

For parameters of stationary processes with zero mean and spectral density, sequential procedures are proposed for constructing fixed size confidence ellipsoidal regions for unknown parameters using a minimum contrast estimator. The confidence ellipsoids are shown to be asymptotically consistent and the associated stopping rules are shown to be asymptotically efficient as the size of the region becomes small when the assumed parametric model is correct. Monte Carlo simulations are given to investigate the performance of our proposed sequential procedures.