On Conditional Least Squares Estimation for Stochastic Processes

Abstract

An estimation procedure for stochastic processes based on the minimization of a sum of squared deviations about conditional expectations is developed. Strong consistency, asymptotic joint normality and an iterated logarithm rate of convergence are shown to hold for the estimators under a variety of conditions. Special attention is given to the widely studied cases of stationary ergodic processes and Markov processes with are asymptotically stationary and ergodic. The estimators and their limiting covariance matrix are worked out in detail for a subcritical branching process with immigration. A brief Monte Carlo study of the performance of the estimators is presented.