On Conditional Least Squares Estimation for Stochastic Processes

Abstract

An estimation procedure for stochastic processes based on the mini- mization 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 asymp- totically stationary and ergodic. The estimators and their limiting co- variance 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.