6 - Estimation of Parameters from Stochastic Processes

Abstract

In cases where the maximum likelihood (ML) estimator is impracticable, it is usually necessary to resort to estimation procedures that do not necessarily have any particular optimality properties. In this regard, the method of conditional least squares (CLS) is considered. It has the advantage that, for the classical scaling, a discussion of the multivariate case poses no additional complications, but optimality questions are not treated. In various cases where the underlying process is Gaussian, it can produce the ML estimators. Under quite mild restrictions, the CLS estimators are, as with the ML estimators, strongly consistent and asymptotically normally distributed. There are many situations in which estimation methods with known or presumed optimality properties are not tractable or even available. In such situations, it is usually possible to resort to the classical method of moments. Estimation by this method cannot be expected to convey any optimality properties, but it is convenient and frequently leads to simple calculations.