Regression parameter estimation with serially correlated errors

Least-squares regression is a standard statistical technique for relating variables by means of functional relationships. On the assumption that the errors are independent of one another and have equal variance, the regression parameter estimators are approximately efficient and the conventional estimators of the variances of these estimators are approximately unbiased. However, if the errors are correlated, then in general neither property holds true. This thesis is directed towards overcoming these deficiences when errors are serially correlated; arising because a series of measurements is made on a single experimental unit, rather than on a number of separate units. Two types of solution are considered: (1) model the error process, either empirically or mechanistically, and estimate any unknown parameters jointly with the regression parameters (chapters 4 to 8); (2) derive estimators of the variances of least-squares regression parameter estimators which take account of the error correlations (chapter 9). The diversity of models considered in the first solution is facilitated computationally by the specification in chapter 2 of a new class of serially-structured error processes, termed generalized autoregressive-moving average processes. In chapter 3 solutions of linear stochastic difference and differential equations are shown to be in this class. Empirical models of the error processes are based entirely on the corresponding data sets; no other information being available on the forms the correlations should take. Basically, a regression