A study of estimation procedures for time series models in economics

Abstract

The thesis is concerned with the formulation and estimation of the autoregressive-moving average (ARMA) model, and its application to econometrics. Chapter 1 considers the origin of ARMA models and provides a discussion on the loss of optimal properties by a number of estimators under such a specification. Having established an a fortiori case for the ARMA model in economics, Chapter 2 derives the likelihood function in both the frequency and time domains, and outlines computational algorithms for its maximization - these being variants of the well known Gauss-Newton and Newton-Raphson techniques for the solution of systems of non-linear equations. Chapters 3 and 4 contain Monte Carlo experiments on the estimators proposed in Chapter 2. These were primarily constructed to assess the likely impact of small samples upon the distribution of the estimators, but, as well, some indication of the sample size at which asymptotic theorems will hold is gained. As the first four chapters were concerned with single-equation problems Chapter 5 provides a generalization of the methodology to systems of equations, and reports on some experiments conducted with the systems estimator. Finally Chapters 6 and 7 deal with applications of the ARMA model in economics. Chapter 6 demonstrates that a number of concepts appearing in economic theory e.g. permanent income, may be formulated as ARMA models, thereby enabling some estimates of these quantities to be made, while Chapter 7 compares the optimal ARMA estimator to ordinary least squares for a number of published studies, in order to demonstrate the extent of bias in conclusions based upon a use of the latter estimator. The final section of Chapter 7 outlines directions for future research.