FINITE SAMPLE PROPERTIES OF THE OLS ESTIMATOR IN A STATIONARY FIRST ORDER AUTOREGRESSIVE MODEL.

Abstract

This thesis investigates the moments of the ordinary least-squares estimator <img class="image" src="http://www.webassign.net/images/phihatbold.gif" alt="phi hat"> in the first-order autoregressive AR(1) model. The application of the ordinary least-squares estimator in time series models have attracted attention because of the bias present under finite sample conditions. The exact distribution of <img class="image" src="http://www.webassign.net/images/phihatbold.gif" alt="phi hat"> remains unknown, but we can make inference about its properties by studying its moments. In this thesis, we explore the use of hyperbolic substitutions to evaluate higher-order moments, and heuristic expressions related to <img class="image" src="http://www.webassign.net/images/phihatbold.gif" alt="phi hat"> . Our study is supplemented with Monte Carlo simulations. For most parts, we found that our numerical results are in close agreement with benchmark works previously published by academic researchers. The hyperbolic substitution method therefore allows us to obtain more extensive numerical results, and these results can subsequently be use to calibrate the <img class="image" src="http://www.webassign.net/images/phihatbold.gif" alt="phi hat"> in practice.