Asymptotic Distribution Of Yule-walker Estimators For Autoregressive Time Series With Linear Trend

Qiu, Shao and Yang(2013) introduced efficient inference for autoregressive coefficients in the presence of trends. The simulation studies showed that their approach was clearly better than the well-known moving average filter method. However, their non-parametric method can only be applied to a slowly varying trend, and it is not appropriate when the trend is linear. In this thesis, we propose a parametric method which estimates a linear trend by the least squares. In addition, since the ordinary least squares estimation(OLS) and the generalized least squares estimation(GLS)for linear trends are asymptotically equivalent according to Lee and Lund(2012),we use the OLS, which greatly reduces the task of calculation. The proposed estimators are efficient: Yule- Walker coefficient estimators in the presence of a linear trend are asymptotically equivalent to those obtained without the trend. It also means that the asymptotic properties of the Yule–Walker estimators of autoregressive coefficients are not altered by the detrending procedure. The simulation studies are also consistent with the theory.