Approximately Median-Unbiased Estimation of Autoregressive Models

Abstract

This article introduces approximately median-unbiased estimators for univariate AR(p) models with time trends. Confidence intervals also are considered. The methods are applied to the Nelson–Plosser macroeconomic data series, the extended Nelson–Plosser macroeconomic data series, and some annual stock-dividend and price series. The results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest. For example, for the extended Nelson–Plosser data set, 8 of the 14 series are estimated to have a unit root, but 6 are estimated to be trend stationary. In contrast, the least squares estimates indicate trend stationarity for all of the series.

KEY WORDS:

• Bias correction
• Macroeconomic time series
• Time trend
• Trend stationary
• Unit root