Unit roots in the presence of moving average errors: tests of consumer price inflation

Abstract

The issue of stationarity is a critical one in time series modelling. Tests designed to detect unit roots are sensitive, however, to model specification. While it has previously been shown that the presence of moving average errors may adversely affect the size of Dickey–Fuller type tests for stationarity in finite samples, this paper demonstrates that the order of the moving average process is also important. Critical values of unit root tests for MA(2) processes are shown to be larger than comparable values for MA(1) processes, which are in turn larger than Dickey–Fuller values. Consumer Price Inflation is estimated as an MA(2) process and is tested for stationarity using the computed critical values for time series with MA(2) errors.