Stochastic linear trends

Abstract

The paper considers stochastic linear trends in series with a higher than annual frequency of observation. Using an approach based on ARIMA models, some of the trend models for the model interpretation of trend estimation filters) most often found in statistics and econometrics are analysed and compared. The properties of the trend optimal estimator are derived, and the analysis is extended to seasonally adjusted and/or detrended series. It is seen that, under fairly general conditions, the estimator of the unobserved component is noninvertible, and will not accept a convergent autoregressive representation. This has implications concerning unit root testing and VAR model fitting.