Modeling Time Series with Both Permanent and Transient Components Using the Partially Autoregressive Model

Abstract

A time series model is discussed that incorporates both permanent and transient effects. Estimation techniques are given, and the power of the likelihood ratio test is assessed. When applied to the monthly price/earnings series of the S&P 500 over the period 1871-2013, both permanent and transient components are found, although the transient component is by far the more dominant effect. When applied to the daily returns of the individual components of the S&P 500 over the period 2002-2013, evidence is found that a statistically significant proportion of these series exhibit both permanent and transient effects.

Keywords: time series, mean reversion

JEL Classification: C22, C32, C52, G12, G14