Modelling long‐run trends and cycles in financial time series data

This paper proposes a very general time series framework to capture the long-run behaviour of financial series. The suggested model includes linear and non-linear time trends, and stationary and nonstationary processes based on integer and/or fractional degrees of differentiation. Moreover, the spectrum is allowed to contain more than a single pole or singularity, occurring at zero and non-zero (cyclical) frequencies. This model is used to analyse four annual time series with a long span, namely dividends, earnings, interest rates and long-term government bond yields. The results indicate that the four series exhibit fractional integration with one or two poles in the spectrum. A forecasting comparison shows that a model with a non-linear trend along with fractional integration outperforms alternative models over long horizons.