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

Caporale, Guglielmo Maria, Cuñado, Juncal and Gil-Alana, Luis A. (2008) Modelling long-run trends and cycles in financial time series data. Centre for International Capital Markets discussion papers, 2008 (11). pp. 1-36. ISSN 1749-3412


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.

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