Predicting Returns with a Co-Fractional VAR Model
49 Pages Posted: 22 Jan 2011
Date Written: January 13, 2011
We use co-fractional models to evaluate the predictive relations between returns and a valuation ratio. The co-fractional model can handle situations where financial returns are predicted using persistent valuation ratios, like dividend to price. For our application we consider very long time series, covering 355 years of real-estate returns and rent to price ratios. We find robust evidence of a fractional root of d=0.75 in the rent to price ratio. The co-fractional model empirically outperforms the traditional triangular time-series model of return predictability. For annual data, the difference in predictive R-squared is about 8%. We conclude that the co-fractional VAR provides an alternative parsimonious model for the interaction between returns and valuation ratios. The long-memory properties of the fractional model have important implications for the fit of present-value models and the term structure of risk.
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