Structural Time-Series Models with Common Trends and Common Cycles

Abstract

This paper models and estimates the Beveridge-Nelson decomposition of multivariate time series in an unobserved components framework. This is an alternative to standard approaches based on VAR and VECM models. The appeal of this method lies in its transparency and structural character. The basic model parsimoniously nests a large set of common trend and common cycle restrictions. It is found that if the cyclical component has a sufficiently rich serial correlation pattern, all covariance terms of the trend and cycle innovations are identified. Tests for common trends are based on a method developed by Nyblom and Harvey (2000), while hypotheses on common cycles are tested using likelihood ratio statistics with standard distributions. This testing framework is used to assess the implications of common trend-common cycle restrictions for the income-consumption relationship in U.S. data. The presence of a common cyclical component yields a rejection of the permanent income hypothesis and evidence is found for the stylized fact that permanent shocks play a more important role for consumption than for income. Out-of-sample forecasts show that common trend and common cycle restrictions improve predictive accuracy.

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