Essays on the decomposition of economic variables

This thesis consists of three essays: Essay Nr. 1 (Kolmogorov-Wiener Filters for Finite Time-Series) describes a framework to implement optimally linear filters in the context of finite time series. The filters under consideration have the property that they minimize the mean squared error compared to some ideal hypothetical filter. It is shown in examples that three commonly used filters, the bandpass filter, the Hodrick-Prescott filter and the digital Butterworth filter need to be adjusted when applied to finite samples of serially correlated or integrated data. An empirical example indicates that the proposed optimal filters improve the end-of-sample performance of standard filters when applied to U.S. GDP data. Essay Nr. 2 (Structural Time-Series Models with Common Trends and Common Cycles) 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, however 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. Essay Nr. 3 (Codependence in Cointegrated Autoregressive Models) investigates codependent cycles, i.e. transitory components that react to common stimuli in a similar, although not necessarily synchronous fashion. In a multivariate system, codepenii dence corresponds to an impulse response function that is collinear except for a small number of initial periods. This essay shows that the number of cofeature combinations that yield the scalar component models associated with codependence is severely limited by the dimension of a finite-order VAR system. The presence of cointegrating relationships imposes additional cross-equation restrictions and further limits the number of permissible cofeatures. For vector-error correction models the distribution of FIML based LR tests is therefore different than that of the limited information tests proposed by Vahid and Engle (1997). Monte-Carlo simulations indicate that LR tests yield an increase in power relative to the alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence among individual components of the U.S. economy.