Multivariate Fractional Unobserved Components and Factor Models for Macroeconomic Analysis and Forecasting

• Applicants: Professor Dr. Rolf Tschernig; Professor Dr. Enzo Weber
• Subject Area: Statistics and Econometrics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 356439312

Unobserved components (UC) models play a key role in applied macroeconomic research. They are used to decompose time series into a long-run trend and a cyclical component, also interpreted as the business cycle, to study equilibrium relations among economic aggregates, and to extract common factors from high-dimensional data. Fractionally integrated models were found to grasp the long-run dynamics of macroeconomic variables well, as they allow for a flexible treatment of shock persistence. During the initial funding period we showed that combining fractional integration methods and UC models is fruitful both from a methodological and an applied perspective. We derived and studied a univariate fractional trend-cycle decomposition, a multivariate UC model with a common fractional trend, and fractional factor models.In the renewal project we build on these results and extend the class of fractional UC models to a multivariate setting with stochastic processes of different integration orders.The multivariate domain allows for crucial advancements of e.g. analyzing long-run co-movements, further increasing the reliability of business cycle estimates, and improving the specification of factor models. We explore such advancements in two parts.Part A of the renewal project sets up multivariate UC models with multiple common fractional trends of possibly different persistence and VAR cycles. Part B develops model selection methods for specifying common fractional trends in a factor model setting, where again different integration orders among both, the factors and the observable variables, are allowed. For each model we discuss identification, derive a computationally feasible estimator for the latent processes, and study the asymptotic properties of the proposed methods. Empirically, we expect new insights on the business cycle, on macroeconomic equilibrium relations, and on the number of fractional cointegration relations in high-dimensional data sets from the new models.

• DFG Programme: Research Grants