Quasi Maximum Likelihood Estimation of Large, Approximate Dynamic Factor Models, with an Application to US output GAP

Abstract:

This work considers Quasi Maximum Likelihood estimation of dynamic factor models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the factor model has a state-space form. We study simultaneous estimation both of the factors and their loadings by means of the Expectation Maximisation algorithm implemented together with the Kalman smoother.

As both the dimension of the panel n and the sample size T diverge to infinity, the factors and loadings are consistently estimated with rate min(√n, √T ). Although the model is estimated under the unrealistic constraint of cross-sectionally uncorrelated idiosyncratic components, we explicitly address the implied mis-specification error and we give asymptotic conditions under which such error becomes negligible. Consistency results are derived also in the case in which we explicitly account for common and idiosyncratic stochastic trends as well as deterministic linear trends. Finally, we use this method to extract a measure of US Output Gap from a large panel of macroeconomic indicators.

Co-author: Matteo Luciani

About Matteo Barigozzi

Matteo is Associate Professor in Statistics at the London School of Economics and Political Science (LSE). Before joining LSE, he was post-doc researcher at ECARES at the Université libre de Bruxelles. He has an MSc degree in Physics from Università degli Studi di Milano, a MSc in Mathematical Modelling from UNESCO International Centre of Theoretical Physics in Trieste, and a PhD in Economics from Sant’Anna School of Advanced Studies in Pisa.

Matteo's research mainly focuses on high-dimensional time series analysis and specifically on large dynamic factor models with extensions to the non-stationary setting, that is in presence of unit roots and cointegration or of change-points. He is interested also in applications to macroeconomic analysis, as monetary policy making, and financial analysis, as volatility forecasting. He is also working on: sequential testing, models for network data and spectral analysis for modelling mixed frequencies data, non-linearities, and spatial dependencies.

For more information www.barigozzi.eu