Low Frequency and Weighted Likelihood Solutions for Mixed Frequency Dynamic Factor Models

Abstract

The multivariate analysis of a panel of economic and financial time series with mixed frequencies is a challenging problem. The standard solution is to analyze the mix of monthly and quarterly time series jointly by means of a multivariate dynamic model with a monthly time index: artificial missing values are inserted for the intermediate months of the quarterly time series. In this paper we explore an alternative solution for a class of dynamic factor models that is specified by means of a low frequency quarterly time index. We show that there is no need to introduce artificial missing values while the high frequency (monthly) information is preserved and can still be analyzed. We also provide evidence that the analysis based on a low frequency specification can be carried out in a computationally more efficient way. A comparison study with existing mixed frequency procedures is presented and discussed. Furthermore, we modify the method of maximum likelihood in the context of a dynamic factor model. We introduce variable-specific weights in the likelihood function to let some variable equations be of more importance during the estimation process. We derive the asymptotic properties of the weighted maximum likelihood estimator and we show that the estimator is consistent and asymptotically normal. We also verify the weighted estimation method in a Monte Carlo study to investigate the effect of different choices for the weights in different scenarios. Finally, we empirically illustrate the new developments for the extraction of a coincident economic indicator from a small panel of mixed frequency economic time series.

Keywords: Asymptotic theory, Forecasting, Kalman filter, Nowcasting, State space

JEL Classification: C13, C32, C53, E17