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.

Real-Time Forecasting and Scenario Analysis using a Large Mixed-Frequency Bayesian VAR

“…"M" in the frequency column indicates the monthly nature of the employment data. Employment, with some exceptions, is released on the first Friday 5 For some discussion on data choice, see McBride (2014). 6 The transformations are broadly consistent with (unreported) unit root test results.…”

“…2 MIDAS regressions (Ghysels et al, 2004) 1 See Foroni, Guérin and Marcellino (2013) for a classical evaluation of a small-scale stacked VAR for the Euroarea in real-time. Blasques et al (2015) provides a weighted maximum likelihood estimation procedure for mixed frequency dynamic factor models considered in the stacked form.…”

The Sufficient Statistic Approach: Predicting the Top of the Laffer Curve

“…The choice of the data series is based on some judgment as to which economic variables are important and is broadly followed by markets and policymakers. 5 For each series listed in the first column, we indicate the original frequency of the data, as well as the transformation used to achieve stationarity. 6 We specify the approximate release date of the series, their publication lags, the dates of the first available vintages, as well as the economic data release report from which the series are obtained.…”

“…Whether or not the adjustment of the shrinkage would make a difference for forecasting is an empirical open question that we leave for future work. 17 There are alternative ways to estimate a VAR as the one in equation (5). We prefer Waggoner and Zha (2003) approach as it provides with an efficient algorithm to estimate a VAR even when the contemporaneous correlation matrix A is overidentified, resulting in a restricted reduced form variance-covariance matrix for the VAR.…”

“…2 MIDAS regressions (Ghysels et al, 2004) 1 See Foroni, Guérin and Marcellino (2013) for a classical evaluation of a small-scale stacked VAR for the Euroarea in real-time. Blasques et al (2015) provides a weighted maximum likelihood estimation procedure for mixed frequency dynamic factor models considered in the stacked form. 2 Giannone et al (2008), Aruoba et al (2009), and others utilize state-space framework to estimate factor models.…”