Particle Filtering, Learning, and Smoothing for Mixed-Frequency State-Space Models

Abstract

A particle filter approach for general mixed-frequency state-space models is considered. It employs a backward smoother to filter high-frequency state variables from low-frequency observations. Moreover, it preserves the sequential nature of particle filters, allows for non-Gaussian shocks and nonlinear state-measurement relation, and alleviates the concern over sample degeneracy. Simulation studies show that it outperforms the commonly used state-augmented approach for mixed-frequency data for filtering and smoothing. In an empirical exercise, predictive mixed-frequency regressions are employed for Treasury bond and US dollar index returns with quarterly predictors and monthly stochastic volatility. Stochastic volatility improves model inference and forecasting power in a mixed-frequency setup but not for quarterly aggregate models.

Keywords: Mixed-frequency, State-space Models, Particle Filtering, Particle Learning, Smoothing, Parameter Estimation, Real-time Learning, Confounded Learning

JEL Classification: C13, C32, C53