# 18-027/III (2018-03-21)

Author(s)
Mengheng Li, VU Amsterdam; Siem Jan (S.J.) Koopman, VU Amsterdam; Tinbergen Institute, The Netherlands
Keywords:
Importance Sampling, Kalman Filter, Monte Carlo Simulation, Stochastic Volatility, Unobserved Components Time Series Model, Inflation
JEL codes:
C32, C53, E31, E37

We consider unobserved components time series models where the components are stochastically evolving over time and are subject to stochastic volatility. It enables the disentanglement of dynamic structures in both the mean and the variance of the observed time series. We develop a simulated maximum likelihood estimation method based on importance sampling and assess its performance in a Monte Carlo study. This modelling framework with trend, seasonal and irregular components is applied to quarterly and monthly US inflation in an empirical study. We find that the persistence of quarterly inflation has increased during the 2008 financial crisis while it has recently returned to its pre-crisis level. The extracted volatility pattern for the trend component can be associated with the energy shocks in the 1970s while that for the irregular component responds to the monetary regime changes from the 1980s. The scale of the changes in the seasonal component has been largest during the beginning of the 1990s. We finally present empirical evidence of relative improvements in the accuracies of point and density forecasts for monthly US inflation.