12:00
The Time-Varying Volatility of U.S. Core Inflation and Its Role in Point, Interval and Density Forecasting
Mengheng Li (VU University Amsterdam)

Inflation forecasting is an important task of central banks. The unobserved components model decomposes a time series into a trend, seasonal and cyclic components, providing a flexible framework for modeling stochastic mean in inflation series. Stock and Watson (2007) extended a simple version of unobserved components model, a local level model, to incorporate stochastic volatility (SV) both in the observation equation and the state equation. In this paper, we refine and extend the local level model with SV to include a seasonal component with SV. Generalizations with more components and SV are straightforward. For similar models only Bayesian estimation approach exists in literature, while we propose a simulated ML estimation procedure using importance sampling. In an empirical study, we model and estimate the U.S. monthly core inflation by a local level plus seasonal model with SV. It shows that the importance sampling estimate of the smoothed SV leads to several interesting findings. For example, volatility of the stochastic trend reflects the response to energy shocks in the 1970s, and that of the observation equation shows response to the monetary framework change in the 1980s. Lastly, we evaluate the improved forecasting ability of the model in terms of point, interval, and density forecast. (Joint with Siem Jan Koopman)

13:00
Bayesian Risk Evaluation in State Space Models using Importance Sampling
Agnieszka Borowska (VU University Amsterdam)

We present a novel approach to Bayesian estimation of two financial risk measures, Value at Risk and Expected Shortfall, in nonlinear, non-Gaussian state space models. In particular, we consider two specifications of the stochastic volatility model: with normal and Student’s t observation disturbances. The key insight behind our proposed importance sampling based approach is to accurately approximate the optimal importance density, which focuses on the augmented parameter subspace corresponding to high losses. By oversampling the extreme scenarios and punishing them by lower importance weights, we achieve a much higher precision in characterising the properties of the left tail. We report substantial gains in the accuracy of estimates in an empirical study on daily financial data. (Joint with Lennart F. Hoogerheide, Siem Jan Koopman)