No. 234 Forecasting Macroeconomic Time Series With Locally Adaptive Signal Extraction

by Paolo Giordani and Mattias Villani

October 2009

Abstract

We introduce a non-Gaussian dynamic mixture model for macroeconomic forecasting. The Locally Adaptive Signal Extraction and Regression (LASER) model is designed to capture relatively persistent AR processes (signal) contaminated by high frequency noise. The distribution of the innovations in both noise and signal is robustly modeled using mixtures of normals. The mean of the process and the variances of the signal and noise are allowed to shift suddenly or gradually at unknown locations and number of times. The model is then capable of capturing movements in the mean and conditional variance of a series as well as in the signal-to-noise ratio. Four versions of the model are used to forecast six quarterly US and Swedish macroeconomic series. We conclude that (i) allowing for infrequent and large shifts in mean while imposing normal iid errors often leads to erratic forecasts, (ii) such shifts/breaks versions of the model can forecast well if robustified by allowing for non-normal errors and time varying variances, (iii) infrequent and large shifts in error variances outperform smooth and continuous shifts substantially when it comes to interval coverage, (iv) for point forecasts, robust time varying specifications improve slightly upon fixed parameter specifications on average, but the relative performances can differ sizably in various sub-samples, v) for interval forecasts, robust versions that allow for infrequent shifts in variances perform substantially and consistently better than time invariant specifications.

Keywords

Bayesian inferene, Foreast evaluation, Regime swithing, State-space modeling, Dynamic Mixture models.