Forecasting Macroeconomic Time Series with Locally Adaptive Signal Extraction

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) which are contaminated by high frequency noise. The distributions of the innovations in both noise and signal are modeled robustly using mixtures of normals. The mean of the process and the variances of the signal and noise are allowed to shift either suddenly or gradually at unknown locations and unknown numbers 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 estimated by Bayesian methods and used to forecast a total of nine quarterly macroeconomic series from the US, Sweden and Australia. We observe that allowing for infrequent and large parameter shifts while imposing normal and homoskedastic errors often leads to erratic forecasts, but that the model typically forecasts well if it is made more robust by allowing for non-normal errors and time varying variances. Our main finding is that, for the nine series we analyze, specifications with infrequent and large shifts in error variances outperform both fixed parameter specifications and smooth, continuous shifts when it comes to interval coverage.

Keywords: Bayesian inference, Forecast evaluation, Regime switching, State space modeling, Dynamic mixture models