  We propose methods to improve the forecasts from generalized autoregressive
score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their
parameters using decision trees and random forests. These methods avoid the
curse of dimensionality faced by kernel-based approaches, and allow one to draw
on information from multiple state variables simultaneously. We apply the new
models to four distinct empirical analyses, and in all applications the
proposed new methods significantly outperform the baseline GAS model. In our
applications to stock return volatility and density prediction, the optimal GAS
tree model reveals a leverage effect and a variance risk premium effect. Our
study of stock-bond dependence finds evidence of a flight-to-quality effect in
the optimal GAS forest forecasts, while our analysis of high-frequency trade
durations uncovers a volume-volatility effect.
