Flexible conditional density estimation for time series

Abstract

Predicting future values of a time series is often insufficient; understanding the complete uncertainty surrounding these predictions is crucial. This necessity has led to the use of conditional density estimators (CDEs). However, many existing CDEs for time series either impose rigid parametric assumptions or exhibit scalability issues when dealing with a high number of covariates. Concurrently, a substantial body of literature has developed around regression methods that offer single-point predictions. In this paper, we introduce a novel approach called FlexCodeTS, which harnesses the power of regression methods to provide enhanced estimates of conditional densities. Through extensive experiments, we demonstrate that FlexCodeTS exhibits strong performance across both real-world and simulated datasets. Furthermore, we establish convergence rates and illustrate how FlexCodeTS can attain rapid convergence by adopting a regression technique that best aligns with the underlying data structure. Finally, we show that FlexCodeTSprovides a straightforward yet accurate measure of variable importance assessment for time series data.