Forecasting crude oil prices with shrinkage methods: Can nonconvex penalty and Huber loss help?

Abstract

This study explores different specifications of shrinkage methods to forecast crude oil prices, and examines the forecasting performances from both statistical and economic perspectives. In addition to the widely-used LASSO, elastic net and ridge, we consider two popular nonvonvex penalties and Huber loss function in penalized regressions. The results indicate that, first, the out-of-sample performance of different shrinkage methods depend on the forecasting horizons. The shrinkage forecasts with nonvonvex penalty and Huber loss outperform the benchmark and competing models within one year; the popular shrinkage methods of LASSO, elastic net and ridge perform relatively well more than one year, whereas, no better than the no-change benchmark. Second, in terms of net-of-transaction-costs portfolio performance for different horizon forecasts, the portfolios based on nonconvex penalties achieve the majority of the largest economic gains, followed by the popular version of LASSO and elastic net. When crude oil prices decline sharply, shrinkage forecasts outperform the benchmark forecast remarkably, both in statistical and economic perspectives. Finally, extended analysis indicates that imposing statistical and economic constraints on coefficient estimation of shrinkage models can further improve forecasting performance in most cases.