Catching the curl: Wavelet thresholding improves forward curve modelling

Abstract

Modelling futures term structures (price forward curves) is essential for commodity-related investments, portfolios, risk management, and capital budgeting decisions. This paper uses a novel strategy, wavelet thresholding, to de-noise futures price data prior to estimation in a state-space framework in order to improve model fit and prediction. Rather than de-noise the raw data, this method de-noises only wavelet coefficients linked to specific timescales, minimizing the amount of information that is accidentally removed. Our findings are that, for the first five futures maturities in our sample data, in-sample (tracking) and 5-day-ahead out-of-sample (forecasting) Root Mean Squared Errors (RMSEs) are smaller both (i) when we increase the number of factors from one to four, and (ii) when we de-noise the data using wavelet thresholding. The improvement due to wavelet thresholding is often greater than the improvement from adding one more factor to the model, which is important because going beyond four factors does not improve model fit. Wavelet-based de-noising thus has the potential to improve considerably the estimation of various economic time series models, helping practitioners and policymakers with better forecasting and risk management.