Estimating and Forecasting of Dynamic linear Gaussian State Space Models for Commodity Futures

Abstract

The Kalman filter is used to estimate the parameters and forecast the observations in a dynamic Nelson-Siegel model a linear Gaussian state space representation for futures contracts on the commodities oil, natural gas, cotton, copper, gold and sugar. The three-factor Nelson-Siegel model is compared to three-factor Nelson-Siegel model with seasonality terms to check for seasonality in the different commodities. Using Wilks’ Theorem we find that natural gas, cotton and sugar has an improved model fit by adding the seasonality term. The Kalman filter is shown to be a great model fit for most commodities except for natural gas and cotton, there needs to be further studies to find out why the parameter estimates for these two commodities are not as expected. For the forecasting of the observations, the Kalman filter performs very well with both three-factor model Nelson-Siegel and the three-factor Nelson-Siegel with a seasonality term. It was not possible to forecast the observations for sugar for the three-factor Nelson-Siegel model because the variance matrix of the prediction error is singular. Thus it does not have an inverse which is crucial for the Kalman filter. This should also be studied further to figure out why this happens for the sugar data.