On Autoregressive Measurement Errors in a Two-Factor Model

In this study, we consider the extended two-factor model, originally introduced by Schwartz and Smith (2000), which has been commonly used for the pricing of commodity derivatives. In this model setup, we assume the latent short and long-term factors represent correlated mean-reverting processes. We develop a Kalman filter for jointly estimating the state variables and unknown parameters. In the measurement equation system, we assume that the residuals are serially correlated and inter-dependent. We derive the Kalman filter under the assumption that these residuals are AR(p) processes. Then the Kalman filter is used for obtaining the marginalised likelihood estimators for the state variables and the model parameters. We provide an extensive, reproducible simulation study for examining the convergence of the estimators in our proposed model. The MATLAB code for this study is available via the link to GitHub ( https://github.com/Junee1992/EUA-Futures-Pricing/tree/main/MATRIX ).