Parameter estimation in commodity markets: A filtering approach

The application of Kalman filtering methods and maximum likelihood parameter estimation to models of commodity prices and futures prices has been considered by several authors. The usual method of finding the maximum likelihood parameter estimates (MLEs) is to numerically maximize the likelihood function. We present, as an alternative to numerical maximization of the likelihood, a filter-based implementation of the expectation maximization (EM) algorithm that can be used to find the MLEs. Finite-dimensional filters are derived that allow the MLEs of a commodity price model to be estimated from futures price data using the EM algorithm without calculating Kalman smoother estimates.