A Stochastic Parameter Regression Approach for Time-Varying Relationship between Gold and Silver Prices

In this thesis, we studied the gold and silver relationship using stochastic-parameter regression models. We formulated their time-varying relationship as a state-space model and used the Kalman filter algorithm to estimate the stochastic regression parameters for gold and silver prices. The data set used in this thesis covers 31 years using the London fix prices between January 1969 and December 2000. The start date was selected as the first full year silver prices were included in the London fix prices. Our stochastic parameter regression model explained well the time-varying relationship between gold and silver prices. As a special case of the stochastic parameter regression model, we also fitted the random walk, the random walk with drift model and random coefficient model. The random walk with drift model appeared to have the closest fit with 12-month forecast errors minimal among those four models considered in this thesis