Investigating the Relationship between Gold and Silver Prices

Abstract

This paper analyses the long-run relationship between gold and silver prices. The three main questions addressed are: the influence of a large bubble from 1979:9 to 1980:3 on the cointegration relationship, the extent to which by including error-correction terms in a non-linear way we can beat the random walk model out-of-sample, and the existence of a strong simultaneous relationship between the rates of return of gold and silver. Different efficient single-equation estimation techniques are required for each of the three questions and this is explained within a simple bivariate cointegrating system. With monthly data from 1971 to 1990, it is found that cointegration could have occurred during some periods and especially during the bubble and post-bubble periods. However, dummy variables for the intercept of the long-run relationships are needed during the full sample. For the price of gold the non-linear models perform better than the random walk in-sample and out-of-sample. In-sample non-linear models for the price of silver perform better than the random walk but this predictive capacity is lost out-of-sample, mainly due to the structural change that occurs (reduction) in the variance of the out-of-sample models. The in-sample and out-of-sample predictive capacity of the non-linear models is reduced when the variables are in logs. Clear and strong evidence is found for a simultaneous relationship between the rates of return of gold and silver. In the three type of relationships that we have analysed between the prices of gold and silver, the dependence is less out-of-sample, possibly meaning that the two markets are becoming separated.