Trends and cycles in historical gold and silver prices

The study proposes an alternative modelling specification for the real prices of gold and silver that allows the long run trend and cyclical behaviour to be modelled simultaneously by incorporating two differencing parameters in a fractional integration framework. However, we also consider the separate cases of a standard I(d) process, with a pole or singularity at the zero frequency and a cyclical I(d) model that incorporates a single pole in the spectrum at a non-zero frequency. We use annual data spanning from 1833 to 2013 for gold and 1792 to 2013 for silver. Based on the more flexible model that permits a pole at both zero (trend) and non-zero (cycle) frequencies, we find that in general the estimates associated to the long run or zero frequency appear to be above 1 in case of gold and below 1 for silver, while the order of integration associated with the cyclical frequency is slightly above 0 in the majority of the cases in the two series. Further, higher orders of integration are associated to the long run component compared with the cyclical one. The implications of these findings are highlighted.