Trends and cycles in historical gold and silver prices

Abstract

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 parameter 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.

The financial economics of white precious metals — A survey

“…In another paper looking at long memory behaviour of the price of silver, Gil-Alana et al (2015a) uses annual silver prices between 1792 and 2013 and finds that real silver prices are mean reverting; indicating that no long-run memory behaviour exists between silver and inflation rate. This indicates that exogenous shocks will affect real silver prices less intensely than gold prices.…”

Persistence in trends and cycles of gold and silver prices: Evidence from historical data

“…However, Gil-Alana et al [39] use monthly data from 1972:1 to 2013:13 and fractional integration techniques, and they find that real gold price is non-mean reverting while real silver price is mean reverting, concluding that in the event of exogenous shocks, the effects will be permanent in gold prices, although temporary in silver prices. Gil-Alana et al [40] use annual data spanning from 1833 to 2013 for gold and 1792 to 2013 for silver and they find fractional order of integration above 1 in case of gold and below 1 for silver, concluding again that gold prices exhibit a non mean-reverting behavior, while they find mean reversion in silver prices. Winkelried [42] reexamines the Prebisch-Singer hypothesis testing for unit roots in commodity prices and find evidence against nonstationarity in at least 20 out of 24 cases, including gold and silver prices.…”

“…Additionally, if gold and silver were perfect inflation hedges, the real price of gold and silver would be stationary [10]. However, despite the vast literature directed to estimate the integration order or persistence of these variables [10,16,[36][37][38][39][40][41][42] the results are not yet conclusive (see, for example, [41], for a recent survey of the literature). For example, Ghoshray [16] reexamines the Prebisch-Singer hypothesis, employing the unit root tests proposed by Lee and Strazicich [43,44] with one and two structural breaks and the results suggest the existence of unit roots in many commodity prices, including gold and silver.…”

“…Second, in a fractional integration framework, we use a model that incorporates simultaneously two fractional differencing parameters, one at the long run or zero frequency and another one at a cyclical frequency. Although a rather similar methodology has already been used in [40], in this paper we use a longer time period that allows us to more precisely estimate the two fractional differencing parameters and of the periods for the length of the cycles. In fact, in [40] the time period goes from 1833 (gold) and 1792 (silver) till 2013 while in this work the period examined is 1257-2016 for gold and 1687-2016 for silver.…”

“…Although a rather similar methodology has already been used in [40], in this paper we use a longer time period that allows us to more precisely estimate the two fractional differencing parameters and of the periods for the length of the cycles. In fact, in [40] the time period goes from 1833 (gold) and 1792 (silver) till 2013 while in this work the period examined is 1257-2016 for gold and 1687-2016 for silver. Moreover, we provide in this paper a more exhaustive analysis of the cyclical periodicity in the two series.…”