Dynamic cointegration and Relevant Vector Machine: the relationship between gold and silver Margherita Gerolimetto 1 , Isabella Procidano 2 , Silio Rigatti Luchini 1 1 Dipartimento di Scienze Statistiche, Universit` a di Padova. e-mail: gerolime@stat.unipd.it, rigatti@stat.unipd.it 2 Dipartimento di Statistica, Universit` a Ca’Foscari Venezia. e-mail: isabella@unive.it Abstract: We use the Relevant Vector Machine, a technique of supervised learning introduced by Tipping (2001), to conduct a dynamic cointegration analysis on the series of the price of gold and silver over the period 1971-2004. Unlike the results of traditional cointegration analysis, this study reveals that there is a dynamic long run relationship over the whole period. Keywords: Dynamic cointegration, Relevance Vector Machine 1. Introduction In this paper we study the dynamic relationship between gold and silver (fig.1) over the period 1971-2004, that covers a very extensive range of economic conditions, political change in major producers and increased sophistication in asset markets generally. Gold and silver have been actively traded for thousands of years and remain important and closely observed markets. They have historically been seen as close substitute for one another and this would suggest that the two markets share the same dynamics. However there are also economic fundamentals that may drive the prices of gold and silver apart. While both are used extensively in industrial processes, there are significant differences between these uses. Therefore it seems that while they share a similar set of drivers they each also have important unique macroeconomic drivers (see for example Figure 1: Gold and silver time series (respectively in black and red) Time 0 100 200 300 400 0 10 20 30