Kohonen Maps and TS Algorithms
Authors: Boyer-Xambeu Marie-Thérèse , Deleplace Ghislain , Gaubert Patrice , Gillard Lucien 
Published: May 2011

In the analysis of a temporal process, Kohonen maps may be used together with time-series (TS) algorithms. Previous research aimed at combining Kohonen algorithms and Markov switching models in order to suggest a periodization of the international bimetallism in the 19th century (Boyer-Xambeu, Deleplace, Gaubert, Gillard and Olteanu, 2006). This research was based on an economic study of the international monetary system ruling at this time in Europe, which combined three monetary zones: a gold-standard one, centred in London, a bimetallic one, centred in Paris, and a silver-standard one, centred in Hamburg (Boyer- Xambeu, Deleplace and Gillard, 2006). The three major financial centres of that system (London, Paris, and Hamburg, hence the label LPH used hereafter) were linked through arbitrage operations between markets for gold and silver and markets for foreign exchange located in those centres. Since two metals, gold and silver, acted as monetary standards in that system, it worked as an international bimetallism. Its growing integration during half a century (from 1821 to 1873) was reflected in the convergence of the observed levels of the relative price of gold to silver in London, Paris, and Hamburg. However, this integration process was subject to various changes, which can be understood as exogenous shocks disturbing that process. One such shock is vastly documented in the literature: the discovery of new gold mines in the United States and Australia, which led to a sudden decline in 1850 of the gold-silver price over all the markets in the world. This decline was not of the same magnitude everywhere, and therefore the spread between the London, Paris, and Hamburg gold-silver prices increased, stopping for a time the integration process of the system. This is what we will call a breaking in that process. The present paper aims at locating the major breakings occurring during the period of international bimetallism; a historical study could link them to special events, which operated as exogenous shocks on that system. The indicator of integration used is the spread between the highest and the lowest among the London, Paris, and Hamburg gold-silver prices. Three algorithms are combined to study this integration: a periodization obtained with the SOM algorithm is confronted to the estimation of a two-regime Markov switching model, in order to give an interpretation of the changes of regime; at the same time changepoints are identified over the whole period providing a more precise interpretation of these varying types of regulation. Section 2 summarizes the results obtained with the SOM algorithm to differentiate the sub-periods obtained using the whole available data. Section 3 presents the kind of model used and the results of its estimation using the new indicator, the spread computed at each period of quotation between the three relative prices of gold in silver. The sub-periods are confronted to the two regimes obtained and some evidence of a relation between the regime and the volatility of the spread is presented. Section 4 presents the technique used to identify change-points in the temporal process and some strong results of breaks in mean and in variance of the spread are obtained. They are interpreted in terms of monetary history as, for some of them, they are quite new in the literature of this domain. Some further directions of research are indicated in conclusion.