Markov and the Duchy of Savoy: segmenting a century with regime-switching models

Abstract

Studying time is at the core of the historian’s research. For the statistician, time is usually a supplementary parameter or a supplementary variable which the models he develops have to take into account. This manuscript is the result of a collaboration between historians and mathematicians, having time as the starting point of a joint work. We are interested in studying a specific time-series, reporting the production of law related to military logistics of the Duchy of Savoy, during the XVIth and XVIIth centuries. The expected outcome is a better understanding of the temporality and of the functioning of the state. Two models based on hidden Markov chains and taking into account the specificities of the data are introduced. They are then estimated on the historical data and provide interesting results, which either confirm the existing historical hypothesis on the subject or bring new insights on the studied period.