Abstract:
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The applicability of Hidden Markov Models in explaining time series observations in general and point processes in particular is widely accepted in statistical literature: Zucchini and MacDonald (2009) show for instance, how a state dependent Poisson choice can adequately model an overdispersed earthquake count series. In the context of rare event modeling, a smoothing statistic termed Empirical Recurrence Rates (ERR) has been proposed by Ho (2008) and evidence of its superior applicability, both in the presence of predominantly seasonal or purely random shocks can be gathered from Tan, Bhaduri and Ho (2014), Amei, Fu and Ho (2012) and Ho and Bhaduri (2015). Empirical Recurrence Rates Ratio (ERRR), a generalized version of ERR, one that is capable of handling two related processes simultaneously, is now introduced and through the use of data sets emerging from volcanology and oceanography, we will explore a novel technique that lets one interpret ERRR as the hidden chain that generates one of the two related series. The method is bereft of computational difficulties and lends further glory to the ERRR statistic.
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