Hidden Markov Models for multivariate functional data
Friday 5th July 2019
Martino, A.; Guatteri, G.; Paganoni, A.M.
Hidden Markov Models (HMMs) are a very popular tool used in many fields to model time series data. In this paper we want to extend the usual HMM framework, where the observed objects are univariate or multivariate data, to the case of functional data. In particular, since we have a sequence of multivariate curves that evolves in time, we want to model the temporal structure of the system using HMMs. The functional observations, which rely on the statistical tools related to Functional Data Analysis (FDA), are linked to the state of the HMM according to a similarity function, which depends on some metric in Hilbert spaces. We first assess our results in a simulation setting and then we apply our model to a case study regarding the climate.