This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states’ sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city.

Quantile hidden semi-Markov models for multivariate time series / Merlo, Luca; Maruotti, Antonello; Petrella, Lea; Punzo, Antonio. - In: STATISTICS AND COMPUTING. - ISSN 1573-1375. - 32:(2022). [10.1007/s11222-022-10130-1]

Quantile hidden semi-Markov models for multivariate time series

Lea Petrella;
2022

Abstract

This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states’ sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city.
2022
EM algorithm; Latent process; Maximum likelihood; Multivariate asymmetric Laplace distribution; Quantile regression ; Sojourn distribution
01 Pubblicazione su rivista::01a Articolo in rivista
Quantile hidden semi-Markov models for multivariate time series / Merlo, Luca; Maruotti, Antonello; Petrella, Lea; Punzo, Antonio. - In: STATISTICS AND COMPUTING. - ISSN 1573-1375. - 32:(2022). [10.1007/s11222-022-10130-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1682182
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