Quantile hidden semi-Markov models for multivariate time series

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. Supplementary Information The online version contains supplementary material available at 10.1007/s11222-022-10130-1.

Expectile hidden Markov regression models for analyzing cryptocurrency returns

“…In this paper, we set this threshold criterion equal to 10 −4 . Following Maruotti et al (2021) and Merlo et al (2022), for fixed τ and K we initialize the EM algorithm by providing the initial states partition, {S…”

“…Quantile regression methods have also been generalized to account for serial heterogeneity. For example, Liu (2016) consider a quantile autoregression in which the parameters are subject to regime shifts determined by the outcome of a latent, discrete-state Markov process, while Adam et al (2019) propose a model-based clustering approach where groups are inferred from conditional quantiles; see also Ye et al (2016), Maruotti et al (2021) and Merlo et al (2022) for other applications of regime-switching models to financial and environmental time series. In longitudinal data, Farcomeni (2012) and Marino et al (2018) introduce linear quantile regression models where time-dependent unobserved heterogeneity is described through dynamic coefficients that evolve according to a homogeneous hidden Markov chain.…”