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.

本文开发了一种分位数隐藏半马尔可夫回归来联合估计多个分位数，用于分析多元时间序列。该方法基于多元非对称拉普拉斯 (MAL) 分布，该分布允许同时对多元响应的所有单变量条件分布的分位数进行建模，并结合结果之间的相关结构。通过引入根据潜在有限状态半马尔可夫链演变的依赖于状态的参数来模拟观察中未观察到的序列异质性。利用 MAL 的分层表示，使用有效的期望最大化算法进行推理，该算法基于所有模型参数的封闭形式更新，没有关于状态的逗留分布的参数假设。