Merlo Luca, Maruotti Antonello, Petrella Lea, Punzo Antonio
Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy.
Department of Mathematics, University of Bergen, Bergen, Norway.
Stat Comput. 2022;32(4):61. doi: 10.1007/s11222-022-10130-1. Epub 2022 Aug 9.
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.
The online version contains supplementary material available at 10.1007/s11222-022-10130-1.
本文开发了一种分位数隐藏半马尔可夫回归方法，用于联合估计多个分位数，以分析多元时间序列。该方法基于多元非对称拉普拉斯（MAL）分布，它能够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，并纳入结果之间的相关结构。通过引入依赖于状态的参数来对观测值之间未观察到的序列异质性进行建模，这些参数根据潜在的有限状态半马尔可夫链演化。利用MAL的层次表示，基于所有模型参数的闭式更新，使用高效的期望最大化算法进行推断，而无需对状态的停留分布进行参数假设。通过模拟研究和对意大利一个小城市空气污染物浓度的实证分析，对所提出方法的有效性进行了分析。
在线版本包含可在10.1007/s11222-022-10130-1获取的补充材料。
