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Quantile hidden semi-Markov models for multivariate time series.

Luca Merlo1, Antonello Maruotti2,3, Lea Petrella4

  • 1Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy.

Statistics and Computing
|August 15, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new quantile regression model for multivariate time series, using the Multivariate Asymmetric Laplace distribution to capture complex data correlations. The method effectively analyzes unobserved heterogeneity and estimates multiple quantiles simultaneously.

Keywords:
EM algorithmLatent processMaximum likelihoodMultivariate asymmetric Laplace distributionQuantile regressionSojourn distribution

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Multivariate time series analysis often requires modeling complex dependencies and unobserved heterogeneity.
  • Existing methods may struggle to simultaneously estimate multiple quantiles while accounting for correlation structures.

Purpose of the Study:

  • To develop a novel quantile regression framework for multivariate time series.
  • To jointly estimate multiple quantiles of conditional distributions, incorporating outcome correlations.
  • To model unobserved serial heterogeneity using a semi-Markov process.

Main Methods:

  • Development of a quantile hidden semi-Markov regression model.
  • Utilizing the Multivariate Asymmetric Laplace (MAL) distribution for simultaneous quantile estimation.
  • Employing an Expectation-Maximization algorithm for efficient inference without state distribution assumptions.

Main Results:

  • The proposed MAL-based model successfully estimates multiple quantiles for multivariate time series.
  • The hidden semi-Markov component effectively captures unobserved serial heterogeneity.
  • Simulation studies and real-world air pollution data analysis validate the methodology's performance.

Conclusions:

  • The developed quantile hidden semi-Markov regression offers a robust approach for analyzing complex multivariate time series.
  • The method provides a flexible tool for understanding conditional dependencies and heterogeneity in data.
  • Empirical application demonstrates its utility in environmental science for pollutant analysis.