Modeling multivariate ordinal time series

Area of Science:

• Statistics
• Time Series Analysis
• Environmental Science

Background:

• Existing models for discrete-valued time series often lack multivariate capabilities.
• Modeling complex dependencies in ordinal time series, especially with spatial components, remains a challenge.

Purpose of the Study:

• To develop novel regression-type models for multivariate ordinal time series.
• To incorporate feedback terms and weighted averages for memory and inter-component dependence.
• To apply these models to analyze daily air quality data with spatial dimensions.

Main Methods:

• Regression-type models inspired by Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-type models.
• Incorporation of lagged observations and feedback terms for temporal dependence.
• Weighted averages based on a proximity matrix to model inter-component dependence.
• Binomial or multinomial marginal conditional distributions.
• Generalization to Vector Autoregressive Moving Average (VARMA)-type models.
• Use of copulas for explicit cross-dependence modeling.

Main Results:

• Development of flexible regression models for multivariate ordinal time series.
• Successful application to daily air quality data from three North China cities.
• Demonstration of capturing both temporal memory and spatial dependencies.

Conclusions:

• The proposed models provide a robust framework for analyzing multivariate ordinal time series with spatial structures.
• The approach is effective for environmental data, such as air quality, offering insights into complex dependencies.
• Future work can extend these models to other spatio-temporal ordinal datasets.