Analytic Standard Errors for Latent Gaussian Discrete-Valued Multivariate Time Series

2026-07-02

AI Summary

This study addresses the lack of general-purpose modeling and inference frameworks for discrete multivariate time series—such as count, binary, or ordinal categorical data—in fields like psychology and education. The authors propose a copula-based multivariate model grounded in latent-variable Gaussian processes, where discrete observations are generated via deterministic transformations. For the first time, they derive analytic standard errors for the latent Gaussian dynamic parameters within this class of models. Theoretical analysis establishes the asymptotic normality of the joint estimators of the latent processes and marginal distribution parameters. Simulation studies and empirical applications demonstrate that the proposed standard errors perform well in finite samples, enabling reliable statistical inference about the underlying latent Gaussian dynamic structure.

Abstract

Unlike their continuous-valued counterparts, there are no universally preferred methodologies for modeling discrete-valued time series. This is especially problematic in fields such as psychology and education, where repeated-measures data often take the form of count, dichotomous, and ordered categorical variables. To address the need for flexible methodology for analyzing discrete-valued time series data, a copula-style multivariate model defined through deterministic functions of a latent stationary Gaussian vector series has been proposed. This model has several promising features, including the ability to accommodate a wide variety of marginal distributions within the same model while also allowing for the most flexible autocorrelation structure possible. We extend this framework by deriving analytic standard errors to facilitate inference on the latent Gaussian dynamics. In so doing, we establish the joint asymptotic normality of estimators of the parameters governing the latent Gaussian series and the marginal distributions. The performance of these analytic standard errors is examined in a simulation study and an empirical application.

Problem

• discrete-valued time series
• latent Gaussian process
• analytic standard errors
• copula model
• multivariate time series

Innovation

• analytic standard errors
• latent Gaussian process
• discrete-valued time series
• copula model
• asymptotic normality