A comparison of statistical models for short categorical or ordinal time series with applications in ecology

Causal coupling inference from multivariate time series based on ordinal partition transition networks

Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupl…

Strong mixing properties of discrete-valued time series with exogenous covariates

We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a mixing condition for the response. Using a coupling method, we first derive mixing conditions for some Markov chains in random environments, which gives a first result for some autoregressive categorical processes with strictly exogenous regressors. Our result is then extended to some infinite memory categorical processes. In the second part of the paper, we stud…

Simultaneous Monitoring of a Large Number of Heterogeneous Categorical Data Streams

This article proposes a powerful scheme to monitor a large number of categorical data streams with heterogeneous parameters or nature. The data streams considered may be either nominal with a number of attribute levels or ordinal with some natural order among their attribute levels, such as good, marginal, and bad. For an ordinal data stream, it is assumed that there is a corresponding latent continuous data stream determining it. Furthermore, different data streams may have different number of attribute levels and different values of level probabilities. Due to high dimensionality, traditiona…

利用傅里叶级数进行多季节性分类时间序列预测及其在加尔各答AQI数据中的应用

Forecasting of Multiple Seasonal Categorical Time Series Using Fourier Series with Application to AQI Data of Kolkata

本文提出利用傅里叶级数和指示函数建模多季节性分类时间序列，通过加尔各答AQI数据验证，提升了预测精度。

一种识别时空有序分类数据中变点的贝叶斯方法：在COVID-19数据中的应用

A Bayesian approach to identify changepoints in spatio-temporal ordered categorical data: An application to COVID-19 data

本研究针对时空有序分类数据变点识别研究不足的问题，提出结合可分离高斯时空过程的贝叶斯时空模型，可检测均值与协方差结构变化，在纽约州COVID-19数据中识别出三个对应疫情波次的变点。

基于散度方法的贝叶斯有序响应模型对异常值的稳健性

Robustness of Bayesian ordinal response model against outliers via divergence approach

针对有序响应模型受异常值影响的问题，提出基于密度幂散度和γ-散度的一般后验方法，实现稳健贝叶斯推断，并通过实验验证其优于普通贝叶斯方法。