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计数随机场的 INARMA 模型综述AI 解读

The thinning-based integer-valued autoregressive moving-average (INARMA) models are popular for count time series. Recently, types of INARMA models have also been developed for count random fields, i.e., for spatial count data located on a regular two-dimensional grid. This article provides a comprehensive survey on existing INARMA random fields, covering approaches with different thinning operators, first- and higher-order models, as well as unilateral and multilateral…

时间序列中的序型转换与代数距离：随机性质及非参数依赖检验AI 解读

The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. This research goes one step further and considers the transcripts being computed from successive OPs in the time series. Transcripts constitute a kind of ``difference'' between successive OPs and thus naturally relate to two algebraic distances between OPs, the Cayley and Kendall edit distances. The original time…

秩相关系数的渐近推断AI 解读

Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for…

二维与三维随机场空间依赖的非参数检验AI 解读

We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert curves. We then apply ordinal pattern-based tests for serial dependence to this series. Because Hilbert curves preserve spatial locality, spatial dependence in the original field manifests as serial dependence in the transformed sequence.…

计数时间序列的 Tobit 模型AI 解读

Several models for count time series have been developed during the last decades, often inspired by traditional autoregressive moving average (ARMA) models for real-valued time series, including integer-valued ARMA (INARMA) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. Both INARMA and INGARCH models exhibit an ARMA-like autocorrelation function (ACF). To achieve negative ACF values within the class of INGARCH models, log and…

基于保均值随机舍入的整数值 ARMA 模型AI 解读

In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the use of the rounding operator is very natural. Because of the discontinuity of the rounding operator, the formulation of the corresponding model identifiability conditions and the computation of parameter estimators need special attention.…

计数时间序列的条件均值乘法算子模型AI 解读

Multiplicative error models (MEMs) are commonly used for real-valued time series, but they cannot be applied to discrete-valued count time series as the involved multiplication would not preserve the integer nature of the data. Thus, the concept of a multiplicative operator for counts is proposed (as well as several specific instances thereof), which are then used to develop a kind of MEMs for count time series (CMEMs). If equipped with a linear conditional mean, the…