Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified dynamic conditional correlation (DCC) model that accommodate external time-varying predictors for the within-person variance. The main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, 3 components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. These models allow for variance spillover effects from one time-series to another. We illustrate the pdBEKK- and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance. Overall, the pdBEKK seems to result in a more straightforward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect nonzero parameters. We provide an R-package bmgarch that facilitates the estimation of these types of models. (PsycInfo Database Record (c) 2020 APA, all rights reserved)

中文翻译：

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研究人体内变异性的新前沿：贝叶斯多元广义自回归条件异方差模型。

个体差异的研究越来越受到关注。迄今为止，心理学研究中讨论的大部分模型主要集中在平均结构的时间发展上。我们扩展了对人内残差变异性的看法，并提出了一种新的模型参数化，该模型参数化源自用于预测金融时间序列波动性的经典多元 GARCH 模型。我们提出了一种新的 pdBEKK 和一种改进的动态条件相关（DCC）模型，可以适应人内方差的外部时变预测因子。这项工作的主要目标是评估 MGARCH 模型在人内变异性研究中的潜在有用性。MGARCH 模型将人内方差至少分为 3 个组成部分：总体恒定且无条件的基线方差、以先前创新或随机冲击为条件引入方差的过程，以及控制先前创新的遗留效应的过程。条件方差，类似于 AR 模型。这些模型允许从一个时间序列到另一个时间序列的方差溢出效应。我们展示了两个人的 pdBEKK- 和 DCC-MGARCH，他们在连续 100 天的时间里对自己的每日积极和消极影响进行了评级。完整模型包含均值的多元 ARMA(1,1) 模型，并包括身体活动作为总体基线方差的调节因素。总体而言，pdBEKK 似乎会产生更直接的心理解释，但 DCC 通常更容易估计并且可以容纳更多同时时间序列。两种模型都需要相当大量的数据点来检测非零参数。我们提供了一个 R 包 bmgarch 来促进这些类型模型的估计。（PsycInfo 数据库记录 (c) 2020 APA，保留所有权利）