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混合矩阵值自回归模型AI 解读

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for instance, countries and economic indices. The matrix autoregressive (MAR) model provides a parsimonious approach for analyzing such data. However, the MAR model, being a linear model with parametric constraints, cannot capture the nonlinear…

基于稀疏张量分解的高维时间序列谱变点估计AI 解读

Abstract Multivariate time series may be subject to partial structural changes over certain frequency band, for instance, in neuroscience. We study the change point detection problem with high-dimensional time series, within the framework of frequency domain. The overarching goal is to locate all change points and delineate which series are activated by the change, over which frequencies. In practice, the number of activated series per change and frequency could span from a…

动态条件角相关AI 解读

We introduce the concept of angular correlation for estimating the instantaneous correlation matrix with a single multivariate realization. The proposed estimator is generally a positive definite correlation matrix and robust in that for bivariate normal data, the sample angular correlation is equally likely to be above or below the population correlation coefficient. We then generalize the dynamic conditional correlation (DCC) model to the dynamic conditional angular…

含外生变量的删失自回归模型的拟似然估计AI 解读

Maximum likelihood estimation of a censored autoregressive model with exogenous variables (CARX) requires computing the conditional likelihood of blocks of data of variable dimensions. As the random block dimension generally increases with the censoring rate, maximum likelihood estimation becomes quickly numerically intractable with increasing censoring. We introduce a new estimation approach using the complete-incomplete data framework with the complete data comprising the…

阈值扩散模型检验AI 解读

The threshold diffusion model assumes a piecewise linear drift term and a piecewise smooth diffusion term, which constitutes a rich model for analyzing nonlinear continuous-time processes. We consider the problem of testing for threshold nonlinearity in the drift term. We do this by developing a quasi-likelihood test derived under the working assumption of a constant diffusion term, which circumvents the problem of generally unknown functional form for the diffusion term.…

门限扩散过程的拟似然估计AI 解读

The threshold diffusion process, first introduced by Tong (1990), is a continuous-time process satisfying a stochastic differential equation with a piecewise linear drift term and a piecewise smooth diffusion term, e.g., a piecewise constant function or a piecewise power function. We consider the problem of estimating the (drift) parameters indexing the drift term of a threshold diffusion process with continuous-time observations. Maximum likelihood estimation of the drift…

通过正则化多分量回归重建源汇关系：北海鳕鱼幼体迁移应用AI 解读

The problem of reconstructing the source-sink dynamics arises in many biological systems. Our research is motivated by marine applications where newborns are passively dispersed by ocean currents from several potential spawning sources to settle in various nursery regions that collectively constitute the sink. The reconstruction of the sparse source-sink linkage pattern, that is, to identify which sources contribute to which regions in the sink, is a challenging task in…

具有稀疏奇异值分解的降秩随机回归AI 解读

Summary For a reduced rank multivariate stochastic regression model of rank r*, the regression coefficient matrix can be expressed as a sum of r* unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank…

不完整多项数据的贝叶斯推断：病原体多样性问题AI 解读

With recent advances in genetic analysis, it has become feasible to classify a pathogen into genetically distinct variants even though they apparently cause an infected subject similar symptoms. The availability of such data opens up the interesting problem of studying the spatiotemporal variation in the diversity of variants of a pathogen. Data on pathogen variants often suffer the problems of (i) low cell counts, (ii) incomplete classification due to laboratory problems…

关于 GARCH 模型不等式约束的一则说明AI 解读

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH( p , q ) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH( p , q ) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH( p , q ) models with p ≥ 3. In…

多元线性过程时间可逆性札记AI 解读

We derive some readily verifiable necessary and sufficient conditions for a multivariate non-Gaussian linear process to be time-reversible, under two sets of conditions on the contemporaneous dependence structure of the innovations. One set of conditions concerns the case of independent-component innovations, in which case a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients consist of essentially asymmetric columns with…