Aastha M. Sathe, N. S. Upadhye
In this article, we propose the fractional lower order covariance method (FLOC) for estimating the parameters of vector autoregressive process (VAR) of order $p$, $p\geq 1$ with symmetric stable noise. Further, we show the efficiency, accuracy, and simplicity of our methods through Monte-Carlo simulation.
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We investigate shrinkage priors on power spectral densities for complex-valued circular-symmetric autoregressive processes. We construct shrinkage predictive power spectral densities, which asymptotically dominate (i) the Bayesian predictive power spectral density based on the Jeffreys prior and (ii) the estimative power spectral density with the maximal likelihood estimator, where the Kullback-Leibler divergence from the true power spectral density to a predictive power spectral density is adopted as a risk. Furthermore, we propose general constructions of objective priors for Kähler paramete…
COPAR - Multivariate time series modeling using the COPula AutoRegressive model
多元时间序列分析是金融、经济等领域的一个常见问题。用于此目的的经典工具是向量自回归模型。然而，这些仅限于线性和对称依赖的建模。我们提出了一种新的基于Copula的模型，它允许非线性和非对称建模的串行以及系列之间的依赖关系。该模型充分利用了仅由二元连接函数建立的藤连接函数的灵活性。我们描述了新模型的统计推断技术，并在三个相关的应用中证明了它的实用性：我们分析了宏观经济指标的时间序列，电力负荷需求和债券投资组合的回报。
We introduce a new class of autoregressive models for spherical time series, where the dimension of the spheres on which the observations of the time series are situated may be finite-dimensional or infinite-dimensional as in the case of a general Hilbert sphere. Spherical time series arise in various settings. We focus here on distributional and compositional time series. Applying a square root transformation to the densities of the observations of a distributional time series maps the distributional observations to the Hilbert sphere, equipped with the Fisher-Rao metric. Likewise, applying a…
Quantile autoregressive moving average models for ratio-based bounded time series
提出分位数单位对数对称自回归移动平均（QULS-ARMA）模型，通过分位数重新参数化将自回归和移动平均动态嵌入条件分位数，用于处理(0,1)区间上的比率数据。
Testing second order dynamics for autoregressive processes in presence of time-varying variance
研究了自回归单变量时间序列的波动率建模问题。基准方法是Engle（1982）的平稳ARCH模型。受真实数据证据的启发，最近引入了具有非常数无条件方差和非线性效应的过程。我们考虑到这种可能的非平稳性，并提出了简单的测试程序的非平稳效应。自适应McLeod和李的portmanteau和ARCH-LM测试检查二阶动力学。这些检验的标准版本，通常由从业者使用，假设恒定的无条件方差。我们用时变无条件方差证明了这些标准检验的失败。通过模拟和实际数据说明了理论结果。
Parametric quantile autoregressive conditional duration models with application to intraday value-at-risk
本文提出一种基于对数对称分布分位数重参数化的新ACD模型，可建模不同百分位数的条件久期，并通过最大似然估计、残差诊断和蒙特卡洛模拟验证，最终应用于价格久期数据以推导半参数日内风险价值模型。
Regularized Estimation of High-Dimensional Matrix-Variate Autoregressive Models
本文针对高维矩阵变量时间序列，提出了带状和LASSO稀疏两种正则化估计方法以降低双线性自回归模型的参数维度，推导了渐近性质，并通过模拟与真实数据验证了其优越的预测性能。
A Spatial Autoregressive Graphical Model with Applications in Intercropping
本文融合多元空间自回归模型与高斯图模型，提出可刻画不同类别相邻位置间非对称空间效应的 SAGM，并通过贝叶斯模拟和间作数据验证其应用价值。
This article introduces the GNAR package, which fits, predicts, and simulates from a powerful new class of generalised network autoregressive processes. Such processes consist of a multivariate time series along with a real, or inferred, network that provides information about inter-variable relationships. The GNAR model relates values of a time series for a given variable and time to earlier values of the same variable and of neighbouring variables, with inclusion controlled by the network structure. The GNAR package is designed to fit this new model, while working with standard ts objects an…
In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real world financial data. It is shown that NIG autoregressive model fit very well the considered financial data and hence could be useful in modeling of various real life time-series data.
Autoregressive Models for Variance Matrices: Stationary Inverse Wishart Processes
我们介绍和探索一类新的平稳时间序列模型的方差矩阵的基础上建设性的定义，利用逆Wishart分布理论。探索的模型的主要类别是一类新的平稳，一阶自回归（AR）过程的锥半正定矩阵。多变量“波动”过程的理论和这些新模型的结构方面进行了详细描述和举例说明。然后，我们通过基于贝叶斯模拟的计算开发模型拟合方法，创建一个依赖于高效创新采样器的自定义过滤方法。然后提供了一个例子，在分析的多变量脑电图（EEG）时间序列在神经学研究。最后，我们讨论了高阶AR模型的潜在进一步发展以及与先前方法的一些联系。
Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. This paper proposes a computationally efficient multivariate Bayesian Circular La…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of t…
The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector AutoRegressive (VAR) model. We narrow this gap with a new optimization-based approach to VARMA identification built upon the principle of parsimony. Among all equivalent data-generating models, we use convex optimization to seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity,…
Bayesian spatiotemporal conditional autoregressive model for local temporal variations
本文提出一种基于条件自回归模型的贝叶斯时空建模框架，通过结合空间邻近和时间相邻信息实现局部自适应时间平滑，并开发吉布斯采样算法，数值实验验证其能有效适应局部时间变化。
This paper introduces a fully Bayesian analysis of mixture autoregressive models with Student t components. With the capacity of capturing the behaviour in the tails of the distribution, the Student t MAR model provides a more flexible modelling framework than its Gaussian counterpart, leading to fitted models with fewer parameters and of easier interpretation. The degrees of freedom are also treated as random variables, and hence are included in the estimation process.
This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model specification. The proposed tests have very respectable power in comparison to the optimal tests for Markov-switching parameters of Carrasco…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial, overlapping, and confusing. Most models focus on one property of the data, while much can be gained by combining the strength of various models and their sources of heterogeneity. We present a structured overview of the literature on autoregressive models with random coefficients. We describe hierarchy and analogies among models, and for each we systematica…
In many applications, data are observed as matrices with temporal dependence. Matrix-variate time series modeling is a new branch of econometrics. Although stylized facts in several fields, the existing models do not account for regime switches in the dynamics of matrices that are not abrupt. In this paper, we extend linear matrix-variate autoregressive models by introducing a regime-switching model capable of accounting for smooth changes, the matrix smooth transition autoregressive model. We present the estimation processes with the asymptotic properties demonstrated with simulated and real …
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood function of these models has similar format to their VAR counterparts. Maximum likelihood estimate can be done by optimizing with gradient over the moving average parameters. These models are inexpensive generalizations of Vector Autoregressive models. We discuss a relationship b…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties…
A self-supervised learning approach for denoising autoregressive models with additive noise: finite and infinite variance cases
本文提出了一种自监督学习方法，用于去噪具有加性噪声的自回归模型，特别针对有限和无限方差情况，通过实验验证其在强噪声下的有效性。
CEDAR: Causal Edge Discovery for Autoregressive Processes
研究稀疏自回归时间序列滞后因果边发现问题，提出CEDAR方法，通过AR(1)残差化等筛选候选滞后，经条件独立性测试、MCI修剪等确定因果边，在数据稀缺等情况效果好，兼具边级可解释性。
Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer product of the size variable. The inner product equation is actually a spatial autocorrelation model. However, the theoretical basis of the inner product equation for Moran's index is not clear. This paper is devoted to revealing the antecedents and consequences of the inner product equation of Moran's index. The method is mathematical derivation and empirical …
Multivariate integer-valued autoregressive models applied to earthquake counts
在保险业、金融业、流行病学等各种情况下，需要表示事件发生次数的联合演变。在本文中，我们提出了一个多变量整数值自回归（MINAR）模型，推导了它的性质，并将该模型应用于地震发生在不同的构造板块对。该模型是Pedelis & Karlis（2011）的扩展，其中考虑了交叉自相关（地震背景下的空间传染）。我们拟合了各种双变量计数模型，发现对于许多相邻的构造板块，空间传染在两个方向上都是显着的。此外，忽略交叉自相关可能会低估短期内发生大量事件的可能性。我们的总体研究结果似乎进一步证实了Parsons & Velasco（2001）。
Vector AutoRegressive Moving Average Models: A Review
本文系统综述了VARMA模型在识别、估计、诊断、因果分析、预测和结构分析等方面的优势与最新进展，旨在推动其在实证应用中替代VAR模型。
Estimation in nonstationary random coefficient autoregressive models
研究了随机系数自回归模型中参数的估计问题。我们考虑了一个非平稳RCA过程，并证明了新息方差参数不能用拟极大似然方法估计。证明了剩余模型参数的拟极大似然估计的渐近正态性，从而证明了随机系数自回归模型不存在单位根问题。
For general panel data, by introducing network structure, network vector autoregressive (NVAR) model captured the linear inter dependencies among multiple time series. In this paper, we propose network vector autoregressive model for dyadic response variables (NVARD), which describes the dynamic process of dyadic data in the case of the dependencies among different pairs are taken into consideration. Besides, due to the existence of heterogeneity between time and individual, we propose time-varying coefficient network vector autoregressive model for dyadic response variables (VCNVARD). Finally…
Linear Transformers as VAR Models: Aligning Autoregressive Attention Mechanisms with Autoregressive Forecasting
本文提出SAMoVAR，一种将Transformer架构与自回归目标对齐的线性变换器变体，通过整合可解释的动态VAR权重，提升时间序列预测的性能和可解释性。
Knowledge of the current state of economies, how they respond to COVID-19 mitigations and indicators, and what the future might hold for them is important. We use recently-developed generalised network autoregressive (GNAR) models, using trade-determined networks, to model and forecast the Purchasing Managers' Indices for a number of countries. We use networks that link countries where the links themselves, or their weights, are determined by the degree of export trade between the countries. We extend these models to include node-specific time series exogenous variables (GNARX models), using t…
Score-driven models, also known as generalized autoregressive score models, represent a class of observation-driven time series models. They possess powerful properties, such as the ability to model different conditional distributions and to consider time-varying parameters within a flexible framework. In this paper, we present ScoreDrivenModels.jl, an open-source Julia package for modeling, forecasting, and simulating time series using the framework of score-driven models. The package is flexible with respect to model definition, allowing the user to specify the lag structure and which parame…
Forecasting with time-varying vector autoregressive models
提出了一种用于多变量时间序列预测的时变向量自回归模型（TV-VAR）。该模型被铸造成一个状态空间的形式，允许灵活的描述和分析。波动协方差矩阵的时间序列建模通过倒Wishart和奇异多变量贝塔分布，允许一个完全共轭贝叶斯推断。模型性能和模型比较通过似然函数、序贯贝叶斯因子、标准化预测误差平方均值、绝对预测误差均值（也称为平均绝对偏差）和平均预测误差进行。贝叶斯因子也用于选择模型的自回归阶数。详细讨论了多步预测，并提出了一个灵活的公式来逼近预测函数。两个例子，包括IBM股票的二元数据和外汇（FX）的8种货币的汇率，说明了方法。对于IBM数据，我们详细讨论了模型性能和多步预测。对于外汇数据，我们讨论了顺序投资组合分配，对于这两个数据集，我们的实证研究结果表明，TV-VAR模型优于广泛使用的VAR模型。
Identifiable Autoregressive Variational Autoencoders for Nonlinear and Nonstationary Spatio-Temporal Blind Source Separation
本文提出可识别的自回归变分自编码器，用于非线性和非平稳时空盲源分离，通过模拟研究验证其有效性。
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to regularize and provide feature selection. The lasso requires the specification of a penalty parameter that determines the degree of sparsity to impose. The most popular penalty parameter selection approaches that respect time dependence are very computationally intensive and are not appropriate for modeling certain classes of time series. We propose enhanci…
Risk Estimate under a Time-Varying Autoregressive Model for Data-Driven Reproduction Number Estimation
本文提出广义时变自回归模型估计COVID-19再生数，通过推广Stein无偏风险估计构建数据驱动预言机选择超参数，提出每周缩放Poisson模型提升鲁棒性，并在合成与真实数据上验证有效性。
The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and fractional autoregressive integrated moving-average (FARIMA) models are analyzed. As examples of infinitely divisible innovations, the class of radially absolute continuous distributions and general non-symmetric stable distributions are considered. The finite dimensional distributionsn of these models are also obtained.
Matrix-variate integer-valued autoregressive processes
本文针对社会学和经济学中矩阵值整数值时间序列的建模需求，提出矩阵值整数值自回归模型，通过左右矩阵薄化算子定义模型，研究其性质，开发投影与迭代最小二乘估计，并证明其优于现有模型。
Hidden Markov Mixture Autoregressive Models: Parameter Estimation
本报告介绍了一个简约的结构，混合自回归模型，其中的权系数确定通过潜在的随机变量的函数，所有过去的观察。这些变量遵循隐马尔可夫模型。我们修改EM和Baum-Welch算法来估计模型的参数。
A new mixture autoregressive model based on Student's $t$-distribution is proposed. A key feature of our model is that the conditional $t$-distributions of the component models are based on autoregressions that have multivariate $t$-distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component model is a linear function of past observations and the conditional variance is also time varying. Compared to previous mixture autoregressive models ou…
Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the model and thereby regularize predictions in the far future. We use MCMC-based inference by deriving relevant full conditional distributions and employ a Metropolis-Hastings within Gibbs Sampler approach to sample from the posterior (predictive) distrib…
Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data (`observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is hig…
Testing stability in a spatial unilateral autoregressive model
研究了空间单边自回归过程$X_{k,\ell}=αX_{k-1,\ell}+βX_{k,\ell-1}+\varepsilon_{k,\ell}$的稳定性参数$\varrho := |α| + |β|$的最小二乘估计。在不稳定的情况下显示了具有比例因子$n^{5/4}$的渐近正态性，即，当$\varrho = 1$，与AR（p）模型$X_k=α_1 X_{k-1}+... +α_p X_{k-p}+ \varepsilon_k$相反，其中稳定性参数$\varrho :=α_1 + ... + α_p$的最小二乘估计在不稳定中不是渐近正态的，即，在单位根的情况下。
Estimation of High-dimensional Nonlinear Vector Autoregressive Models
本文提出了一种高维非线性向量自回归模型估计方法，通过基函数展开构建模型，并推导了收敛速率和模型选择一致性，同时展示了在基因表达时间序列数据中的应用优势。
Selecting Optimal Variable Order in Autoregressive Ising Models
本文提出通过学习图结构来优化自回归伊辛模型中的变量顺序，以提高生成样本的保真度。
A new matrix-variate integer-valued autoregressive process with matrical negative binomial thinning
本文针对矩阵值整数时间序列的过度离散问题，提出带矩阵负二项稀疏的新型整数自回归模型，开发两种估计方法并验证其性能，该模型拟合效果优于两类对比模型。
WAVE: Weighted Autoregressive Varying Gate for Time Series Forecasting
WAVE通过整合ARMA结构提升时间序列预测性能，结合自回归和移动平均组件，实现更高效的长程和局部时间模式捕捉。
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is Hölder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A precise control of this method demands a delicate analysis of extremes of certain weakly dependent processes, our main result being a concentration inequality for such quantities. Based on our analysis, upper and matching minimax lower bounds are derived, showing the optimality of our estimators. Unlike the regular case, the information theoretic complexity depen…
Some Probabilistic and Statistical Properties of a Random Coefficient Autoregressive Model
Robinson（1978）研究了随机系数一阶自回归模型$[RCAR(1)]$的统计推断，其中系数随个体而变化。本文试图将这一结果推广到$p$ $[RCAR(p)]$阶随机系数自回归模型。将导出该模型的平稳性条件。
Hidden Markov Mixture Autoregressive Models: Stability and Moments
本文提出了混合自回归模型的一种新的简约结构。所述权系数是根据隐马尔可夫模型通过潜在随机变量确定的。本文提出了一种应用于预测的动态规划算法。我们还得到了过程的无条件一阶矩的极限行为和方差极限值的一个合适的上界。这可以被认为是进程的长期运行行为。最后证明了二阶矩的收敛性和稳定性。此外，我们通过模拟和预测来说明所提出的模型的有效性。
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for fitting sparse VAR models to such time series. Attention is paid to the different sparsity assumptions imposed on the VAR parameters and how these sparsity assumptions are related to the particular consistency properties of the estimators established. A sparsity scheme for high-dimensional VAR models is proposed which is found to be more appropriate for the tim…
Neural autoregressive models are explicit density estimators that achieve state-of-the-art likelihoods for generative modeling. The D-dimensional data distribution is factorized into an autoregressive product of one-dimensional conditional distributions according to the chain rule. Data completion is a more involved task than data generation: the model must infer missing variables for any partially observed input vector. Previous work introduced an order-agnostic training procedure for data completion with autoregressive models. Missing variables in any partially observed input vector can be i…
Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in …
In this paper, we propose multi-variable LSTM capable of accurate forecasting and variable importance interpretation for time series with exogenous variables. Current attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, the multi-variable LSTM equipped with tensorized hidden states is developed to learn hidden states for individual variables, which give rise to our mixture temporal and variable attention. Based on such attention mechanism, we infer and quantify variable importance. Ext…
Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are compared and contrasted, explaining the premises behind each and how they are interrelated,…
Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have become available very recently. We, instead, consider multiple stable autoregressive processes that share an unknown lag. We use information across the different processes to simultaneously select the lag and estimate the parameters. We prove that the estimated process is stable, and we establish rates for the forecasting error that can outmatch the known rate in…
We propose a regularized factor-augmented vector autoregressive (FAVAR) model that allows for sparsity in the factor loadings. In this framework, factors may only load on a subset of variables which simplifies the factor identification and their economic interpretation. We identify the factors in a data-driven manner without imposing specific relations between the unobserved factors and the underlying time series. Using our approach, the effects of structural shocks can be investigated on economically meaningful factors and on all observed time series included in the FAVAR model. We prove cons…
In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, our multi-variable LSTM equipped with tensorized hidden states is developed to learn variable specific representations, which give rise to both temporal and variable level attention. Preliminary experiments demonstrate comparable prediction performance of multi-variable L…
Geometric Infinitely Divisible Autoregressive Models
本文研究了几何无穷可分随机变量及其性质，提出了具有 gid 边缘分布的 AR 模型，并将其推广至 k 阶，同时给出了 AR(1) 过程的参数估计方法。
Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we introduce a class of quantile ARMAX models based on log-symmetric distributions. This class is indexed by quantile and dispersion parameters. It not only accommodates the possibility to model bimodal and/or light/heavy-tailed distributed data but also accommodates heteroscedasticity. We estimate the model parameters by using the conditional maximum likelihood metho…
Bayesian estimation of a multivariate TAR model when the noise process distribution belongs to the class of Gaussian variance mixtures
本文提出一种基于贝叶斯方法的多变量TAR模型估计与预测框架，采用高斯方差混合类分布描述噪声过程以增强对异常值的鲁棒性，并通过MCMC算法、DIC/WAIC准则及R语言包验证了方法有效性。
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