S Satheesh, E Sandhya
The family of semi-stable laws is shown to be semi-selfdecomposable. Thus they qualify to model stationary first order autoregressive schemes. A connection between these autoregressive schemes with semi-stable marginals and semi-selfsimilar processes is given.
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A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes, transforming the autocorrelation of the non-Gaussian process to that of a Gaussian process based on a piece-wise linear marginal transform from non-Gaussian to Gaussian marginal. The extension to multivariate processes involves the derivation of the autocorrelation matrix from the marginal transforms, which determines the generating vector autoregressive process. The …
State-dependent marginal emission factors with autoregressive components
本文提出基于马尔可夫切换自回归模型的状态依赖边际排放因子方法，揭示了燃料价格动态对电网制度的影响，指出传统线性模型在评估减排潜力时的不足。
INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling limitation is that it is difficult to justify the choice of the operator. To overcome these drawbacks, we propose a new flexible approach to build an INAR model: we pre-specify the marginal and innovation distributions. Hence, the operator is a consequence of specifying the desired marginal and innovation distributions. Our new INAR model has both marginal and…
Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the mo…
A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data
针对含测量误差与高比例响应缺失的大规模SAR模型估计难题，提出计算复杂度为$O(n^{3/2})$的边际极大似然方法，经模拟与真实数据验证有效。
In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It is shown that the distribution of the error term is infinitely divisible. Parameter estimation of the introduced TAR(1) process is done by adopting the conditional least square and method of moments based approach and the performance of the proposed methods are evaluated on simulated data. Also we study an autoregressive model of order one with tempered stab…
On the Efficient Marginalization of Probabilistic Sequence Models
本研究针对现实序列数据的复杂长程概率查询需求，提出一类模型无关的高效序列模型边缘化近似技术，可适配离散序列模型、标记时间点过程等多类模型，仅需预训练自回归模型的下一步条件分布即可实现。
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。
In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we show that a kernel type estimate based on the residuals can be root-n consistent even if the noise density is unknown. Our results, which are shown to be valid for classical time series models such as ARMA or GARCH processes, extend substantially the existing results obtained for some homoscedatic time series models. Asymptotic expansion of our estimator is …
Testing the goodness-of-fit of a functional autoregressive model
针对函数型时间序列中的线性自相关模型，提出基于经验过程的拟合优度检验，推导了经验过程收敛到时间变换的Wiener过程的函数中心极限定理，并验证了检验在简单和复合原假设下的大样本性质及一致性。
The recently proposed mask-predict decoding algorithm has narrowed the performance gap between semi-autoregressive machine translation models and the traditional left-to-right approach. We introduce a new training method for conditional masked language models, SMART, which mimics the semi-autoregressive behavior of mask-predict, producing training examples that contain model predictions as part of their inputs. Models trained with SMART produce higher-quality translations when using mask-predict decoding, effectively closing the remaining performance gap with fully autoregressive models.
Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/ extreme-semi-selfdecomposable or, sum/ extreme stable with respect to Harris distribution.
The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we consider the problem of testing for a change in the tail index of time series data. As a test, we employ the cusum test and investigate its null limiting distribution. Further, we derive the null limiting distribution of the cusum test based on the residuals from autoregressive models. Simulation results are provided for illustration.
A time series is a sequence of observations taken sequentially in time. The autoregressive integrated moving average is a class of the model more used for times series data. However, this class of model has two critical limitations. It fits well onlyGaussian data with the linear structure of correlation. Here, I present a new model named as generalized autoregressive neural networks, GARNN. The GARNN is an extension of the generalized linear model where the mean marginal depends on the lagged values via the inclusion of the neural network in the link function. A practical application of the mo…
Methods of construction of Max-semi-selfdecompsable laws are given. Implications of this method in random time changed extremal processes are discussed. Max-autoregressive model is introduced and characterized using the max-semi-selfdecompsable laws and exponential max-semi-stable laws. Max-semi-selfddecomposability of max-semi-stable laws are proved.
A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by embedding regularized estimators for the state-dependent covariance matrices and autoregression matrices in the M-step. The performance of the proposed regularized estimators is evaluated both in the simulation experiments and on the New York Stock Exchange financial portfolio data.
Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of the time series is specified and an appropriate distribution for the innovation sequence is sought. Whereas in the backward setting, the roles are reversed. The common distribution of the innovation sequence is specified and the distributional properties of the marginal distribution of the time series are studied. In this article we focus on the backward app…
We discuss semi-selfdecomposable laws in the minimum scheme and characterize them using an autoregressive model. Semi-Pareto and semi-Weibull laws of Pillai (1991) are shown to be semi-selfdecomposable in this scheme. Methods for deriving this class of laws are then attempted from the angle of randomization. Finally, discrete analogues of these results are also considered.
The structure of stationary first order max-autoregressive schemes with max-semi-stable marginals is studied. A connection between semi-selfsimilar extremal processes and this max-autoregressive scheme is discussed resulting in their characterizations. Corresponding cases of max-stable and selfsimilar extremal processes are also discussed.
Evaluating Approximations of Count Distributions and Forecasts for Poisson-Lindley Integer Autoregressive Processes
本文针对离散时间序列使用连续 Gaussian 模型导致预测不一致的问题，通过模拟比较了 PLINAR 模型与 Gaussian 预测变体的预测效果，并利用三种参数估计方法验证了其实用性。
In this work we consider the problem of anomaly detection in heterogeneous, multivariate, variable-length time series datasets. Our focus is on the aviation safety domain, where data objects are flights and time series are sensor readings and pilot switches. In this context the goal is to detect anomalous flight segments, due to mechanical, environmental, or human factors in order to identifying operationally significant events and provide insights into the flight operations and highlight otherwise unavailable potential safety risks and precursors to accidents. For this purpose, we propose a f…
Latent Block-Diffusion Temporal Point Processes: A Semi-Autoregressive Framework for Asynchronous Event Sequence Generation
提出潜在块扩散时间点过程（LBDTPP），通过潜在空间中的块级自回归和块内高斯扩散，实现可变长度、高质量的事件序列生成，理论证明可减少误差累积，实验优于现有方法。
DAMNETS: A Deep Autoregressive Model for Generating Markovian Network Time Series
本文提出DAMNETS，一种可扩展的深度自回归生成模型，用于生成马尔可夫网络时间序列，并在真实与合成数据集上全面超越现有方法。
Estimation and Autoregressive Modeling of Mittag-Leffler Distributions with Application in Finance
本文提出利用经验拉普拉斯变换方法估计Mittag-Leffler分布参数，并建立自回归模型用于高频交易数据分析。
Max-semistable extreme value laws for autoregressive processes with Cantor-like marginals
本文研究边缘分布类似康托尔函数的自动回归过程，证明其边缘分布属于极大半稳定分布的吸引域，并通过引入极值指数得到该过程的极值律，同时揭示其与确定性动力系统极值的联系。
We investigate in this paper a Bickel-Rosenblatt test of goodness-of-fit for the density of the noise in an autoregressive model. Since the seminal work of Bickel and Rosenblatt, it is well-known that the integrated squared error of the Parzen-Rosenblatt density estimator, once correctly renormalized, is asymptotically Gaussian for independent and identically distributed (i.i.d.) sequences. We show that the result still holds when the statistic is built from the residuals of general stable and explosive autoregressive processes. In the univariate unstable case, we prove that the result holds w…
The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in noisy estimates, unstable predictions and difficult-to-interpret temporal dependence. To overcome such drawbacks, we propose a 2-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects non-zero AR coefficients based on an estimate of the partial spectral coherence (PSC) together with the use of B…
Dynamic Network Autoregressive Models for Functional Panel Data
本文提出了一种功能网络自回归模型，用于分析面板数据中功能结果的相互作用，并通过实证研究展示了其在自行车共享服务需求分析中的应用。
Marginal Inference for Hierarchical Generalized Linear Mixed Models with Patterned Covariance Matrices Using the Laplace Approximation
本文基于拉普拉斯近似和Newton-Raphson更新，为具有复杂模式化协方差结构的分层广义线性混合模型开发了完整的边际推断方法，支持六种分布并经模拟与真实数据验证了有效性。
glmSTARMA -- An R-Package for fitting autoregressive spatio-temporal models following generalized linear models
该研究介绍R包glmSTARMA，它基于广义线性模型方法，统一分析空间计数时间序列，实现自回归时空模型，还能对双广义线性模型推断，提供模型相关函数并举例说明，为时空数据分析提供新工具。
Efficient Autoregressive Inference for Transformer Probabilistic Models
本文提出一种高效自回归缓冲机制，结合集基和自回归方法，实现多预测联合分布推断，提升采样和密度评估效率，实验显示性能接近全上下文重编码，速度和内存使用更优。
The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal distribution. However, this distribution does not allow describing data with outliers and asymmetric behavior. In this paper, we study the AR models with normal inverse Gaussian (NIG) innovations. The NIG distribution belongs to the class of semi heavy-tailed distributions with wide range of shapes and thus allows for describing real-life data with possible jump…
Margin-closed vector autoregressive time series models
本文推导了高斯VAR($k$)模型具有同阶自回归边缘的条件，利用边缘封闭性质提出多阶段估计方法，并扩展至非高斯边缘，提升了高维时间序列建模的灵活性。
We study four different approaches to model time-dependent extremal behavior: dynamics introduced by (a) a state-space model (SSM), (b) a shot-noise-type process with GPD marginals, (c) a copula-based autoregressive model with GPD marginals, and (d) a GLM with GPD marginals (and previous extremal events as regressors). Each of the models is fit against data, and from the fitted data, we simulate corresponding paths according to the respective fitted models. At this simulated data, the respective dependence structure is analyzed in copula plots and judged against its capacity to fit the corresp…
In this paper, we propose an unsupervised data-driven approach to predict real-time locational marginal prices (RTLMPs). The proposed approach is built upon a general data structure for organizing system-wide heterogeneous market data streams into the format of market data images and videos. Leveraging this general data structure, the system-wide RTLMP prediction problem is formulated as a video prediction problem. A video prediction model based on generative adversarial networks (GAN) is proposed to learn the spatio-temporal correlations among historical RTLMPs and predict system-wide RTLMPs …
A new class of functional conditional autoregressive models
本文提出了一种新的条件自回归模型，用于空间依赖的功能数据，通过给定邻近功能观测的条件均值进行建模，并通过协方差算子和空间依赖参数进行表征。研究方法包括估计协方差算子、估计空间依赖参数以及应用新的基于轮廓的方法。理论结果证明了协方差估计器的一致性和空间依赖参数估计器的超一致性，为功能数据的空间依赖性提供了新的统计推断方法。
Marginal Analysis of Count Time Series in the Presence of Missing Observations
本文针对存在缺失观测的计数时间序列，利用振幅调制概念，推导离散度和偏度统计量的闭式渐近公式，并通过模拟和真实数据验证其性能。
We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary, first-order autoregressive (AR) processes on the cone of positive semi-definite matrices. Aspects of the theory and structure of these new models for multivariate "volatility" processes are described in detail and exemplified. We then develop approaches to model fitting via Bayesian simulation-based computations, creating a custom filtering method that reli…
Joint semi-parametric INAR bootstrap inference for model coefficients and innovation distribution
本文提出一种半参数 INAR 自助法程序，证明其对模型系数与新息分布的联合估计具有一致性，并应用于拟合优度检验、预测推断与离散指数分析，通过模拟和实际数据验证了其有限样本性能。
Multivariate Continuous-Time Autoregressive Moving Average Processes for Astronomical Multiband Time Series
本文提出MCARMA框架处理天文多波段不规则采样时间序列，通过两阶段估计和联合建模利用跨波段依赖，提升参数与谱恢复，并在SDSS类星体数据中验证。Python包mcarma实现。
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。
In this research, a functional time series model was introduced to predict future realizations of river flow time series. The proposed model was constructed based on a functional time series's correlated lags and the essential exogenous climate variables. Rainfall, temperature, and evaporation variables were hypothesized to have substantial functionality in river flow simulation. Because an actual time series model is unspecified and the input variables' significance for the learning process is unknown in practice, it was employed a variable selection procedure to determine only the significan…
A Random Graph-based Autoregressive Model for Networked Time Series
本文提出一种基于随机图的联网时间序列自回归模型，通过引入灵活的潜在变量刻画同质性，并结合一阶差分法与邻居平滑技术实现参数估计，无需指定网络生成机制，理论证明与实验均验证了其有效性。
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We obtain a non-standard limit theorem where the limiting distribution is a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. In particular, we provide conditions for the l…
In this note we correct an omission in our paper (Satheesh and Sandhya, 2005) in defining semi-selfdecomposable laws and also show with examples that the marginal distributions of a stationary AR(1) process need not even be infinitely divisible.
Construction and limit theorems for supCAR fields
本文构造了一类由连续自回归场叠加而成的supCAR随机场，证明其存在性并推导泛函极限定理，可用于统计推断。
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from copula theory, such marginal standardization is carried out by the pointwise probability integral transform. Certain situations, however, call for stochastic models whose trajectories are not continuous but merely upper semicontinuous (usc). Unfortunately, the pointwise application of the probability integral transform to a usc process does in general not preserv…
Multivariate continuous-time autoregressive moving-average processes on cones
该研究引入带Lévy噪声的矩阵值多元连续时间自回归滑动平均（MCARMA）过程，推导其取值于凸锥的充要条件及两类典型情形的可操作条件，并论证其在多元随机波动率模型中的应用价值。
It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of generalized s-selfdecomposable and selfdecomposable distributions. Some application are given to the moving average fractional Lévy process (MAFLP).
We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek (2013) and by Hobson and Neuberger (2008). We recast this dual …
Markovian projections for Itô semimartingales with jumps
本文为带跳 Itô 半鞅构造了匹配一维边际分布的 Markovian 投影，证明其边际分布流为非局部 FPKEs 的解，并展示了其在构建兼具局部与随机特征的校准扩散/跳跃模型中的应用。
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