We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters. Statistical inference in our setting is much more involved since standard procedures, like the delta-method, do not apply. By using local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters associated with the VAR system. We then obtain estimators of the structural impulse responses by combining the aforementioned de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix, also taking into account the high-dimensionality of the system. We show that the distribution of the derived estimators of structural impulse responses has a Gaussian limit. We also present a valid bootstrap procedure to estimate this distribution. Applications of the inference procedure in the construction of confidence intervals for impulse responses as well as in tests for forecast error variance decomposition are presented. Our procedure is illustrated by means of simulations.
Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference for the transition matrices of VAR models are crucial for practitioners to make decisions in fields such as economics and finance. However, when the number of variables is larger than the sample size, it remains a challenge to perform statistical inference of the model parameters. In this article, we propose the de-biased Lasso and two bootstrap de-biased Lasso methods to construct confidence intervals for the elements of the transition matrices of …
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to…
In this paper we propose a new time-varying econometric model, called Time-Varying Poisson AutoRegressive with eXogenous covariates (TV-PARX), suited to model and forecast time series of counts. {We show that the score-driven framework is particularly suitable to recover the evolution of time-varying parameters and provides the required flexibility to model and forecast time series of counts characterized by convoluted nonlinear dynamics and structural breaks.} We study the asymptotic properties of the TV-PARX model and prove that, under mild conditions, maximum likelihood estimation (MLE) yie…
University of California, Los Angeles（加州大学洛杉矶分校）；Imperial College London（帝国理工学院）；University of Oxford（牛津大学）；Oxford-Man Institute of Quantitative Finance, University of Oxford（牛津大学牛津量化金融牛津曼研究所）；The Alan Turing Institute（艾伦·图灵研究所）；University of Bologna（博洛尼亚大学）
We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We pro…
Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on vector autoregressive models (VAR) has been investigated in depth in the literature, more complex network structures that involve low rank and group sparse components have received considerably less attention, despite their presence in data. Failure to account for low-rank structures results in spurious connectivity among the observed time series, which may lead …
We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimens…
High-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence of anomalies. However, the problem of detecting the structural changes in a real-time manner has not been well studied. To fill this gap, we propose a dynamic sparse subspace learning approach for online structural change-point detection of high-dimensional streaming data. A novel multiple structural change-point model is proposed and the asymptotic properti…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The structure is also practically meaningful when the order of component time series is arranged appropriately. The convergence rates for the estimated banded autoregressive coefficient matrices are established. We also propose a Bayesian information criterion for determining the width of the bands in the coefficient matrices, which is proved to be consistent. By explo…
Mixed-frequency Vector AutoRegressions (MF-VAR) model the dynamics between variables recorded at different frequencies. However, as the number of series and high-frequency observations per low-frequency period grow, MF-VARs suffer from the "curse of dimensionality". We curb this curse through a regularizer that permits hierarchical sparsity patterns by prioritizing the inclusion of coefficients according to the recency of the information they contain. Additionally, we investigate the presence of nowcasting relations by sparsely estimating the MF-VAR error covariance matrix. We study predictive…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their consistency and asymptotic normality, which reveals an oracle property. However, the penalized estimators for the incidenta…
We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and therefore, the proposal is radically different from the existing literature on the inference for high-dimensional banded covari…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to lie in the stationary region. However, the stationary region has a highly complex geometry which impedes specification of a prior distribution. In this work, an unconstrained reparameterization of a stationary vector autoregression is presented. The new parameters are partial autocorrelation matrices, which are interpretable, and can be transfor…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the unde…
Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks in such applications that poses a challenge for statistical inference is the presence of a small number of strongly interconnected nodes in a network which are called hubs. For example, in microbiome research hubs or microbial taxa play a significant role in maintaining stability of the microbial community structure. In this paper, we investigate the problem …
High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is: how much harder? In this paper, we study the properties of a partially-observed Vector AutoRegressive process, which is a state-space model endowed with a stochastic observation mechanism.Our goal is to estimate its sparse transition matrix, but we only have access to a small and noisy subsample of the state components.Interestingly, the sampling process itsel…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain connectivity analysis from neuroimaging data, structural analysis of a large panel of macroeconomic indicators, and studying linkages among financial firms for more robust financial regulation. These applications have led to renewed interest in developing principled statistical methods and theory for estimating large time series models given only a relative…
Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a hierarchical sparse Bayesian learning framework with the goal of reducing the source of ill-conditioning in the stiffness loss inversion problem for damage detection. Sparse Bayesian learning methodologies automatically prune away irrelevant or inactive features from a set of potential candidates, and so they are effective probabilistic tools for producing sparse ex…
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameter…
Spike-and-slab shrinkage priors for structurally sparse Bayesian neural networks
Computational Science Initiative, Brookhaven National Laboratory（布鲁克海文国家实验室计算科学倡议）；Department of Statistics and Probability, Michigan State University（密歇根州立大学统计与概率系）
Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the model response and due to the lack of local metamodel error estimates. We propose a new method to provide local metamodel error estimates based on bootstrap resampling and sparse PCE. An initial experimental design is iteratively updated based on the current estimation of the limit-state surface in an active learning algorithm. The greedy algorithm uses the b…
Integrative analyses of different high dimensional data types are becoming increasingly popular. Similarly, incorporating prior functional relationships among variables in data analysis has been a topic of increasing interest as it helps elucidate underlying mechanisms among complex diseases. In this paper, the goal is to assess association between transcriptomic and metabolomic data from a Predictive Health Institute (PHI) study including healthy adults at high risk of developing cardiovascular diseases. To this end, we develop statistical methods for identifying sparse structure in canonical…
Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this work we propose an integral SINDy (ISINDy) method to simultaneously identify model structure and parameters of nonlinear ordinary differential equations (ODEs) from noisy time-series observations. First, the states are estimated via penalized spline smoothing and then substituted into the integral-form numerical discretization solver, leading to a pseudo-li…
We propose a novel structure selection method for high dimensional (d > 100) sparse vine copulas. Current sequential greedy approaches for structure selection require calculating spanning trees in hundreds of dimensions and fitting the pair copulas and their parameters iteratively throughout the structure selection process. Our method uses a connection between the vine and structural equation models (SEMs). The later can be estimated very fast using the Lasso, also in very high dimensions, to obtain sparse models. Thus, we obtain a structure estimate independently of the chosen pair copulas an…
Proper function of a wastewater treatment plant (WWTP) relies on maintaining a delicate balance between a multitude of competing microorganisms. Gaining a detailed understanding of the complex network of interactions therein is essential to maximising not only current operational efficiencies, but also for the effective design of new treatment technologies. Metagenomics offers an insight into these dynamic systems through the analysis of the microbial DNA sequences present. Unique taxa are inferred through sequence clustering to form operational taxonomic units (OTUs), with per-taxa abundance …
We consider weighted directed networks for analysing, over the period 2000-2013, the interdependencies between volatilities of a large panel of stocks belonging to the S\&P100 index. In particular, we focus on the so-called {\it Long-Run Variance Decomposition Network} (LVDN), where the nodes are stocks, and the weight associated with edge $(i,j)$ represents the proportion of $h$-step-ahead forecast error variance of variable $i$ accounted for by variable $j$'s innovations. To overcome the curse of dimensionality, we decompose the panel into a component driven by few global, market-wide, facto…
