Searcharxiv⌕ Search

arXiv subjects

Ruey S. Tsay

Publications and source records attributed to Ruey S. Tsay.

27 records · Page 2Linked to original sources
arXiv2020

A Two-Way Transformed Factor Model for Matrix-Variate Time Series

We propose a new framework for modeling high-dimensional matrix-variate time series by a two-way transformation, where the transformed data consist of a matrix-variate factor process, which is dynamically dependent, and three other blocks of white noises. Specifically, for a given $p_1\times p_2$ matrix-variate time series, we seek common nonsingular transformations to project the rows and columns onto another $p_1$ and $p_2$ directions according to the strength of the dynamic dependence of the series on the past values. Consequently, we treat the data as nonsingular linear row and column transformations of dynamically dependent common factors and white noise idiosyncratic components. We propose a common orthonormal projection method to estimate the front and back loading matrices of the matrix-variate factors. Under the setting that the largest eigenvalues of the covariance of the vectorized idiosyncratic term diverge for large $p_1$ and $p_2$, we introduce a two-way projected Principal Component Analysis (PCA) to estimate the associated loading matrices of the idiosyncratic terms to mitigate such diverging noise effects. A diagonal-path white noise testing procedure is proposed to estimate the order of the factor matrix. %under the assumption that the idiosyncratic term is a matrix-variate white noise process. Asymptotic properties of the proposed method are established for both fixed and diverging dimensions as the sample size increases to infinity. We use simulated and real examples to assess the performance of the proposed method. We also compare our method with some existing ones in the literature and find that the proposed approach not only provides interpretable results but also performs well in out-of-sample forecasting.

econ.EM↗
arXiv2020

Tensor Canonical Correlation Analysis with Convergence and Statistical Guarantees

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this paper, we study convergence and statistical properties of two-dimensional canonical correlation analysis \citep{Lee2007Two} under an assumption that data come from a probabilistic model. We show that carefully initialized the power method converges to the optimum and provide a finite sample bound. Then we extend this framework to tensor-valued data and propose the higher-order power method, which is commonly used in tensor decomposition, to extract the canonical directions. Our method can be used effectively in a large-scale data setting by solving the inner least squares problem with a stochastic gradient descent, and we justify convergence via the theory of Lojasiewicz's inequalities without any assumption on data generating process and initialization. For practical applications, we further develop (a) an inexact updating scheme which allows us to use the state-of-the-art stochastic gradient descent algorithm, (b) an effective initialization scheme which alleviates the problem of local optimum in non-convex optimization, and (c) a deflation procedure for extracting several canonical components. Empirical analyses on challenging data including gene expression and air pollution indexes in Taiwan, show the effectiveness and efficiency of the proposed methodology. Our results fill a missing, but crucial, part in the literature on tensor data.

stat.ML↗
arXiv2020

Modeling High-Dimensional Unit-Root Time Series

This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a $p$-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence. The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method for both fixed and diverging $p$ as the sample size $n$ increases, and use simulation and a real example to demonstrate the performance of the proposed method in finite samples. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM$_{2.5}$ series in Taiwan.

stat.ME↗
arXiv2020

Modeling High-Dimensional Time Series: A Factor Model with Dynamically Dependent Factors and Diverging Eigenvalues

This article proposes a new approach to modeling high-dimensional time series by treating a $p$-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate factor models, we assume that the factors capture all the non-trivial dynamics of the data, but the cross-sectional dependence may be explained by both the factors and the idiosyncratic components. Under the proposed model, (a) the factor process is dynamically dependent and the idiosyncratic component is a white noise process, and (b) the largest eigenvalues of the covariance matrix of the idiosyncratic components may diverge to infinity as the dimension $p$ increases. We propose a white noise testing procedure for high-dimensional time series to determine the number of white noise components and, hence, the number of common factors, and introduce a projected Principal Component Analysis (PCA) to eliminate the diverging effect of the idiosyncratic noises. Asymptotic properties of the proposed method are established for both fixed $p$ and diverging $p$ as the sample size $n$ increases to infinity. We use both simulated data and real examples to assess the performance of the proposed method. We also compare our method with two commonly used methods in the literature concerning the forecastability of the extracted factors and find that the proposed approach not only provides interpretable results, but also performs well in out-of-sample forecasting. Supplementary materials of the article are available online.

stat.ME↗
arXiv2017

Spatio-temporal models with space-time interaction and their applications to air pollution data

It is of utmost importance to have a clear understanding of the status of air pollution and to provide forecasts and insights about the air quality to the general public and researchers in environmental studies. Previous studies of spatio-temporal models showed that even a short-term exposure to high concentrations of atmospheric fine particulate matters can be hazardous to the health of ordinary people. In this study, we develop a spatio-temporal model with space-time interaction for air pollution data. The proposed model uses a parametric space-time interaction component along with the spatial and temporal components in the mean structure, and introduces a random-effects component specified in the form of zero-mean spatio-temporal processes. For application, we analyze the air pollution data (PM2.5) from 66 monitoring stations across Taiwan.

stat.ME↗
arXiv2013

Independent Component Analysis via Distance Covariance

This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a versatile resampling-based procedure for inference. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method that simultaneously minimizes all forms of dependence among the components. U-statistics of certain Euclidean distances between sample elements are combined in succession to construct a statistic for testing the existence of mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for mutual independence. When independent components exist, one may apply univariate analysis to study or model each component separately. Univariate models may then be combined to obtain a multivariate model for the original observations. We prove the consistency of our estimator under minimal regularity conditions without assuming the existence of independent components a priori, and all assumptions are placed on the observations directly, not on the latent components. We demonstrate the improvements of the proposed method over competing methods in simulation studies. We apply the proposed ICA approach to two real examples and contrast it with principal component analysis.

stat.ME↗
arXiv2011

A Conversation with George C. Tiao

George C. Tiao was born in London in 1933. After graduating with a B.A. in Economics from National Taiwan University in 1955 he went to the US to obtain an M.B.A from New York University in 1958 and a Ph.D. in Economics from the University of Wisconsin, Madison in 1962. From 1962 to 1982 he was Assistant, Associate, Professor and Bascom Professor of Statistics and Business at the University of Wisconsin, Madison, and in the period 1973--1975 was Chairman of the Department of Statistics. He moved to the Graduate School of Business at the University of Chicago in 1982 and is the W. Allen Wallis Professor of Econometrics and Statistics (emeritus). George Tiao has played a leading role in the development of Bayesian Statistics, Time Series Analysis and Environmental Statistics. He is co-author, with G.E.P. Box, of Bayesian Inference in Statistical Analysis and is the developer of a model-based approach to seasonal adjustment (with S. C. Hillmer), of outlier analysis in time series (with I. Chang), and of new ways of vector ARMA model building (with R. S. Tsay). He is the author/co-author/co-editor of 7 books and over 120 articles in refereed econometric, environmental and statistical journals and has been thesis advisor of over 25 students. He is a leading figure in the development of Statistics in Taiwan and China and is the Founding President of the International Chinese Statistical Association 1987--1988 and the Founding Chair Editor of the journal Statistica Sinica 1988--1993. He played a leading role (over the 20 year period 1979--1999) in the organization of the annual NBER/NSF Time Series Workshop and he was a founding member of the annual conference "Making Statistics More Effective in Schools of Business" 1986--2006.

stat.ME↗
arXiv2007

Multivariate volatility models

Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality quickly becomes an issue as the number of correlations is $k(k-1)/2$ for $k$ assets. In this paper, we review some of the commonly used models for multivariate volatility and propose a simple approach that is parsimonious and satisfies the positive definite constraints of the time-varying correlation matrix. Real examples are used to demonstrate the proposed model.

math.ST↗