arXiv subjects

Qiwei Yao

Publications and source records attributed to Qiwei Yao.

At least 37 records · Page 2Linked to original sources

arXiv2022

Blind Source Separation over Space

We propose a new estimation method for the blind source separation model of Bachoc et al. (2020). The new estimation is based on an eigenanalysis of a positive definite matrix defined in terms of multiple normalized spatial local covariance matrices, and, therefore, can handle moderately high-dimensional random fields. The consistency of the estimated mixing matrix is established with explicit error rates even when the eigen-gap decays to zero slowly. The proposed method is illustrated via both simulation and a real data example.

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arXiv2022

An autocovariance-based learning framework for high-dimensional functional time series

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated from the fact that the autocovariance function of observed functional time series automatically filters out the noise term, we propose a three-step procedure by first performing autocovariance-based dimension reduction, then formulating a novel autocovariance-based block regularized minimum distance estimation framework to produce block sparse estimates, and based on which obtaining the final functional sparse estimates. We investigate theoretical properties of the proposed estimators, and illustrate the proposed estimation procedure via three sparse high-dimensional functional time series models. We demonstrate via both simulated and real datasets that our proposed estimators significantly outperform the competitors.

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arXiv2022

Modelling matrix time series via a tensor CP-decomposition

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method improves significantly the finite-sample performance of the estimation. The asymptotic theory has been established under a general setting without the stationarity. It shows, for example, that all the component coefficient vectors in the CP-decomposition are estimated consistently with certain convergence rates. The proposed model and the estimation method are also illustrated with both simulated and real data; showing effective dimension-reduction in modelling and forecasting matrix time series.

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arXiv2022

Autoregressive Networks

We propose a first-order autoregressive (i.e. AR(1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and efficient statistical inference methods including a permutation test for diagnostic checking for the fitted network models. The proposed model can be applied to the network processes with various underlying structures but with independent edges. As an illustration, an AR(1) stochastic block model has been investigated in depth, which characterizes the latent communities by the transition probabilities over time. This leads to a new and more effective spectral clustering algorithm for identifying the latent communities. We have derived a finite sample condition under which the perfect recovery of the community structure can be achieved by the newly defined spectral clustering algorithm. Furthermore the inference for a change point is incorporated into the AR(1) stochastic block model to cater for possible structure changes. We have derived the explicit error rates for the maximum likelihood estimator of the change-point. Application with three real data sets illustrates both relevance and usefulness of the proposed AR(1) models and the associate inference methods.

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arXiv2021

Testing for unit roots based on sample autocovariances

We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ only assumes that the process concerned is $I(0)$ without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function (ACVF) converges to the finite population ACVF for an $I(0)$ process while it diverges to infinity for a process with unit-roots. Therefore the new test rejects $H_0$ for the large values of the sample ACVF. To address the technical challenge `how large is large', we split the sample and establish an appropriate normal approximation for the null-distribution of the test statistic. The substantial discriminative power of the new test statistic is rooted from the fact that it takes finite value under $H_0$ and diverges to infinity under $H_1$. This allows us to truncate the critical values of the test to make it with the asymptotic power one. It also alleviates the loss of power due to the sample-splitting. The test is implemented in a user-friendly R-function.

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arXiv2020

Probabilistic Forecasting for Daily Electricity Loads and Quantiles for Curve-to-Curve Regression

Probabilistic forecasting of electricity load curves is of fundamental importance for effective scheduling and decision making in the increasingly volatile and competitive energy markets. We propose a novel approach to construct probabilistic predictors for curves (PPC), which leads to a natural and new definition of quantiles in the context of curve-to-curve linear regression. There are three types of PPC: a predictive set, a predictive band and a predictive quantile, all of which are defined at a pre-specified nominal probability level. In the simulation study, the PPC achieve promising coverage probabilities under a variety of data generating mechanisms. When applying to one day ahead forecasting for the French daily electricity load curves, PPC outperform several state-of-the-art predictive methods in terms of forecasting accuracy, coverage rate and average length of the predictive bands. The predictive quantile curves provide insightful information which is highly relevant to hedging risks in electricity supply management.

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arXiv2020

Estimation of subgraph density in noisy networks

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and non-standard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks.

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arXiv2020

Modeling Multivariate Spatial-Temporal Data with Latent Low-Dimensional Dynamics

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies in large data sets. In this paper, we propose a new approach to utilize the correlations in variable, space and time to achieve dimension reduction and to facilitate spatial/temporal predictions in the high-dimensional settings. The multivariate spatial-temporal process is represented as a linear transformation of a lower-dimensional latent factor process. The spatial dependence structure of the factor process is further represented non-parametrically in terms of latent empirical orthogonal functions. The low-dimensional structure is completely unknown in our setting and is learned entirely from data collected irregularly over space but regularly over time. We propose innovative estimation and prediction methods based on the latent low-rank structures. Asymptotic properties of the estimators and predictors are established. Extensive experiments on synthetic and real data sets show that, while the dimensions are reduced significantly, the spatial, temporal and variable-wise covariance structures are largely preserved. The efficacy of our method is further confirmed by the prediction performances on both synthetic and real data sets.

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arXiv2018

On testing for high-dimensional white noise

Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in relation to the sample size $T$, the popular omnibus tests including the multivariate Hosking and Li-McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first $q$ lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (upto the time lag $q$) within and across all component series. Using the tools from random matrix theory and assuming both $p$ and $T$ diverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, non trivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite $(p,T)$ combinations, therefore ensuring wide applicability in practice. In particular, the new tests are consistently superior to the traditional Hosking and Li-McLeod tests.

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arXiv2018

Banded Spatio-Temporal Autoregressions

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 covariance matrices. Due to the innate endogeneity, we apply the least squares method based on a Yule-Walker equation to estimate autoregressive coefficient matrices. The estimators based on multiple Yule-Walker equations are also studied. A ratio-based method for determining the bandwidth of autoregressive matrices is also proposed. Some asymptotic properties of the inference methods are established. The proposed methodology is further illustrated using both simulated and real data sets.

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arXiv2018

Confidence regions for entries of a large precision matrix

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for high-dimensional time dependent observations. Specifically, we propose a data-driven procedure to construct a class of simultaneous confidence regions for the precision coefficients within an index set of interest. The confidence regions can be applied to test for specific structures of a precision matrix and to recover its nonzero components. We first construct an estimator of the underlying precision matrix via penalized node-wise regressions, and then develope the Gaussian approximation results on the maximal difference between the estimated and true precision matrices. A computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure. Theoretical results indicate that the proposed procedure works well without the second order cross-time stationary assumption on the data and sparse structure conditions on the long-run covariance of the estimates. Simulation studies and a real example on S&P 500 stock return data confirm the performance of the proposed approach.

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arXiv2018

Krigings Over Space and Time Based on Latent Low-Dimensional Structures

We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods (Section 7.1.3 of Cressie and Wikle, 2011), the fundamental difference is that the low-dimensional structure is completely unknown in our setting, which is learned from the data collected irregularly over space but regularly over time. Furthermore a graph Laplacian is incorporated in the learning in order to take the advantage of the continuity over space, and a new aggregation method via randomly partitioning space is introduced to improve the efficiency. We do not impose any stationarity conditions over space either, as the learning is facilitated by the stationarity in time. Krigings over space and time are carried out based on the learned low-dimensional structure, which is scalable to the cases when the data are taken over a large number of locations and/or over a long time period. Asymptotic properties of the proposed methods are established. Illustration with both simulated and real data sets is also reported.

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arXiv2018

Identifying Cointegration by Eigenanalysis

We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain non-negative definite matrix. Our setting is model-free, and we allow the integer-valued integration orders of the observable series to be unknown, and to possibly differ. Consistency of estimates of the cointegration space and cointegration rank is established both when the dimension of the observable time series is fixed as sample size increases, and when it diverges slowly. The proposed methodology is also extended and justified in a fractional setting. A Monte Carlo study of finite-sample performance, and a small empirical illustration, are reported.

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arXiv2017

Multivariate Spatial-temporal Prediction on Latent Low-dimensional Functional Structure with Non-stationarity

Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable dependencies simultaneously. In this paper, we propose a new approach to represent non-parametrically the linear dependence structure of a multivariate spatio-temporal process in terms of latent common factors. The matrix structure of observations from the multivariate spatio-temporal process is well reserved through the matrix factor model configuration. The spatial loading functions are estimated non-parametrically by sieve approximation and the variable loading matrix is estimated via an eigen-analysis of a symmetric non-negative definite matrix. Though factor decomposition along the space mode is similar to the low-rank approximation methods in spatial statistics, the fundamental difference is that the low-dimensional structure is completely unknown in our setting. Additionally, our method accommodates non-stationarity over space. The estimated loading functions facilitate spatial prediction. For temporal forecasting, we preserve the matrix structure of observations at each time point by utilizing the matrix autoregressive model of order one MAR(1). Asymptotic properties of the proposed methods are established. Performance of the proposed method is investigated on both synthetic and real datasets

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arXiv2017

Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.

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arXiv2017

Testing for high-dimensional white noise using maximum cross-correlations

We propose a new omnibus test for vector white noise using the maximum absolute auto-correlations and cross-correlations of the component series. Based on the newly established approximation by the $L_\infty$-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing the departure from non-IID white noise. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods including, for example, the Lagrange multiplier test and the multivariate Box-Pierce portmanteau tests especially when the dimension of time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to the pre-transformed data obtained via the time series principal component analysis proposed by Chang, Guo and Yao (2014). The proposed procedures have been implemented in an R-package HDtest and is available online at CRAN.

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arXiv2016

Modelling and forecasting daily electricity load curves: a hybrid approach

We propose a hybrid approach for the modelling and the short-term forecasting of electricity loads. Two building blocks of our approach are (i) modelling the overall trend and seasonality by fitting a generalised additive model to the weekly averages of the load, and (ii) modelling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors. The key idea behind the proposed methodology is the dimension reduction based on a singular value decomposition in a Hilbert space, which reduces the curve regression problem to several ordinary (i.e. scalar) linear regression problems. We illustrate the hybrid method using the French electricity loads between 1996 and 2009, on which we also compare our method with other available models including the EDF operational model.

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arXiv2016

High Dimensional and Banded Vector Autoregressions

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 exploring some approximate banded structure for the auto-covariance functions of banded vector autoregressive processes, consistent estimators for the auto-covariance matrices are constructed.

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