arXiv subjects

Kexin Lu

Publications and source records attributed to Kexin Lu.

3 recordsLinked to original sources

arXiv2024

SARMA: Scalable Low-Rank High-Dimensional Autoregressive Moving Averages via Tensor Decomposition

Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less considered. This paper introduces a Tucker-low-rank framework to efficiently capture VARMA-type dynamics for high-dimensional time series, named the Scalable ARMA (SARMA) model. It generalizes the Tucker-low-rank finite-order VAR model to the infinite-order case via flexible parameterizations of the AR coefficient tensor along the temporal dimension. The resulting model enables dynamic factor extraction across response and predictor variables, facilitating interpretation of group patterns. Additionally, we consider sparsity assumptions on the factor loadings to accomplish automatic variable selection and greater estimation efficiency. Both rank-constrained and sparsity-inducing estimators are developed for the proposed model, along with algorithms and model selection methods. The validity of our theory and empirical advantages of our approach are confirmed by simulation studies and real data examples.

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arXiv2023

Supervised Factor Modeling for High-Dimensional Linear Time Series

Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model with two factor modelings being conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso estimation is considered for high-dimensional linear time series. Its non-asymptotic properties are discussed thoughtfully by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with thresholding is designed to search for high-dimensional estimates, and its theoretical justifications, including statistical and convergence analysis, are also provided. Theoretical and computational properties of the proposed methodology are verified by simulation experiments, and the advantages over existing methods are demonstrated by two real examples.

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arXiv2023

HAR-Ito models and high-dimensional HAR modeling for high-frequency data

It is an important task to model realized volatilities for high-frequency data in finance and economics and, as arguably the most popular model, the heterogeneous autoregressive (HAR) model has dominated the applications in this area. However, this model suffers from three drawbacks: (i.) its heterogeneous volatility components are linear combinations of daily realized volatilities with fixed weights, which limit its flexibility for different types of assets, (ii.) it is still unknown what is the high-frequency probabilistic structure for this model, as well as many other HAR-type models in the literature, and (iii.) there is no high-dimensional inference tool for HAR modeling although it is common to encounter many assets in real applications. To overcome these drawbacks, this paper proposes a multilinear low-rank HAR model by using tensor techniques, where a data-driven method is adopted to automatically select the heterogeneous components. In addition, HAR-Itô models are introduced to interpret the corresponding high-frequency dynamics, as well as those of other HAR-type models. Moreover, non-asymptotic properties of the high-dimensional HAR modeling are established, and a projected gradient descent algorithm with theoretical justifications is suggested to search for estimates. Theoretical and computational properties of the proposed method are verified by simulation studies, and the necessity of using the data-driven method for heterogeneous components is illustrated in real data analysis.

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