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

Zhaoxing Gao, Ruey S. Tsay

arXiv 18 Nov 2020 · Econometrics · publishedEconometrics and Statistics (2021) · 6 citations (OpenAlex)

arXiv:2011.09029 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

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39
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Wang, D., Liu, X. and Chen, R (2019) Factor Models for Matrix-Valued High-Dimensional Time Series0.97614593%
2Gao, Z. and Tsay, R. S (2020) Modeling high-dimensional time series: a factor model with dynamically dependent factors and diverging eigenvalues self0.86620665%
3Lam, C., Yao, Q. and Bathia, N (2011) Estimation of latent factors for high-dimensional time series0.8434375%
4Gao, Z. and Tsay, R. S (2019) A structural-factor approach for modeling high-dimensional time series and space-time data self0.84333100%
5Tiao, G. C. and Tsay, R. S. (1989). Model specification in multivari… Journal of the Royal Statistical Society, B51, 157–213 self0.73732100%
6Tsay, R. S (2020) Testing for serial correlations in high-dimensional time series via extreme value theory self0.73732100%
7Chang, J., Yao, Q. and Zhou, W (2017) Testing for high-dimensional white noise using maximum cross-correlations0.6443267%
8Tsay, R. S (2014) Multivariate Time Series Analysis self0.64422100%
9Chen, R., Xiao, H., and Yang, D (2020) Autoregressive models for matrix-valued time series0.64422100%
10Pan, J. and Yao, Q (2008) Modelling multiple time series via common factors0.64422100%

Showing the top 10 of 39 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Determination of the effective cointegration rank in high-dimensional time-series predictive regressions0.51121
2A Hybrid Framework Combining Autoregression and Common Factors for Matrix Time Series0.40511
3High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting0.40511
4High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions0.40511
5Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon in High-Dimensional Time Series0.00011