Threshold factor models for high-dimensional time series

Liu, Xialu; Chen, Rong

doi:10.1016/j.jeconom.2020.01.005

Cited by 22 publications

(27 citation statements)

References 41 publications

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“…Qs,i is estimated by the eigenvectors of Ms,i (r LCR , rLCR ) corresponding to the k s,i largest eigenvalues. From Table 2, it can be seen that our method outperforms the one by Liu and Chen (2020).…”

Section: Ta B L Ementioning

confidence: 87%

“…Lam and Yao (2012) only prove that the probability to underestimate the number of factors goes to zero asymptotically. Although the consistency of the ratio-based estimator cannot obtained, the method performs well in numerical experiments; see examples in Chang et al (2015), Liu and Chen (2016), Liu and Chen (2020), Liu and Zhang (2022), Wang et al (2019).…”

Section: When the Numbers Of Factors Are Unknownmentioning

confidence: 98%

“…When the numbers of factors are correctly specified or overestimated, our method can estimate loading spaces precisely. Compared the proposed estimators with the ones in Liu and Chen (2020), ours performs much better when sample size is relatively small or there are weak factors. When sample size is large (T = 400) and factors are strong, two methods can both estimate B s,i in (11) very well, so the estimation results are very close.…”

Section: Ta B L Ementioning

confidence: 99%

“…First, we consider the case where dimensions of the latent factor matrix may vary in different regimes. This removes the limitation of the methods proposed in Massacci (2017), Liu and Chen (2020), and Wu (2021), all of which require the number of factors to remain the same across regimes. Second, our algorithm is able to identify the thresholding mechanism when the number of thresholds is unknown.…”

Section: Introductionmentioning

confidence: 99%

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Identification and estimation of threshold matrix‐variate factor models

Liu

Chen

2022

Scandinavian J Statistics

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Motivated by the growing availability of complex time series observed in real applications, we propose a threshold matrix‐variate factor model, which simultaneously addresses the sample‐wise and time‐wise complexities of a time series. The sample‐wise complexity is characterized by modeling matrix‐variate observations directly, while the time‐wise complexity is modeled by a threshold variable to describe the nonlinearity in time series. The estimators for loading spaces and threshold values are introduced and their asymptotic properties are investigated. Our matrix‐variate models compress data more efficiently than traditional vectorization‐based models. Furthermore, we greatly extend the scope of current research on threshold factor models by removing several restrictive assumptions, including existence of only one threshold, fixed factor dimensions across different regimes, and stationarity within regime. Under the relaxed assumptions, the proposed estimators are consistent even when the numbers of factors are overestimated. Simulated and real examples are presented to illustrate the proposed methods.

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Section: Ta B L Ementioning

confidence: 87%

Section: When the Numbers Of Factors Are Unknownmentioning

confidence: 98%

Section: Ta B L Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification and estimation of threshold matrix‐variate factor models

Liu

Chen

2022

Scandinavian J Statistics

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“…Extensions and applications of the matrix factor model include the dynamic transport network in the context of international trade flows by Chen and Chen (2020), the constrained matrix factor model by Chen et al (2020b), and the threshold matrix factor model in Liu and Chen (2020).…”

Section: Introductionmentioning

confidence: 99%

Matrix Factor Analysis: From Least Squares to Iterative Projection

He¹,

Kong²,

Liu³

et al. 2021

Preprint

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In the article we focus on large-dimensional matrix factor models and propose estimators of factor loading matrices and factor score matrix from the perspective of minimizing least squares objective function. The resultant estimators turns out to be equivalent to the corresponding projected estimators in Yu et al. (2021), which enjoys the nice properties of reducing the magnitudes of the idiosyncratic error components and thereby increasing the signal-to-noise ratio. We derive the convergence rate of the theoretical minimizers under sub-Gaussian tails, instead of the one-step iteration estimators by Yu et al. (2021). Motivated by the least squares formulation, we further consider a robust method for estimating large-dimensional matrix factor model by utilizing Huber Loss function. Theoretically, we derive the convergence rates of the robust estimators of the factor loading matrices under finite fourth moment conditions. We also propose an iterative procedure to estimate the pair of row and column factor numbers robustly. We conduct extensive numerical studies to investigate the empirical performance of the proposed robust methods relative to the sate-of-theart ones, which show the proposed ones perform robustly and much better than the existing ones when data are heavy-tailed while perform almost the same (comparably) with the projected estimators when data are light-tailed, and as a result can be used as a safe replacement of the existing ones. An application to a Fama-French financial portfolios dataset illustrates its empirical usefulness.

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