Estimation of high dimensional factor model with multiple threshold-type regime shifts

Wu, Jianhong

doi:10.1016/j.csda.2020.107153

Cited by 3 publications

(7 citation statements)

References 17 publications

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“…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%

“…The most widely studied model in econometrics, called approximate factor model, searches for common factors that affect the dynamics of most of time series in the cross‐section dimension, and allows limited time‐series and cross‐section dependence in the idiosyncratic component; see Assumptions B and C in Bai (2003). Many existing theoretical results on factor models were derived under this setting; see examples Chen et al (2014), Barigozzi et al (2018), Barigozzi and Cho (2020), Massacci (2017), Ma and Su (2018), Wu (2021) and references therein. Following the assumptions in the approximate factor model, Chen and Fan (2021) extended the model for matrix‐variate time series analysis.…”

Section: Introductionmentioning

confidence: 99%

“…However, literature has shown the presence of nonlinearity in many time series data (Fan & Yao, 2008; Tong & Lim, 1980; Tsay, 1989; Tsay, 1998). Particularly, the threshold effect is observed in many cases of factor models (Liu & Chen, 2020; Massacci, 2017; Wu, 2021). For example, CAPM theory indicates that the expected market return is an important factor for the expected return of various assets, and Liu and Chen (2016) found that its impact (loadings) on any individual asset may be different depending on whether a stock market is volatile or stable.…”

Section: Introductionmentioning

confidence: 99%

“…Liu and Chen (2020) developed a projection‐based objective function to estimate the threshold value. Wu (2021) discussed the case when the threshold variable divides the data into multiple regimes and proposed an algorithm to identify regime shifts. Our threshold matrix‐variate factor model generalizes its vector‐variate counterpart to directly handle the intrinsic matrix structure.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, current literature in threshold factor models (Liu & Chen, 2020; Massacci, 2017) only allows one threshold to divide data in two regimes. Third, the proposed estimation procedure can be applied to data that neither the factor or the noise process is stationary, while the method in Wu (2021) is limited to data in which latent factor and noise process are both strictly stationary. We only require the factor process to satisfy the mixing condition and the moments of factor and noise processes to be bounded.…”

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: Introductionmentioning

confidence: 99%