The likelihood ratio test for structural changes in factor models

Jushan Bai; Jiangtao Duan; Xu Han

doi:10.1016/j.jeconom.2023.105631

The likelihood ratio test for structural changes in factor models

Jushan Bai
, Jiangtao Duan
, Xu Han^*

^*Corresponding author for this work

Department of Economics and Finance

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

15 Citations (Scopus)

Abstract

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data.

© 2023 Elsevier B.V. All rights reserved.

Original language	English
Article number	105631
Journal	Journal of Econometrics
Volume	238
Issue number	2
Online published	2 Jan 2024
DOIs	https://doi.org/10.1016/j.jeconom.2023.105631
Publication status	Published - Jan 2024

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This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Research Keywords

High-dimensional factor models
Structural breaks
LR test

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10.1016/j.jeconom.2023.105631

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title = "The likelihood ratio test for structural changes in factor models",

abstract = "A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data. {\textcopyright} 2023 Elsevier B.V. All rights reserved.",

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T1 - The likelihood ratio test for structural changes in factor models

AU - Bai, Jushan

AU - Duan, Jiangtao

AU - Han, Xu

PY - 2024/1

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N2 - A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data. © 2023 Elsevier B.V. All rights reserved.

AB - A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data. © 2023 Elsevier B.V. All rights reserved.

KW - High-dimensional factor models

KW - Structural breaks

KW - LR test

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85181773645&origin=recordpage

U2 - 10.1016/j.jeconom.2023.105631

DO - 10.1016/j.jeconom.2023.105631

M3 - RGC 21 - Publication in refereed journal

SN - 0304-4076

VL - 238

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

M1 - 105631

ER -

The likelihood ratio test for structural changes in factor models

Abstract

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