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Least squares estimation of large dimensional threshold factor models

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  • Massacci, Daniele

Abstract

This paper studies large dimensional factor models with threshold-type regime shifts in the loadings. We estimate the threshold by concentrated least squares, and factors and loadings by principal components. The estimator for the threshold is superconsistent, with convergence rate that depends on the time and cross-sectional dimensions of the panel, and it does not affect the estimator for factors and loadings: this has the same convergence rate as in linear factor models. We propose model selection criteria and a linearity test. Empirical application of the model shows that connectedness in financial variables increases during periods of high economic policy uncertainty.

Suggested Citation

  • Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    • Handle: RePEc:eee:econom:v:197:y:2017:i:1:p:101-129
    DOI: 10.1016/j.jeconom.2016.11.001
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    4. Thomas Despois & Catherine Doz, 2021. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," PSE Working Papers halshs-02235543, HAL.
    5. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    6. Bai, Jushan & Han, Xu & Shi, Yutang, 2020. "Estimation and inference of change points in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 219(1), pages 66-100.
    7. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    8. Zhou, Ruichao & Wu, Jianhong, 2023. "Determining the number of change-points in high-dimensional factor models by cross-validation with matrix completion," Economics Letters, Elsevier, vol. 232(C).
    9. Giovanni Urga & Fa Wang, 2022. "Estimation and Inference for High Dimensional Factor Model with Regime Switching," Papers 2205.12126, arXiv.org, revised Apr 2023.
    10. Aslanidis, Nektarios & Hartigan, Luke, 2021. "Is the assumption of constant factor loadings too strong in practice?," Economic Modelling, Elsevier, vol. 98(C), pages 100-108.
    11. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    12. Matteo Barigozzi, 2022. "On Estimation and Inference of Large Approximate Dynamic Factor Models via the Principal Component Analysis," Papers 2211.01921, arXiv.org, revised Jul 2023.
    13. Xialu Liu & John Guerard & Rong Chen & Ruey Tsay, 2024. "Improving Estimation of Portfolio Risk Using New Statistical Factors," Papers 2409.17182, arXiv.org.
    14. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    15. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2021. "Estimating and testing high dimensional factor models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 220(2), pages 349-365.
    16. Urga, Giovanni & Wang, Fa, 2022. "Estimation and Inference for High Dimensional Factor Model with Regime Switching," MPRA Paper 117012, University Library of Munich, Germany, revised 10 Apr 2023.
    17. Thomas Despois & Catherine Doz, 2021. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Working Papers halshs-02235543, HAL.
    18. Wu, Jianhong, 2021. "Estimation of high dimensional factor model with multiple threshold-type regime shifts," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    19. Xialu Liu & Elynn Y. Chen, 2022. "Identification and estimation of threshold matrix‐variate factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1383-1417, September.
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    More about this item

    Keywords

    Large threshold factor model; Least squares estimation; Model selection; Linearity testing; Connectedness;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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