IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v157y2021ics0167947320302553.html
   My bibliography  Save this article

Principal component analysis using frequency components of multivariate time series

Author

Listed:
  • Sundararajan, Raanju R.

Abstract

Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. A spectral domain method is developed for multivariate second-order stationary time series that linearly transforms the observed series into several groups of lower-dimensional multivariate subseries. These multivariate subseries have non-zero spectral coherence among components within a group but have zero spectral coherence among components across groups. The observed series is expressed as a sum of frequency components whose variances are proportional to the spectral matrices at the respective frequencies. The demixing matrix is then estimated using an eigendecomposition on the sum of the variance matrices of these frequency components and its asymptotic properties are derived. Finally, a consistent test on the cross-spectrum of pairs of components is used to find the desired segmentation into the lower-dimensional subseries. The numerical performance of the proposed method is illustrated through simulation examples and an application to modeling and forecasting wind data is presented.

Suggested Citation

  • Sundararajan, Raanju R., 2021. "Principal component analysis using frequency components of multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302553
    DOI: 10.1016/j.csda.2020.107164
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320302553
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.107164?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.
    2. Jiazhu Pan & Qiwei Yao, 2008. "Modelling multiple time series via common factors," Biometrika, Biometrika Trust, vol. 95(2), pages 365-379.
    3. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, October.
    4. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    5. Giovanni Motta & Hernando Ombao, 2012. "Evolutionary Factor Analysis of Replicated Time Series," Biometrics, The International Biometric Society, vol. 68(3), pages 825-836, September.
    6. Pan, Jiazhu & Yao, Qiwei, 2008. "Modelling multiple time series via common factors," LSE Research Online Documents on Economics 22876, London School of Economics and Political Science, LSE Library.
    7. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2018. "Principal component analysis for second-order stationary vector time series," LSE Research Online Documents on Economics 84106, London School of Economics and Political Science, LSE Library.
    8. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    9. Amanda Lenzi & Ingelin Steinsland & Pierre Pinson, 2018. "Benefits of spatiotemporal modeling for short‐term wind power forecasting at both individual and aggregated levels," Environmetrics, John Wiley & Sons, Ltd., vol. 29(3), May.
    10. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    11. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    12. Kaizô I. BeltraTo & Peter Bloomfield, 1987. "Determining The Bandwidth Of A Kernel Spectrum Estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 21-38, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fayed Alshammri & Jiazhu Pan, 2021. "Moving dynamic principal component analysis for non-stationary multivariate time series," Computational Statistics, Springer, vol. 36(3), pages 2247-2287, September.
    2. Daniel Peña & Victor J. Yohai, 2016. "Generalized Dynamic Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1121-1131, July.
    3. repec:cte:wsrepe:27047 is not listed on IDEAS
    4. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised Jul 2024.
    5. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    6. Xia, Qiang & Liang, Rubing & Wu, Jianhong, 2017. "Transformed contribution ratio test for the number of factors in static approximate factor models," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 235-241.
    7. Zhaoxing Gao & Ruey S. Tsay, 2020. "A Two-Way Transformed Factor Model for Matrix-Variate Time Series," Papers 2011.09029, arXiv.org.
    8. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    9. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    10. Yuefeng Han & Dan Yang & Cun-Hui Zhang & Rong Chen, 2021. "CP Factor Model for Dynamic Tensors," Papers 2110.15517, arXiv.org, revised Apr 2024.
    11. Zhaoxing Gao & Ruey S. Tsay, 2021. "Divide-and-Conquer: A Distributed Hierarchical Factor Approach to Modeling Large-Scale Time Series Data," Papers 2103.14626, arXiv.org.
    12. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "Estimation of Cross-Sectional Dependence in Large Panels," Papers 1904.06843, arXiv.org.
    13. Gao, Zhaoxing & Tsay, Ruey S., 2021. "Modeling high-dimensional unit-root time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1535-1555.
    14. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 9/19, Monash University, Department of Econometrics and Business Statistics.
    15. Xialu Liu & John Guerard & Rong Chen & Ruey Tsay, 2024. "Improving Estimation of Portfolio Risk Using New Statistical Factors," Papers 2409.17182, arXiv.org.
    16. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    17. Zhaoxing Gao & Ruey S. Tsay, 2020. "Modeling High-Dimensional Unit-Root Time Series," Papers 2005.03496, arXiv.org, revised Aug 2020.
    18. He, Lingyu & Huang, Fei & Shi, Jianjie & Yang, Yanrong, 2021. "Mortality forecasting using factor models: Time-varying or time-invariant factor loadings?," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 14-34.
    19. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    20. Jiti Gao & Guangming Pan & Yanrong Yang, 2016. "CEstimation of Structural Breaks in Large Panels with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 12/16, Monash University, Department of Econometrics and Business Statistics.
    21. Chen Tang & Yanlin Shi, 2021. "Forecasting High-Dimensional Financial Functional Time Series: An Application to Constituent Stocks in Dow Jones Index," JRFM, MDPI, vol. 14(8), pages 1-13, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302553. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.