IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v42y2021i2p201-221.html
   My bibliography  Save this article

Estimating wold matrices and vector moving average processes

Author

Listed:
  • Jonas Krampe
  • Timothy L. McMurry

Abstract

The Wold decomposition gives a moving average (MA) representation of a purely non‐deterministic stationary process. In this article, we derive estimates of the Wold matrices for a d‐dimensional process by using a Cholesky decomposition of a banded and tapered version of the sample autocovariance matrix, and we derive convergence rates for the estimation error of the (possibly infinite) sequence of Wold matrices. By analogy to lag‐window estimates of the spectral density, this method can be used to obtain finite vector MA models with an adaptive lag‐order. We additionally show how these results can be applied to impulse response analysis and to derive a bootstrap procedure. Our theoretical results are complemented by simulations which investigate the finite sample performance of the estimator.

Suggested Citation

  • Jonas Krampe & Timothy L. McMurry, 2021. "Estimating wold matrices and vector moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 201-221, March.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:2:p:201-221
    DOI: 10.1111/jtsa.12562
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12562
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12562?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
    ---><---

    References listed on IDEAS

    as
    1. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575.
    2. Takemura, Akimichi, 2016. "Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 207-210.
    3. McMurry, Timothy L & Politis, D N, 2010. "Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap," University of California at San Diego, Economics Working Paper Series qt5h9259mb, Department of Economics, UC San Diego.
    4. Timothy L. McMurry & Dimitris N. Politis, 2010. "Banded and tapered estimates for autocovariance matrices and the linear process bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 471-482, November.
    5. Timothy L. McMurry & Dimitris N. Politis, 2018. "Estimating MA Parameters through Factorization of the Autocovariance Matrix and an MA†Sieve Bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(3), pages 433-446, May.
    6. Heather Mitchell & Peter Brockwell, 1997. "Estimation Of The Coefficients Of A Multivariate Linear Filter Using The Innovations Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 157-179, March.
    7. Jonas Krampe & Jens‐Peter Kreiss & Efstathios Paparoditis, 2018. "Estimated Wold representation and spectral‐density‐driven bootstrap for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 703-726, September.
    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. Tianming Xu & Yuesong Wei, 2023. "Ratio Test for Mean Changes in Time Series with Heavy-Tailed AR( p ) Noise Based on Multiple Sampling Methods," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    2. Petropoulos, Fotios & Hyndman, Rob J. & Bergmeir, Christoph, 2018. "Exploring the sources of uncertainty: Why does bagging for time series forecasting work?," European Journal of Operational Research, Elsevier, vol. 268(2), pages 545-554.
    3. Gonçalves, Sílvia & Perron, Benoit, 2020. "Bootstrapping factor models with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 218(2), pages 476-495.
    4. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
    5. Politis, Dimitris, 2014. "High-dimensional autocovariance matrices and optimal linear prediction," University of California at San Diego, Economics Working Paper Series qt3k58p0xr, Department of Economics, UC San Diego.
    6. Zhao, Shi & Bakoyannis, Giorgos & Lourens, Spencer & Tu, Wanzhu, 2020. "Comparison of nonlinear curves and surfaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    7. Ryan Janicki & Tucker S. McElroy, 2016. "Hermite expansion and estimation of monotonic transformations of Gaussian data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 207-234, March.
    8. Meira, Erick & Cyrino Oliveira, Fernando Luiz & de Menezes, Lilian M., 2021. "Point and interval forecasting of electricity supply via pruned ensembles," Energy, Elsevier, vol. 232(C).
    9. Jiang Wang & Dimitris N. Politis, 2021. "Consistent autoregressive spectral estimates: Nonlinear time series and large autocovariance matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 580-596, September.
    10. Tommaso Proietti & Alessandro Giovannelli, 2018. "A Durbin–Levinson regularized estimator of high-dimensional autocovariance matrices," Biometrika, Biometrika Trust, vol. 105(4), pages 783-795.
    11. Konrad Furmańczyk, 2021. "Estimation of autocovariance matrices for high dimensional linear processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 595-613, May.
    12. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
    13. Fotios Petropoulos & Evangelos Spiliotis, 2021. "The Wisdom of the Data: Getting the Most Out of Univariate Time Series Forecasting," Forecasting, MDPI, vol. 3(3), pages 1-20, June.
    14. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    15. Holger Dette & Weichi Wu, 2020. "Prediction in locally stationary time series," Papers 2001.00419, arXiv.org, revised Jan 2020.
    16. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
    17. Zou, Nan & Politis, Dimitris N., 2019. "Linear process bootstrap unit root test," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 74-80.
    18. Rajapaksha, Dilini & Bergmeir, Christoph & Hyndman, Rob J., 2023. "LoMEF: A framework to produce local explanations for global model time series forecasts," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1424-1447.
    19. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.
    20. Hendry, David F. & Martinez, Andrew B., 2017. "Evaluating multi-step system forecasts with relatively few forecast-error observations," International Journal of Forecasting, Elsevier, vol. 33(2), pages 359-372.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:42:y:2021:i:2:p:201-221. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.