IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v168y2022ics0167947321002176.html
   My bibliography  Save this article

Confidence intervals for parameters in high-dimensional sparse vector autoregression

Author

Listed:
  • Zhu, Ke
  • Liu, Hanzhong

Abstract

Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference of the transition matrices of VAR models are crucial for practitioners to make decisions in fields such as economics and finance. However, when the number of variables is larger than the sample size, it remains a challenge to perform inference of the model parameters. The de-biased Lasso and two bootstrap de-biased Lasso methods are proposed to construct confidence intervals for the elements of the transition matrices of high-dimensional VAR models. The proposed methods are asymptotically valid under appropriate sparsity and other regularity conditions. Moreover, feasible and parallelizable algorithms are developed to implement the proposed methods, which save a large amount of computational cost required by the nodewise Lasso and bootstrap. Simulation studies illustrate that the proposed methods perform well in finite-samples. Finally, the proposed methods are applied to analyze the price data of stocks in the S&P 500 index. Some stocks, such as the largest producer of gold in the world, Newmont Corporation, are found to have significant predictive power over most stocks.

Suggested Citation

  • Zhu, Ke & Liu, Hanzhong, 2022. "Confidence intervals for parameters in high-dimensional sparse vector autoregression," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
  • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002176
    DOI: 10.1016/j.csda.2021.107383
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321002176
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2021.107383?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. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    2. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    3. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    4. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 685-719, December.
    5. Nicholson, William B. & Matteson, David S. & Bien, Jacob, 2017. "VARX-L: Structured regularization for large vector autoregressions with exogenous variables," International Journal of Forecasting, Elsevier, vol. 33(3), pages 627-651.
    6. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    7. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    8. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    9. Wilms, Ines & Gelper, Sarah & Croux, Christophe, 2016. "The predictive power of the business and bank sentiment of firms: A high-dimensional Granger Causality approach," European Journal of Operational Research, Elsevier, vol. 254(1), pages 138-147.
    10. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.
    11. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pagnottoni, Paolo & Spelta, Alessandro, 2023. "The motifs of risk transmission in multivariate time series: Application to commodity prices," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).

    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. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    2. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 21(3), pages 915-958.
    3. Claude Renaux & Laura Buzdugan & Markus Kalisch & Peter Bühlmann, 2020. "Hierarchical inference for genome-wide association studies: a view on methodology with software," Computational Statistics, Springer, vol. 35(1), pages 1-40, March.
    4. Zachary F. Fisher & Younghoon Kim & Barbara L. Fredrickson & Vladas Pipiras, 2022. "Penalized Estimation and Forecasting of Multiple Subject Intensive Longitudinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 1-29, June.
    5. Christophe Chorro & Emmanuelle Jay & Philippe De Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Documents de travail du Centre d'Economie de la Sorbonne 21013, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series 1327, University of St. Gallen, School of Economics and Political Science.
    7. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "Rejoinder on: High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 751-758, December.
    8. Victor Chernozhukov & Wolfgang Härdle & Chen Huang & Weining Wang, 2018. "LASSO-driven inference in time and space," CeMMAP working papers CWP36/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Camehl, Annika, 2023. "Penalized estimation of panel vector autoregressive models: A panel LASSO approach," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1185-1204.
    10. Christophe Chorro & Emmanuelle Jay & Philippe de Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Post-Print halshs-03216938, HAL.
    11. Matteo Barigozzi & Marc Hallin, 2017. "A network analysis of the volatility of high dimensional financial series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 581-605, April.
    12. Nicholson, William B. & Matteson, David S. & Bien, Jacob, 2017. "VARX-L: Structured regularization for large vector autoregressions with exogenous variables," International Journal of Forecasting, Elsevier, vol. 33(3), pages 627-651.
    13. Christophe Chorro & Emmanuelle Jay & Philippe de Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03216938, HAL.
    14. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Papers 1510.05118, arXiv.org, revised Jul 2016.
    15. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    16. Dominik Bertsche & Ralf Brüggemann & Christian Kascha, 2023. "Directed graphs and variable selection in large vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 223-246, March.
    17. Gianluca Cubadda & Marco Mazzali, 2023. "The Vector Error Correction Index Model: Representation, Estimation and Identification," CEIS Research Paper 556, Tor Vergata University, CEIS, revised 04 Apr 2023.
    18. Calvo-Pardo, Hector & Mancini, Tullio & Olmo, Jose, 2021. "Granger causality detection in high-dimensional systems using feedforward neural networks," International Journal of Forecasting, Elsevier, vol. 37(2), pages 920-940.
    19. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    20. Zhou, Jia & Zheng, Zemin & Zhou, Huiting & Dong, Ruipeng, 2021. "Innovated scalable efficient inference for ultra-large graphical models," Statistics & Probability Letters, Elsevier, vol. 173(C).

    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:168:y:2022:i:c:s0167947321002176. 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.