IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v129y2019icp30-46.html
   My bibliography  Save this article

Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap

Author

Listed:
  • Dickhaus, Thorsten
  • Sirotko-Sibirskaya, Natalia

Abstract

Statistical inference methodology in dynamic factor models (DFMs) is extended to the multiple testing context based on a central limit theorem for empirical Fourier transforms of multivariate time series. This theoretical result allows for employing a vector of Wald-type test statistics which asymptotically follows a multivariate chi-square distribution under the global null hypothesis when the observation horizon tends to infinity. Multiplicity-adjusted asymptotic multiple test procedures based on Wald statistics are compared with a model-based bootstrap procedure proposed in recent previous work. Monte Carlo simulations demonstrate that both the asymptotic multiple chi-square test with an appropriate multiplicity adjustment and the bootstrap-based multiple test procedure keep the family-wise error rate approximately at the predefined significance level. The estimation algorithm as well as the implementation of the testing procedures are described in detail and a real-life application is performed on European commodity data.

Suggested Citation

  • Dickhaus, Thorsten & Sirotko-Sibirskaya, Natalia, 2019. "Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 30-46.
    • Handle: RePEc:eee:csdana:v:129:y:2019:i:c:p:30-46
    DOI: 10.1016/j.csda.2018.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301956
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.08.012?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. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    3. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, January.
    4. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    5. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
    6. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    7. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    8. Geweke, John F & Singleton, Kenneth J, 1981. "Maximum Likelihood "Confirmatory" Factor Analysis of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 37-54, February.
    9. Jean Boivin & Marc P. Giannoni & Benoît Mojon, 2008. "How Has the Euro Changed the Monetary Transmission?," NBER Working Papers 14190, National Bureau of Economic Research, Inc.
    10. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    11. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    12. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    13. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    14. R. Lockhart, 1967. "Asymptotic sampling variances for factor analytic models identified by specified zero parameters," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 265-277, September.
    15. Thorsten Dickhaus, 2012. "Simultaneous Statistical Inference in Dynamic Factor Models," SFB 649 Discussion Papers SFB649DP2012-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    17. 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.
    18. Chris Heaton & Victor Solo, 2004. "Identification of causal factor models of stationary time series," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 618-627, December.
    19. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    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. 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.
    2. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    3. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    4. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," PSE Working Papers halshs-02262202, HAL.
    5. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers halshs-02262202, HAL.
    6. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    7. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    8. Ma, Tao & Zhou, Zhou & Antoniou, Constantinos, 2018. "Dynamic factor model for network traffic state forecast," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 281-317.
    9. Bates, Brandon J. & Plagborg-Møller, Mikkel & Stock, James H. & Watson, Mark W., 2013. "Consistent factor estimation in dynamic factor models with structural instability," Journal of Econometrics, Elsevier, vol. 177(2), pages 289-304.
    10. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.
    11. Bork, Lasse, 2009. "Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach," Finance Research Group Working Papers F-2009-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    12. Ortega, Jose Antonio & Poncela, Pilar, 2005. "Joint forecasts of Southern European fertility rates with non-stationary dynamic factor models," International Journal of Forecasting, Elsevier, vol. 21(3), pages 539-550.
    13. Francisco Corona & Pedro Orraca, 2019. "Remittances in Mexico and their unobserved components," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 28(8), pages 1047-1066, November.
    14. André Nunes Maranhão & Nicole Rennó Castro, 2023. "Dissecting Brazilian agriculture business cycles in high-dimensional and time-irregular span contexts," Empirical Economics, Springer, vol. 65(4), pages 1543-1578, October.
    15. Lippi, Marco & Deistler, Manfred & Anderson, Brian, 2023. "High-Dimensional Dynamic Factor Models: A Selective Survey and Lines of Future Research," Econometrics and Statistics, Elsevier, vol. 26(C), pages 3-16.
    16. Kihwan Kim & Norman Swanson, 2013. "Diffusion Index Model Specification and Estimation Using Mixed Frequency Datasets," Departmental Working Papers 201315, Rutgers University, Department of Economics.
    17. Jason Angelopoulos, 2017. "Creating and assessing composite indicators: Dynamic applications for the port industry and seaborne trade," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 19(1), pages 126-159, March.
    18. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    19. Xu Cheng & Bruce E. Hansen, 2012. "Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach, Second Version," PIER Working Paper Archive 13-061, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Sep 2013.
    20. Ard H.J. den Reijer, 2005. "Forecasting Dutch GDP using Large Scale Factor Models," DNB Working Papers 028, Netherlands Central Bank, Research Department.

    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:129:y:2019:i:c:p:30-46. 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.