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Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes

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  • Paparoditis, Efstathios

Abstract

We consider anr-dimensional multivariate time series {yt, t[set membership, variant]Z} which is generated by an infinite order vector autoregressive process. We show that a bootstrap procedure which works by generating time series replicates via an estimated finitek-order vector autoregressive process (k-->[infinity] at an appropriate rate with the sample size) gives asymptotically valid approximations to the joint distribution of the growing set of estimated autoregressive coefficients and to the corresponding set of estimated moving average coefficients (impuls responses).

Suggested Citation

  • Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
  • Handle: RePEc:eee:jmvana:v:57:y:1996:i:2:p:277-296
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    Cited by:

    1. Berkowitz, J. & Birgean, I. & Kilian, L., 1999. "On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series," Papers 99-01, Michigan - Center for Research on Economic & Social Theory.
    2. Ionel Birgean & Lutz Kilian, 2002. "Data-Driven Nonparametric Spectral Density Estimators For Economic Time Series: A Monte Carlo Study," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 449-476.
    3. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    4. Meyer, Marco & Jentsch, Carsten & Kreiss, Jens-Peter, 2015. "Baxter`s inequality and sieve bootstrap for random fields," Working Papers 15-06, University of Mannheim, Department of Economics.
    5. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    7. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 10-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Laura Mayoral, 2013. "Heterogeneous Dynamics, Aggregation, And The Persistence Of Economic Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 1295-1307, November.
    9. Jentsch, Carsten & Kreiss, Jens-Peter, 2010. "The multiple hybrid bootstrap -- Resampling multivariate linear processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2320-2345, November.
    10. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    11. Pesaran, Mohammad Hashem & Holly, Sean & Dees, Stephane & Smith, L. Vanessa, 2007. "Long Run Macroeconomic Relations in the Global Economy," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 1, pages 1-20.
    12. Psaradakis, Zacharias, 2001. "On bootstrap inference in cointegrating regressions," Economics Letters, Elsevier, vol. 72(1), pages 1-10, July.
    13. Ricardo Cao, 1999. "An overview of bootstrap methods for estimating and predicting in time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 95-116, June.
    14. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Marco Meyer & Jens-Peter Kreiss, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 377-397, May.
    15. Marian Vavra, 2015. "On a Bootstrap Test for Forecast Evaluations," Working and Discussion Papers WP 5/2015, Research Department, National Bank of Slovakia.
    16. Zacharias Psaradakis & Marian Vavra, 2017. "Normality Tests for Dependent Data," Working and Discussion Papers WP 12/2017, Research Department, National Bank of Slovakia.
    17. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    18. Bouhaddioui, Chafik & Roy, Roch, 2006. "On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 58-68, January.
    19. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(03), pages 647-681, June.
    20. Chafik Bouhaddioui & Roch Roy, 2004. "A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2004s-06, CIRANO.
    21. Peter Brockwell & Jens-Peter Kreiss & Tobias Niebuhr, 2014. "Bootstrapping continuous-time autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 75-92, February.
    22. Chafik Bouhaddioui & Roch Roy, 2003. "On the Distribution of the Residual Cross-Correlations between Two Uncorrelated Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2003s-41, CIRANO.
    23. You, Jinhong & Zhou, Xian & Zhu, Li-Xing, 2009. "Inference on a regression model with noised variables and serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1182-1197, July.
    24. Richard T. Baillie & George Kapetanios & Fotis Papailias, 2015. "Inference for Impulse Response Coefficients From Multivariate Fractionally Integrated Processes," Working Paper series 15-46, Rimini Centre for Economic Analysis.

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