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Inference for Impulse Response Coefficients From Multivariate Fractionally Integrated Processes

Author

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  • Richard T. Baillie

    (Department of Economics, Michigan State University, USA; School of Economics and Finance, Queen Mary University of London, UK; The Rimini Centre for Economic Analysis, Italy)

  • George Kapetanios

    (School of Economics and Finance, Queen Mary University of London, UK)

  • Fotis Papailias

    (Queen's University Management School, Queen's University Belfast, UK; quantf research, www.quantf.com)

Abstract

This paper considers a multivariate system of fractionally integrated time series and investigates the most appropriate way for estimating Impulse Response (IR) coefficients and their associated confidence intervals. The paper extends the univariate analysis recently provided by Baillie and Kapetanios (2013), and uses a semi parametric, time domain estimator, based on a vector autoregression (VAR) approximation. Results are also derived for the orthogonalized estimated IRs which are generally more practically relevant. Simulation evidence strongly indicates the desirability of applying the Kilian small sample bias correction, which is found to improve the coverage accuracy of confidence intervals for IRs. The most appropriate order of the VAR turns out to be relevant for the lag length of the IR being estimated.

Suggested Citation

  • 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.
    • Handle: RePEc:rim:rimwps:15-46
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    1. Diebold, Francis X & Husted, Steven & Rush, Mark, 1991. "Real Exchange Rates under the Gold Standard," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1252-1271, December.
    2. Poskitt, D.S., 2016. "Vector autoregressive moving average identification for macroeconomic modeling: A new methodology," Journal of Econometrics, Elsevier, vol. 192(2), pages 468-484.
    3. D. S. Poskitt, 2005. "Autoregressive Approximation in Nonstandard Situations: The Non-Invertible and Fractionally Integrated Cases," Monash Econometrics and Business Statistics Working Papers 16/05, Monash University, Department of Econometrics and Business Statistics.
    4. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    5. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    6. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    7. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    8. Baillie, Richard T., 1987. "Inference in dynamic models containing 'surprise' variables," Journal of Econometrics, Elsevier, vol. 35(1), pages 101-117, May.
    9. Richard T. Baillie & George Kapetanios, 2013. "Estimation and inference for impulse response functions from univariate strongly persistent processes," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 373-399, October.
    10. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 697-725, December.
    11. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
    12. Pesavento, Elena & Rossi, Barbara, 2007. "Impulse response confidence intervals for persistent data: What have we learned?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2398-2412, July.
    13. Wright, Jonathan H, 2000. "Confidence Intervals for Univariate Impulse Responses with a Near Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 368-373, July.
    14. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    15. Lütkepohl, Helmut, 1988. "Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process," Econometric Theory, Cambridge University Press, vol. 4(1), pages 77-85, April.
    16. Schmidt, Peter, 1973. "The Asymptotic Distribution of Dynamic Multipliers," Econometrica, Econometric Society, vol. 41(1), pages 161-164, January.
    17. Mark J. Jensen, 2009. "The Long‐Run Fisher Effect: Can It Be Tested?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(1), pages 221-231, February.
    18. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
    19. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    20. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    21. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    22. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    23. Baillie, Richard T. & Chung, Sang-Kuck, 2002. "Modeling and forecasting from trend-stationary long memory models with applications to climatology," International Journal of Forecasting, Elsevier, vol. 18(2), pages 215-226.
    24. Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    25. Lutkepohl, Helmut, 1989. "A note on the asymptotic distribution of impulse response functions of estimated var models with orthogonal residuals," Journal of Econometrics, Elsevier, vol. 42(3), pages 371-376, November.
    26. Schmidt, Peter, 1977. "Some Small Evidence on the Distribution of Dynamic Simulation Forecasts," Econometrica, Econometric Society, vol. 45(4), pages 997-1005, May.
    27. Efrem Castelnuovo & Paolo Surico, 2010. "Monetary Policy, Inflation Expectations and The Price Puzzle," Economic Journal, Royal Economic Society, vol. 120(549), pages 1262-1283, December.
    28. 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.
    29. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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