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Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors

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Johansen (2000) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables are fat-tailed and often skewed, there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using a non-parametric bootstrap to approximate a Bartlett-type correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than estimating the p-value of the observed statistic.

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  • Canepa, Alessandra, 2021. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202108, University of Turin.
    • Handle: RePEc:uto:dipeco:202108
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    1. Denisard Alves & Regina Celia Cati & Vera Lucia Fava, 2001. "Purchasing power parity in Brazil: a test for fractional cointegration," Applied Economics, Taylor & Francis Journals, vol. 33(9), pages 1175-1185.
    2. Jean Imbs & Haroon Mumtaz & Morten O. Ravn & Hélène Rey, 2005. "PPP Strikes Back: Aggregation And the Real Exchange Rate," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 1-43.
    3. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    4. Weshah Razzak, 2018. "The Purchasing Power Parity Puzzle: An Update," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 61(2), pages 77-104.
    5. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    6. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    7. Boswijk, H. Peter & Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2016. "Inference on co-integration parameters in heteroskedastic vector autoregressions," Journal of Econometrics, Elsevier, vol. 192(1), pages 64-85.
    8. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert & Taylor, A.M. Robert, 2016. "Tests for explosive financial bubbles in the presence of non-stationary volatility," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 548-574.
    9. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    10. Nicholas Ford & Charles Yuji Horioka, 2017. "The ‘real’ explanation of the Feldstein–Horioka puzzle," Applied Economics Letters, Taylor & Francis Journals, vol. 24(2), pages 95-97, January.
    11. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    12. Kees Jan van Garderen, 1999. "Exact Geometry of Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 1-21, January.
    13. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    14. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2015. "Bootstrap Testing of Hypotheses on Co‐Integration Relations in Vector Autoregressive Models," Econometrica, Econometric Society, vol. 83, pages 813-831, March.
    15. Johansen, Søren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(5), pages 740-778, October.
    16. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.
    17. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    18. Antonio Costa & Nuno Crato, 2001. "Long-run versus short-run behaviour of the real exchange rates," Applied Economics, Taylor & Francis Journals, vol. 33(5), pages 683-688.
    19. A. Canepa & L. G. Godfrey, 2007. "Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 434-453, May.
    20. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    21. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    22. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2020. "Bartlett correction of frequency domain empirical likelihood for time series with unknown innovation variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1159-1173, October.
    23. A. Mansur & M. Masih & Rumi Masih, 2004. "Fractional cointegration, low frequency dynamics and long-run purchasing power parity: an analysis of the Australian dollar over its recent float," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 593-605.
    24. Doornik, Jurgen A. & O'Brien, R. J., 2002. "Numerically stable cointegration analysis," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 185-193, November.
    25. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
    26. Canepa, Alessandra, 2020. "Bootstrap Bartlett Adjustment for Hypotheses Testing on Cointegrating Vectors," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202006, University of Turin.
    27. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(1), pages 243-269, February.
    28. Carsten Jentsch & Kurt G. Lunsford, 2019. "The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States: Comment," American Economic Review, American Economic Association, vol. 109(7), pages 2655-2678, July.
    29. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    30. Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    31. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
    32. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    33. Psaradakis, Zacharias, 1994. "A comparison of tests of linear hypotheses in cointegrated vector autoregressive models," Economics Letters, Elsevier, vol. 45(2), pages 137-144, June.
    34. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    35. Canepa, Alessandra, 2006. "Small sample corrections for linear restrictions on cointegrating vectors: A Monte Carlo comparison," Economics Letters, Elsevier, vol. 91(3), pages 330-336, June.
    36. Charles Yuji Horioka & Nicholas Ford, 2017. "A possible explanation of the ‘Exchange Rate Disconnect Puzzle’: a common solution to three macroeconomic puzzles?," Applied Economics Letters, Taylor & Francis Journals, vol. 24(13), pages 918-922, July.
    37. Roman Frydman & Michael D. Goldberg & Søren Johansen & Katarina Juselius, 2008. "A Resolution of the Purchasing Power Parity Puzzle: Imperfect Knowledge and Long Swings," Discussion Papers 08-31, University of Copenhagen. Department of Economics.
    38. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    39. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    40. Gredenhoff, Mikael & Jacobson, Tor, 2001. "Bootstrap Testing Linear Restrictions on Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 63-72, January.
    41. Rolf Larsson, 1998. "Bartlett Corrections for Unit Root Test Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 425-438, July.
    42. Jacobson, Tor & Larsson, Rolf, 1999. "Bartlett corrections in cointegration testing," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 203-225, August.
    43. Bravo, Francesco, 1999. "A Correction Factor For Unit Root Test Statistics," Econometric Theory, Cambridge University Press, vol. 15(2), pages 218-227, April.
    44. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2016. "Bartlett Correction of Empirical Likelihood for Non-Gaussian Short-Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 624-649, September.
    45. Nalini Ravishanker & Edward L. Melnick & Chih‐Ling Tsai, 1990. "Differential Geometry Of Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 259-274, May.
    46. Canepa, Alessandra, 2016. "A note on Bartlett correction factor for tests on cointegrating relations," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 296-304.
    47. Podivinsky, Jan M., 1992. "Small sample properties of tests of linear restrictions on cointegrating vectors and their weights," Economics Letters, Elsevier, vol. 39(1), pages 13-18, May.
    48. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    49. Bernardo M. Lagos & Pedro A. Morettin, 2004. "Improvement of the Likelihood Ratio Test Statistic in ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 83-101, January.
    50. Kazem Falahati, 2019. "Time, Arbitrage, and the Law of One Price: The Case for a Paradigm Shift," Journal of Economic Issues, Taylor & Francis Journals, vol. 53(1), pages 115-154, January.
    51. Roger Fujihara & Keehwan Park, 1990. "The probability distribution of futures prices in the foreign exchange market: A comparison of candidate processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 10(6), pages 623-641, December.
    52. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    53. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
    54. Tucker, Alan L & Pond, Lallon, 1988. "The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 638-647, November.
    55. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    56. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators," Journal of Econometrics, Elsevier, vol. 152(1), pages 19-27, September.
    57. Haug, Alfred A., 2002. "Testing Linear Restrictions On Cointegrating Vectors: Sizes And Powers Of Wald And Likelihood Ratio Tests In Finite Samples," Econometric Theory, Cambridge University Press, vol. 18(2), pages 505-524, April.
    58. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    59. Zeng-Hua Lu, 2016. "Extended MaxT Tests of One-Sided Hypotheses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 423-437, March.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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