Application of bootstrap methods in investigation of size of the Granger causality test for integrated VAR systems

Lach, Łukasz (2010): Application of bootstrap methods in investigation of size of the Granger causality test for integrated VAR systems. Published in: Managing Global Transitions: International Research Journal , Vol. 8, (2010): pp. 167-186.

Abstract

This paper examines the size performance of Toda-Yamamoto test for Granger causality in case of trivariate integrated-cointegrated VAR systems and relatively small sample size. The standard asymptotic distribution theory and the residual-based bootstrap approach are applied. A variety of types of distribution of error term is considered. The impact of misspecification of initial parameters as well as the influence of increase of sample size and number of bootstrap replications on size performance of Toda-Yamamoto test statistics is also examined. The results of conducted simulation study confirm that standard asymptotic distribution theory may often cause significant over-rejection. Application of bootstrap methods usually leads to improvement of size performance of Toda-Yamamoto test. However, in some cases considered bootstrap method also leads to serious size distortion and performs worse than the traditional approach based on distribution.

• Item Type: MPRA Paper
• Language: English
• Keywords: bootstrap methods
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General

References

[1] Chou P.H. and Zhou G. (2006) Using Bootstrap to Test Portfolio Efficiency. Annals of economics and finance, 2, 217–249.

[2] Davidson R. and MacKinnon J.G (1996) The size distortion of bootstrap tests. Working paper, Department of Economics, Queen’s University, Canada.

[3] Davison A.C. and Hinkley D.V. (1999) Bootstrap Methods and Their Application. Cambridge University Press, Cambridge.

[4] Dolado J.J. and Lütkepohl H. (1996) Making Wald tests work for cointegrated VAR systems. Econometrics Reviews, 15, 369–386.

[5] Efron B. (1979) Bootstrap methods: Another look at the Jacknife. Annals of Statistics, 7, 1–26.

[6] Engle R.F. and Granger C.W.J. (1987) Cointegration and error correction: representation, estimation and testing. Econometrica, 55, 251–281.

[7] Granger C.W.J. (1969) Investigating causal relations by econometric models and cross–spectral methods. Econometrica, 37, 424–438.

[8] Granger C.W.J. and Newbold P. (1974), Spurious regression in econometrics. Journal of Econometrics, 2, 111–120.

[9] Granger C.W.J. (1988) Some recent developments in the concept of causality. Journal of Econometrics, 39, 199–211.

[10] Hacker R.S. and Hatemi-J A. (2006) Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application. Applied Economics, 38, 1489–1500.

[11] Hatemi-J A. (2003) A new method to choose optimal lag order in stable and unstable VAR models. Applied Economics Letters, 103, 135–137.

[12] Horowitz J.L. (1995) Advances in Economics and Econometrics: Theory and Applications, Chapter 7 : Bootstrap methods in econometrics: Theory and numerical performance. Cambridge University Press.

[13] Horowitz J.L. (1994) Bootstrap-based critical values for the information matrix test. Journal of Econometrics, 61, 395–411.

[14] Hylleberg S., Engle R.F., Granger C.W.J. and Yoo S. (1990) Seasonal Integration and Cointegration. Journal of Econometrics, 44, 215–238.

[15] Johansen S. and Schaumburg E. (1988) Likelihood Analysis of Seasonal Cointegration. Journal of Econometrics, 88, 301–339.

[16] Johansen S. (1991) Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59, 1551–1580.

[17] Johansen S. (1996) Likelihood Based Inference in Cointegrated Vector Autoregressive Models 2nd edn.. Oxford University Press.

[18] MacKinnon J.G. (1992) Model specification tests and artificial regressions. Journal of Economic Literature, 30, 102–146.

[19] Maddala G.S. (1992) Introduction to Econometrics, 2nd ed. New York: Maxwell Macmillan.

[20] Mantalos P. (2000) A Graphical Investigation of the Size and Power of the Granger-Causality Tests in Integrated-Cointegrated VAR Systems. Studies in Nonlinear Dynamics & Econometrics, Volume 4, Issue 1, 2000, Article no. 2

[21] Phillips C.P. (1986) Understanding the spurious regression in econometrics. Journal of Econometrics, 33, 311–340.

[22] Toda H.Y. and Yamamoto T. (1995) Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66, 225–250.