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EMPIRICAL LIKELIHOOD TEST FOR CAUSALITY OF BIVARIATE AR(1) PROCESSES

Published online by Cambridge University Press:  10 October 2013

D. Li,
N. H. Chan and
L. Peng
D. Li*
Affiliation:
Fudan University
N. H. Chan
Affiliation:
Chinese University of Hong Kong and Renmin University of China
L. Peng
Affiliation:
Georgia Institute of Technology
*
*Address correspondence to D. Li, Department of Statistics, School of Management, Fudan University, 670 Guoshun Road, Shanghai 200433, P.R. China; e-mail: deyuanli@fudan.edu.cn.
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Abstract

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Testing for causality is of critical importance for many econometric applications. For bivariate AR(1) processes, the limit distributions of causality tests based on least squares estimation depend on the presence of nonstationary processes. When nonstationary processes are present, the limit distributions of such tests are usually very complicated, and the full-sample bootstrap method becomes inconsistent as pointed out in Choi (2005, Statistics and Probability Letters 75, 39–48). In this paper, a profile empirical likelihood method is proposed to test for causality. The proposed test statistic is robust against the presence of nonstationary processes in the sense that one does not have to determine the existence of nonstationary processes a priori. Simulation studies confirm that the proposed test statistic works well.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 2 , April 2014, pp. 357 - 371
Copyright
Copyright © Cambridge University Press 2013 

References

REFERENCES

Chan, N.H., Li, D., & Peng, L. (2012) Toward a unified interval estimation of autoregressions. Econometric Theory 28, 705–717.Google Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050–1063.Google Scholar
Choi, I. (2005a) Inconsistency of bootstrap for nonstationary, vector autoregressive processes. Statistics and Probability Letters 75, 39–48.CrossRefGoogle Scholar
Choi, I. (2005b) Subsampling vector autoregressive tests of linear constraints. Journal of Econometrics 124, 55–89.Google Scholar
Granger, C.W.J. (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438.Google Scholar
Kurozumi, E. & Yamamoto, T. (2000) Modified lag augmented vector autoregressions. Econometric Review 19, 207–231.Google Scholar
Owen, A. (2001) Empirical Likelihood. Chapman and Hall.Google Scholar
Phillips, P.C.B. (1995) Fully modified least squares and vector autoregression. Econometrica 63, 1023–1078.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating functions. Annals of Statistics 22, 300–325.Google Scholar
Toda, H.Y. & Phillips, P.C.B. (1993) Vector autoregressions and causality. Econometrica 61, 1367–1393.Google Scholar
Toda, H.Y. & Phillips, P.C.B. (1994) Vector autoregression and causality: A theoretical overview and simulation study. Econometric Reviews 13, 259–285.Google Scholar
Toda, H.Y. & Yamamoto, (1995) Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66, 225–250.Google Scholar
Yamada, H. & Toda, H.Y. (1998) Inference in possibly integrated vector autoregressive models: Finite sample evidence. Journal of Econometrics 86, 55–95.CrossRefGoogle Scholar