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Weak convergence of non-stationary multivariate marked processes with applications to martingale testing

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  • Escanciano, J. Carlos

Abstract

This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown's martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 98 (2007)
Issue (Month): 7 (August)
Pages: 1321-1336

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Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1321-1336

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Keywords: Marked empirical processes Weak convergence Martingale hypothesis Non-stationary time series;

References

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  1. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
  2. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  3. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
  4. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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Cited by:
  1. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
  2. Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
  3. Ferger, Dietmar, 2009. "Argmax-stable marked empirical processes," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1203-1206, May.
  4. Juan Carlos Escanciano & Chuan Goh, 2010. "Specification Analysis of Structural Quantile Regression Models," Working Papers tecipa-415, University of Toronto, Department of Economics.

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