Generalized spectral tests for the martingale difference hypothesis
Abstract
This article proposes a test for the martingale difference hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n-1/2, with n the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach could be extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S&P 500 stock index and exchange rates highlights the merits of our approach.(This abstract was borrowed from another version of this item.)
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Bibliographic Info
Article provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 134 (2006)
Issue (Month): 1 (September)
Pages: 151-185
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Related research
Keywords:Other versions of this item:
- J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
- Escanciano, Juan Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4360, Universidad Carlos III de Madrid.
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- George Kapetanios & Andrew P. Blake, 2007. "Testing the Martingale Difference Hypothesis Using Neural Network Approximations," Working Papers 601, Queen Mary, University of London, School of Economics and Finance.
- Charles, Amélie & Darné, Olivier & Kim, Jae H., 2011.
"Small sample properties of alternative tests for martingale difference hypothesis,"
Economics Letters,
Elsevier, vol. 110(2), pages 151-154, February.
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- Amélie Charles & Olivier Darné & Jae H Kim, 2010. "Small Sample Properties of Alternative Tests for Martingale Difference Hypothesis," Working Papers 2010.07, School of Economics, La Trobe University.
- Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
- Juan Carlos Escanciano, 2005.
"Goodness-of-fit Tests for Linear and Non-linear Time Series Models,"
Faculty Working Papers
02/05, School of Economics and Business Administration, University of Navarra.
- Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
- Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
- Juan Carlos Escanciano & Silvia Mayoral, .
"Data-Driven Smooth Tests for the Martingale Difference Hypothesis,"
Faculty Working Papers
01/07, School of Economics and Business Administration, University of Navarra.
- Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.
- Juan Carlos Escanciano & Carlos Velasco, 2008.
"Specification Tests of Parametric Dynamic Conditional Quantiles,"
Caepr Working Papers
2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
- Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
- J. Carlos Escanciano & Carlos Velasco, 2010. "Specification tests of parametric dynamic conditional quantiles," Post-Print peer-00732534, HAL.
- Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
- Escanciano, J. C. & Olmo, J., 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," Working Papers 07/11, Department of Economics, City University London.
- Juan Carlos Escanciano & Carlos Velasco, .
"Testing the Martingale Difference Hypothesis Using Integrated Regression Functions,"
Faculty Working Papers
06/06, School of Economics and Business Administration, University of Navarra.
- Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
- Escanciano, Juan Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4361, Universidad Carlos III de Madrid.
- Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series 1115, Economics, The University of Manchester.
- Escanciano, J. Carlos, 2007. "Weak convergence of non-stationary multivariate marked processes with applications to martingale testing," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1321-1336, August.
- Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra.
- Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra.
- Alexandru Todea & Dorina Lazar, 2012. "Global Crisis and Relative Efficiency: Empirical Evidence from Central and Eastern European Stock Markets," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 4(1), pages 045-053, June.
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