Generalized spectral tests for the martingale difference hypothesisReportar como inadecuado




Generalized spectral tests for the martingale difference hypothesis - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Issued date: 2003-10

Serie-No.: UC3M Working Papers. Statistics and Econometrics;2003-12

Abstract:^aThis 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.^aThis 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 Pitmans 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 can be easily 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 and P 500 stock index and exchange rates highlights the merits of our approach.+-





Autor: Escanciano, Juan Carlos; Velasco, Carlos

Fuente: http://e-archivo.uc3m.es


Introducción



Working Paper 03-53 Statistics and Econometrics Series 12 October, 2003 Departamento de Estadística y Econometría Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624-98-49 GENERALIZED SPECTRAL TESTS FOR THE MARTINGALE DIFFERENCE HYPOTHESIS J.
Carlos Escanciano and Carlos Velasco* 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 Pitmans 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 can be easily 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 and P 500 stock index and exchange rates highlights the merits of our approach. Keywords and Phrases: Martingale Difference Hypothesis; Hilbert Spaces; Generalized Spectral Distribution; Characteristic Function; S and P 500 Stock Index; Exchange Rates. *Department of Statistics and Econometrics; Universidad Carlos III de M...





Documentos relacionados