Testing for Autocorrelation Using a Modified Box-Pierce Q Test

This article investigates the finite-sample performance of a modified Box-Pierce Q statistic (Q*) for testing that financial time series are uncorrelated without assuming statistical independence. The finite-sample rejection probabilities of the Q* test under the null and its power are examined in experiments using time series generated by an MA (1) process where the errors are generated by a GARCH (1, 1) model and by a long memory stochastic volatility model. The tests are applied to daily currency returns.

[1]  Peter C. B. Phillips,et al.  Testing for Autocorrelation and Unit Roots in the Presence of Conditional Heteroskedasticity of Unknown Form , 2001 .

[2]  Ignacio N. Lobato.  A Consistent Test for the Martingale Difference Assumption , 2000 .

[3]  Ignacio N. Lobato,et al.  A Robust Test For Autocorrelation in the Presence of Statistical Dependence , 1999 .

[4]  Ekaterini Kyriazidou,et al.  Testing for serial correlation in multivariate regression models , 1998 .

[5]  F. Breidt,et al.  The detection and estimation of long memory in stochastic volatility , 1998 .

[6]  Kenneth G. Hamilton,et al.  Acceleration of RANLUX , 1997 .

[7]  Ignacio N. Lobato,et al.  Real and Spurious Long-Memory Properties of Stock-Market Data , 1996 .

[8]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[9]  Jonathan R. M. Hosking,et al.  Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series , 1996 .

[10]  Joseph P. Romano,et al.  Inference for Autocorrelations under Weak Assumptions , 1996 .

[11]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[12]  William A. Brock,et al.  Nonlinear Time Series, Complexity Theory, and Finance , 1995 .

[13]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

[14]  Ching-Fan Chung.  A note on calculating the autocovariances of the fractionally integrated ARMA models , 1994 .

[15]  Anil K. Bera,et al.  ARCH Models: Properties, Estimation and Testing , 1993 .

[16]  B. LeBaron,et al.  Simple Technical Trading Rules and the Stochastic Properties of Stock Returns , 1992 .

[17]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[18]  P. Robinson,et al.  Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression , 1991 .

[19]  R. Cumby,et al.  Testing the Autocorrelation Structure of Disturbances in Ordinary Least Squares and Instrumental Variables Regressions , 1990 .

[20]  Daniel B. Nelson.  Stationarity and Persistence in the GARCH(1,1) Model , 1990, Econometric Theory.

[21]  A. Lo,et al.  The Size and Power of the Variance Ratio Test in Finite Samples: a Monte Carlo Investigation , 1988 .

[22]  R. Davies,et al.  Tests for Hurst effect , 1987 .

[23]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[24]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[25]  M. Taqqu.  Weak convergence to fractional brownian motion and to the rosenblatt process , 1975, Advances in Applied Probability.

[26]  E. J. Hannan,et al.  On Limit Theorems for Quadratic Functions of Discrete Time Series , 1972 .

[27]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .