Hostname: page-component-76c49bb84f-s7zp8 Total loading time: 0 Render date: 2025-07-12T12:49:12.819Z Has data issue: false hasContentIssue false
  • English
  • Français

A TEST OF THE GARCH(1, 1) SPECIFICATION FOR DAILY STOCK RETURNS

Published online by Cambridge University Press:  10 May 2010

Richard A. Ashley  and
Douglas M. Patterson
Richard A. Ashley
Affiliation:
Virginia Tech (VPI)
Douglas M. Patterson*
Affiliation:
Virginia Tech (VPI)
*
Address correspondence to: Douglas M. Patterson, Department of Finance (0221), Virginia Tech, Blacksburg, VA 24061, USA; e-mail: amex@vt.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1, 1) processes. Here we test this specification using new model evaluation technology developed by Ashley and Patterson that examines the ability of the estimated model to reproduce features of particular interest: various aspects of nonlinear serial dependence, in the present instance. Using daily returns to the CRSP equally weighted stock index, we find that the GARCH(1, 1) specification cannot be rejected; thus, this model appears to be reasonably adequate in terms of reproducing the kinds of nonlinear serial dependence addressed by the battery of nonlinearity tests used here.

Keywords

GARCHStock ReturnsVolatilityModel Evaluation

Information

Type
Articles
Information
Macroeconomic Dynamics , Volume 14 , Supplement S1: Nonlinear Time Series , May 2010 , pp. 137 - 144
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ashley, R. (1998) A new technique for postsample model selection and validation. Journal of Economic Dynamics and Control 22, 647–665.CrossRefGoogle Scholar
Ashley, R. (2009) On the Origins of Conditional Heteroscedasticity in Time Series. Available at http://ashleymac.econ.vt.edu/working_papers/origins_of_conditional_heteroscedasticity.pdf.Google Scholar
Ashley, R. and Patterson, D.M. (1986) A non-parametric, distribution-free test for serial dependence in stock returns. Journal of Financial and Quantitative Analysis 21, 221–227.CrossRefGoogle Scholar
Ashley, R. and Patterson, D.M. (2006) Evaluating the effectiveness of state-switching models for U.S. real output. Journal of Business and Economic Statistics 24 (3), 266–277.CrossRefGoogle Scholar
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.CrossRefGoogle Scholar
Bollerslev, T., Chou, R., and Kroner, K. (1992) ARCH modeling in finance. Journal of Econometrics 52, 5–59.CrossRefGoogle Scholar
Brock, W.A., Dechert, W., and Scheinkman, J. (1996) A test for independence based on the correlation dimension. Econometric Reviews 15, 197–235.CrossRefGoogle Scholar
Dalle Molle, J.W. and Hinich, M.J. (1995) Trispectral analysis of stationary random time series. Journal of the Acoustical Society of America 97, 2963–2978.CrossRefGoogle Scholar
Diebold, F.X. and Mariano, R.S. (1995) Comparing predictive accuracy. Journal of Business and Economic Statistics 13 (3), 253–263.Google Scholar
Engle, Robert F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.CrossRefGoogle Scholar
Hansen, B.E. (1999) Testing for linearity. Journal of Economic Surveys 13, 551–576.CrossRefGoogle Scholar
Harding, D. and Pagan, A. (2002) Dissecting the cycle: A methodological investigation Journal of Monetary Economics 49, 365–81.CrossRefGoogle Scholar
Hinich, M. (1982) Testing for Gaussianity and linearity of a stationary time series. Journal of Time Series Analysis 3, 169–76.CrossRefGoogle Scholar
Hinich, M. and Patterson, D.M. (1985) Evidence of nonlinearity in daily stock returns. Journal of Business and Economic Statistics 3 (1), 69–77.Google Scholar
Hinich, M. and Patterson, D.M. (2006) Detecting epochs of transient dependence in white noise. In Belongia, M.T. and Binner, J.M. (eds.), Money, Measurement and Computation, 61–75. New York: Palgrave Macmillan.Google Scholar
Kaplan, D.T. (1993) Exceptional events as evidence for determinism. Physica D 73, 38–48.CrossRefGoogle Scholar
McCracken, M.W. (2007) Asymptotics for out of sample tests of Granger causality. Journal of Econometrics 140 (2), 719–52.CrossRefGoogle Scholar
McLeod, A.I. and Li, W.K. (1983) Diagnostic checking ARMA time series models using squared-residual autocorrelations. Journal of Time Series Analysis 4, 269–273.CrossRefGoogle Scholar
Mizrach, B. (1991) A Simple Nonparametric Test for Independence. Unpublished manuscript, Department of Economics, Rutgers University.Google Scholar
Nychka, D., Ellner, S., Gallant, A.R., and McCaffrey, D. (1992) Finding chaos in noisy systems. Journal of the Royal Statistical Society B 54, 399–426.Google Scholar
Patterson, D.M. and Ashley, R. (2000) A Nonlinear Time Series Workshop: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence. Boston: Kluwer Academic.CrossRefGoogle Scholar
Ramsey, J.B. (1969) Tests for specification errors in classical linear least squares regression analysis. Journal of the Royal Statistical Society B 31, 350–371.Google Scholar
Ramsey, J.B. and Rothman, P. (1996) Time irreversibility and business cycle asymmetry. Journal of Money, Credit, and Banking 28, 1–21.CrossRefGoogle Scholar
Saikkonen, P. and Luukkonen, R. (1988) Lagrange multiplier tests for testing nonlinearities in time series models. Scandinavian Journal of Statistics 15, 55–68.Google Scholar
Tsay, R.S. (1986) Nonlinearity tests for time series. Biometrika 73, 461–466.CrossRefGoogle Scholar
Verbrugge, R. (1997) Investigating cyclical asymmetries. Studies in Nonlinear Dynamics and Econometrics 2, 15–22.Google Scholar
White, H. (1989) Some asymptotic results for learning in single hidden-layer feedforward network models. Journal of the American Statistical Association 84, 1003–1013.CrossRefGoogle Scholar