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A GENERALIZED PORTMANTEAU GOODNESS-OF-FIT TEST FOR TIME SERIES MODELS

Published online by Cambridge University Press:  10 February 2004

Willa W. Chen  and
Rohit S. Deo
Willa W. Chen
Affiliation:
Texas A&M University
Rohit S. Deo
Affiliation:
New York University
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Abstract

We present a goodness-of-fit test for time series models based on the discrete spectral average estimator. Unlike current tests of goodness of fit, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short- or long-range dependence model. Our test is in the frequency domain, is easy to compute, and does not require the calculation of residuals from the fitted model. This is especially advantageous when the fitted model is not a finite-order autoregressive model. The test statistic is a frequency domain analogue of the test by Hong (1996, Econometrica 64, 837–864), which is a generalization of the Box and Pierce (1970, Journal of the American Statistical Association 65, 1509–1526) test statistic. A simulation study shows that our test has power comparable to that of Hong's test and superior to that of another frequency domain test by Milhoj (1981, Biometrika 68, 177–187).

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 2 , April 2004 , pp. 382 - 416
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Beran, J. (1992) A goodness-of-fit test for time series with long range dependence. Journal of the Royal Statistical Society, Series B 54, 749–760.Google Scholar
Beran, J. (1994) Statistic for Long Memory Processes. Chapman & Hall.
Box, G.E.P. & D.A. Pierce (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65, 1509–1526.Google Scholar
Brockwell, P. & R. Davis (1996) Time Series: Theory and Methods, 2nd ed. Springer.
Dahlhaus, R. (1989) Efficient parameter estimation for self-similar processes. Annals of Statistics 17, 1749–1766.Google Scholar
Davies, R.B. & D.S. Harte (1987) Tests for Hurst effect. Biometrika 74, 95–102.Google Scholar
Deo, R.S. & W.W. Chen (2000) On the integral of the squared periodogram. Stochastic Processes and Their Applications 85, 159–176.Google Scholar
Granger, C.W.J. & R. Joyeux (1980) An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15–29.Google Scholar
Grenander, U. & M. Rosenblatt (1957) Statistical Analysis of Stationary Time Series. Wiley.
Hong, Y. (1996) Consistent testing for serial correlation of unknown form. Econometrica 64, 837–864.Google Scholar
Hosking, J.R.M. (1981) Fractional differencing. Biometrika 68, 165–176.Google Scholar
Hurvich, C.M., R.S. Deo, & J. Brodsky (1998) The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis 19, 19–46.Google Scholar
Mandelbrot, B.B. & J.W. Van Ness (1968) Fractional Brownian motions, fractional noises, and applications. SIAM Review 10, 422–437.Google Scholar
Milhoj, A. (1981) A test of fit in time series models. Biometrika 68, 177–187.Google Scholar
Moulines, E. & P. Soulier (1999) Broadband log-periodogram regression of time series with long-range dependence. Annals of Statistics 27, 1415–1439.Google Scholar
Yajima, Y. (1993) Asymptotic properties of estimates in incorrect ARMA models for long-memory time series. In New Directions in Time Series Analysis, part 2, pp. 375–382.
Zygmund, A. (1977) Trigonometric Series. Cambridge University Press.