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  • Miguel A. Delgado (a1), Javier Hidalgo (a2) and Carlos Velasco (a3)

This paper proposes bootstrap assisted specification tests for the autoregressive fractionally integrated moving average model based on the Bartlett Tp-process with estimated parameters whose limiting distribution under the null depends on the estimated model and the estimation method employed. The computation of the asymptotic critical values is not easy if at all possible under these circumstances. To circumvent this problem Delgado, Hidalgo, and Velasco (2005, Annals of Statistics 33, 2568–2609) proposed an asymptotically pivotal transformation of the Tp-process with estimated parameters. The aim of this paper is twofold. First, to examine alternative methods based on bootstrap algorithms for estimating the distribution of the test under the null, showing its validity. And second, to study the finite-sample performance of the different alternative procedures via Monte Carlo simulation.

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*Address correspondence to Javier Hidalgo, Economics Department, London School of Economics, London, United Kingdom; e-mail:
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Anderson, T.W. (1993) Goodness of fit tests for spectral distributions. Annals of Statistics 21, 830847.
Bartlett, M.S. (1954) Problèmes de l’analyse spectral des séries temporelles stationnaires. Publications de l’Institut de Statistique de l’Université de Paris III-3, 119134.
Beran, J. (1998) Statistics for Long-Memory Processes. Chapman and Hall.
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.
Box, G.E.P., Pierce, D.A. (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series model. Journal of the American Statistical Association 65, 15091526.
Bloomfield, P. (1973) An exponential model in the spectrum of a scalar time series. Biometrika 60, 217226.
Brown, R.L., Durbin, J., & Evans, J.M. (1975) Techniques for testing constancy of regression relationships over time (with discussion). Journal of the Royal Statistical Society, Series B. 37, 149192.
Chen, H. & Romano, J.P. (1999) Bootstrap-assisted goodness-of-fit tests in the frequency domain. Journal of Time Series Analysis 20, 619654.
Delgado, M.A., Hidalgo, J., & Velasco, C. (2005) Distribution free goodness-of-fit tests for linear processes. Annals of Statistics 33, 25682609.
Delgado, M.A. & Stute, W. (2008) Distribution-free specification tests of conditional models. Journal of Econometrics 143, 3755.
Giacomini, R., Politis, D.N., & White, H. (2007) A Warp-Speed Method for Conducting Monte Carlo Experiments Involving Bootstrap Estimators, Preprint, University College London.
Giné, E. & Zinn, S. (1990) Bootstrapping general empirical measures. Annals of Probability 18, 851869.
Götze, F. (1979) Asymptotic expansions for bivariate von Mises functionals. Zeitschrift für Wahrscheinlichskeitstheorie and Verwondte Gebiete 50, 333355.
Götze, F. (1984) Expansions for von Mises functionals. Zeitschrift für Wahrscheinlichskeitstheorie and Verwondte Gebiete 65, 599625.
Granger, C. (1980) Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14, 227238.
Granger, C. & Joyeux, R. (1980) An introduction to long-range time series models and fractional differencing. Journal of Time Series Analysis 1, 1530.
Hall, P. (1992) The Bootstrap and Edgeworth Expansion. Springer-Verlag.
Hidalgo, J. (2003) An alternative bootstrap to moving blocks for time series regression models. Journal of Econometrics 117, 369399.
Hidalgo, J. (2009) Goodness of fit for lattice processes. Journal of Econometrics 151, 113128.
Hidalgo, J. & Kreiss, J.-P. (2006) Bootstrap specification tests for linear covariance stationary processes. Journal of Econometrics 133, 807839.
Hong, Y. (1996) Consistent testing for serial-correlation of unknown form. Econometrica 64, 837864.
Hosking, J.R.M. (1981) Fractional differencing. Biometrika 68, 165176.
Khmaladze, E.K. (1981) A martingale approach in the theory of goodness-of-fit tests. Theory of Probability and Its Applications 26, 240257.
Koenker, R. & Xiao, Z. (2002) Inference on the quantile regression process. Econometrica 81, 15831612.
Koul, H. & Stute, W. (1999) Nonparametric model checks in time series. Annals of Statistics 27, 204237.
Ljung, G.M. & Box, G.E.P. (1978) On a measure of a lack of fit in time series models. Biometrika 65, 297303.
Robinson, P.M. (1978) Statistical inference for a random coefficient autoregressive model. Scandinavian Journal of Statistics 5, 163168.
Robinson, P.M. (1994a) Time series with strong dependence. In Sims, C.A. (ed.), Advances in Econometrics: Sixth World Congress, vol. 1, pp. 4796. Cambridge University Press.
Robinson, P.M. (1994b) Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association 89, 14201437.
Robinson, P.M. (1995a) Log-periodogram regression of time series with long range dependence. Annals of Statistics 23, 10481072.
Robinson, P.M. (1995b) Gaussian semiparametric estimation of long range dependence. Annals of Statistics 23, 16301661.
Shao, J. & Tu, D. (1995) The Jackknife and Bootstrap. Springer-Verlag.
Velasco, C. & Robinson, P.M. (2000) Whittle pseudo-maximum likelihood estimates of non-stationary time series. Journal of the American Statistical Association 95, 12291243.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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