Goodness-of-fit tests in long-range dependent processes under fixed alternatives
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 432-443.

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239-258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.

DOI : 10.1051/ps/2012006
Classification : 60F05, 62F03
Mots-clés : Long-range dependence, goodness-of-fit test, asymptotic power, periodogram 
@article{PS_2013__17__432_0,
     author = {Dette, Holger and Sen, Kemal},
     title = {Goodness-of-fit tests in long-range dependent processes under fixed alternatives},
     journal = {ESAIM: Probability and Statistics},
     pages = {432--443},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2012006},
     mrnumber = {3066387},
     zbl = {1284.62524},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps/2012006/}
}
TY  - JOUR
AU  - Dette, Holger
AU  - Sen, Kemal
TI  - Goodness-of-fit tests in long-range dependent processes under fixed alternatives
JO  - ESAIM: Probability and Statistics
PY  - 2013
SP  - 432
EP  - 443
VL  - 17
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ps/2012006/
DO  - 10.1051/ps/2012006
LA  - en
ID  - PS_2013__17__432_0
ER  - 
%0 Journal Article
%A Dette, Holger
%A Sen, Kemal
%T Goodness-of-fit tests in long-range dependent processes under fixed alternatives
%J ESAIM: Probability and Statistics
%D 2013
%P 432-443
%V 17
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ps/2012006/
%R 10.1051/ps/2012006
%G en
%F PS_2013__17__432_0
Dette, Holger; Sen, Kemal. Goodness-of-fit tests in long-range dependent processes under fixed alternatives. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 432-443. doi : 10.1051/ps/2012006. http://archive.numdam.org/articles/10.1051/ps/2012006/

[1] M.A. Arcones, Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probab. 22 (1994) 2242-2274. | MR | Zbl

[2] J. Beran, A goodness-of-fit test for time series with long-range dependence. J. R. Stat. Soc., Ser. B Stat. Methodol. 54 (1992) 749-760. | MR | Zbl

[3] J.O. Berger and M. Delampady, Testing precise hypotheses. Stat. Sci. 2 (1987) 317-335. | MR | Zbl

[4] W.W. Chen and R.S. Deo, A generalized Portmanteau goodness-of-fit test for time series models. Econ. Theory 20 (2004) 382-416. | MR | Zbl

[5] W.W. Chen and R.S. Deo, Estimation of misspecified long-memory models. J. Econom. 134 (2006) 257-281. | MR

[6] R. Dahlhaus, Efficient parameter estimation for self-similar processes. Ann. Stat. 17 (1989) 1749-1766. | MR | Zbl

[7] R.S. Deo and W.W. Chen, On the integral of the squared periodogram. Stoc. Proc. Appl. 85 (2000) 159-176. | MR | Zbl

[8] H. Dette, A consistent test for the functional form of a regression based on a difference of variance estimators. Ann. Statist. 27 (1999) 1012-1040. | MR | Zbl

[9] H. Dette, A consistent test for heteroscedasticity in nonparametric regression based on the kernel method. J. Statist. Plann. Inference 103 (2002) 311-329. | MR | Zbl

[10] H. Dette and A. Munk, Some methodological aspects of validation of models in nonparametric regression. Stat. Neerl. 57 (2003) 207-244. | MR | Zbl

[11] H. Dette and I. Spreckelsen, A note on a specification test for time series models based on spectral density estimation. Scand. J. Stat. 30 (2003) 481-491. | MR | Zbl

[12] G. Fay and A. Philippe, Goodness-of-fit test for long range dependent processes. ESAIM: PS 6 (2002) 239-258. | Numdam | MR

[13] R. Fox and M.S. Taqqu, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Stat. 14 (1986) 517-532. | MR | Zbl

[14] L. Giraitis and D. Surgailis, A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate. Probab. Theory Relat. Fields 86 (1990) 87-104. | MR | Zbl

[15] M.T. Greene and B.D. Fielitz, Long-term dependence in common stock returns. J. Financ. Econ. 4 (1977) 339-349.

[16] C. Hurvich, E. Moulines and P. Soulier, The FEXP estimator for potentially non-stationary linear time series. Stochastic Processes Appl. 97 (2002) 307-340. | MR | Zbl

[17] D. Koutsoyiannis, C. Makropoulos, A. Langousis, S. Baki, A. Efstratiadis, A. Christofides, G. Karavokiros and N. Mamassis, HESS opinions: climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability. Hydrol. Earth Syst. Sci. 13 (2009) 247-257.

[18] A. Mokkadem, A measure of information and its applications to test for randomness against ARMA alternatives and to goodness-of-fit test. Stochastic Processes Appl. 72 (1997) 145-159. | MR | Zbl

[19] E. Paparoditis, Spectral density based goodness-of-fit tests for time series models. Scand. J. Statist. 27 (2000) 143-176. | MR | Zbl

[20] K. Park and W. Willinger, Self-similar network traffic: an overview, in Self-Similar Network Traffic and Performance Evaluation, edited by K. Park and W. Willinger. Wiley Interscience, New York (2000) 1-39.

[21] E. Stroe-Kunold, T. Stadnytska, J. Werner and S. Braun, Estimating long-range dependence in time series: An evaluation of estimators implemented in R. Behavior Res. Methods 41 (2009) 909-923.

[22] P. Whittle, Estimation and information in stationary time series. Ark. Mat. 1 (1953) 423-434. | MR | Zbl

Cité par Sources :