Abstract
We prove that the distributions of spectral mean estimates from linear processes admit Edgeworth expansions. As a consequence, Edgeworth expansions are valid for Whittle estimates.
Similar content being viewed by others
References
Bentkus, R. and Rudzkis, R. A. (1982). On the distribution of some statistical estimates of spectral density,Theory Probab. Appl.,27, 795–814.
Bhattacharya, R. N. and Ghosh, J. K. (1978). On the validity of the formal Edgeworth expansion,Ann. Statist.,6, 434–451.
Bose, A. (1988). Higher order approximations for autocovariances from linear processes with applications,Statistics,19, 259–269.
Brillinger, D. R. (1981).Time Series, Data Analysis and Theory, McGraw-Hill, New York.
Chibisov, D. M. (1972). An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion,Theory Probab. Appl.,17, 620–630.
Dahlhaus, R. (1983). Spectral analysis with tapered data,J. Time Ser. Anal.,4, 163–175.
Dzhaparidze, K. O. and Yaglom, A. M. (1983). Spectrum parameter estimation in time series analysis,Developments in Statistics, Vol. 4 (d. P. R. Krishnaiah), Academic Press, New York.
Götze, F. and Hipp, C. (1983). Asymptotic expansions for sums of weakly dependent random vectors,Z. Wahrsch. Verw. Gebiete,64, 211–239.
Taniguchi, M. (1991).Higher Order Asymptotic Theory for Time Series Analysis, Springer, New York.
Author information
Authors and Affiliations
About this article
Cite this article
Janas, D. Edgeworth expansions for spectral mean estimates with applications to Whittle estimates. Ann Inst Stat Math 46, 667–682 (1994). https://doi.org/10.1007/BF00773475
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773475