Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T11:45:01.656Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic inference in stationary Gaussian time-series

Published online by Cambridge University Press:  01 July 2016

Robert B. Davies
Robert B. Davies*
Affiliation:
DSIR, Wellington, N. Z.
Get access Rights & Permissions [Opens in a new window]

Abstract

Conditions are given for the family of distributions of a stationary, discrete-time, Gaussian, vector-valued time-series with covariance structure given up to a finite number of parameters to satisfy the asymptotic differentiability conditions introduced by Le Cam (1969).

Keywords

ASYMPTOTIC INFERENCECONTIGUITYFOURIER SERIESPERIODOGRAMSPECTRUMSTATIONARY GAUSSIAN TIME-SERIESTOEPLITZ MATRIX
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 469 - 497
Copyright
Copyright © Applied Probability Trust 1973 

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.)

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Daniel, C. and Wood, F. S. (1971) Fitting Equations to Data. Wiley, New York.Google Scholar
Grenander, U. and Szegö, G. (1958) Toeplitz Forms and their Applications. University of California Press, Berkeley.CrossRefGoogle Scholar
Hannan, E. J. (1970) Multiple Time Series Analysis. Wiley, New York.CrossRefGoogle Scholar
Lancaster, P. (1969) Theory of Matrices. Academic Press, New York.Google Scholar
Le Cam, L. M. (1960) Locally asymptotically normal families of distributions. University of California Publications in Statistics 3, 37–98.Google Scholar
Le Cam, L. M. (1969) Théorie Asymptotique de la Décision Statistique. Montreal University Press.Google Scholar
Mann, H. and Wald, A. (1943) On the statistical treatment of linear stochastic difference equations. Econometrica 11, 173–220.Google Scholar
Neyman, J. (1959) Optimal asymptotic tests of composite statistical hypotheses. Probability and Statistics, The Harald Cramér Volume. (Ed. Grenander, U.) Wiley, New York.Google Scholar
Parzen, E. (1971) Efficient estimation of stationary time series mixed schemes. Bull. Inst. Internat. Statist. 44, 315–319.Google Scholar
Roussas, G. G. (1972) Contiguity of Probability Measures: Some Applications in Statistics. Cambridge University Press, Cambridge.Google Scholar
Walker, A. M. (1964) Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series. J. Austral. Math. Soc. 4, 363–384.Google Scholar
Whittle, P. (1951) Hypothesis Testing in Time Series Analysis. Almquist and Wicksell, Uppsala.Google Scholar
Whittle, P. (1953) The analysis of multiple stationary time series. J. R. Statist. Soc. B 15, 125–139.Google Scholar
Whittle, P. (1962) Gaussian estimation in stationary time series. Bull. Inst. Internat. Statist. 39, 105–129.Google Scholar