Skip to main content
Log in

Asymptotic properties of dynamic stochastic parameter estimates

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Anderson, T. W. (1959). On asymptotic distributions of estimates of parameters of stochastic difference equations,Ann. Math. Statist.,30, 676–687.

    MathSciNet  Google Scholar 

  2. Anderson, T. W. (1971).The Statistical Analysis of Time Series, John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  3. Box, G. E. P. and Jenkins, G. M. (1970).Time Series Analysis, Forecasting, and Control, Holden-Day, San Francisco.

    MATH  Google Scholar 

  4. Doob, J. L. (1953).Stochastic Processes, John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  5. Dunford, N. and Schwartz, T. J. (1957).Linear Operators, Part I: General Theory, Interscience Publishers, Inc., New York.

    Google Scholar 

  6. Hannan, E. J. (1970).Multiple Time Series, John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  7. Loève, M. (1960).Probability Theory, 2nd edition, D. Van Nostrand Company, Inc., Princeton.

    MATH  Google Scholar 

  8. Mann, H. B. and Wald, A. (1943). On the statistical treatment of linear stochastic difference equations,Econometrica,11, 173–220.

    Article  MathSciNet  Google Scholar 

  9. Muench, T. J. (1971). Consistency of least squares estimates of coefficients of stochastic difference equations, (mimeographed), Department of Economics, University of Minnesota, Minneapolis.

    Google Scholar 

  10. Rao, M. M. (1961). Consistency and limit distributions of estimators of parameters in explosive stochastic difference equations.Ann. Math. Statist.,32, 195–218.

    MathSciNet  Google Scholar 

  11. Rubin, H. (1950). Consistency of maximum likelihood estimates in the explosive case, inStatistical Inference in Dynamic Economic Models, Ed. T. C. Koopmans, Cowles Commission Monograph No. 10, John Wiley and Sons, Inc., New York.

    Google Scholar 

  12. Stigum, B. P. (1963). Dynamic stochastic processes,Ann. Math. Statist.,34, 274–283.

    MathSciNet  Google Scholar 

  13. White, J. S. (1958). The limiting distribution of the serial correlation coefficient in the explosive case,Ann. Math. Statist.,29, 1188–1197.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.

This paper was written while the author was visiting professor at the Mathematics Research Center, The University of Wisconsin-Madison, June–September, 1972. Thanks are due to Professors H. F. Karreman and R. B. Miller for constructive criticism of an earlier version of the paper, and to Professor J. M. Yohe and other members of the MRC for helpful discussions. Thanks are also due to Professor E. J. Hannan where helpful comments enabled us to do without certain fourth-moment assumptions which we made in the original version of the paper.

About this article

Cite this article

Stigum, B.P. Asymptotic properties of dynamic stochastic parameter estimates. Ann Inst Stat Math 28, 49–75 (1976). https://doi.org/10.1007/BF02504730

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02504730

Keywords

Navigation