Estimation of variances in a heteroscedastic RCA(1) model

Hana Janečková

Kybernetika (2002)

  • Volume: 38, Issue: 4, page [405]-424
  • ISSN: 0023-5954

Abstract

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The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form X t = b t X t - 1 + Y t . Two different procedures for estimating σ t 2 = E Y t 2 , σ b 2 = E b t 2 or σ B 2 = E ( b t - E b t ) 2 , respectively, are described under the special seasonal behaviour of σ t 2 . For both types of estimators strong consistency and asymptotic normality are proved.

How to cite

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Janečková, Hana. "Estimation of variances in a heteroscedastic RCA(1) model." Kybernetika 38.4 (2002): [405]-424. <http://eudml.org/doc/33592>.

@article{Janečková2002,
abstract = {The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form $X_t=b_tX_\{t-1\}+Y_t$. Two different procedures for estimating $\sigma _t^2=EY_t^2, \sigma _b^2=Eb_t^2$ or $\sigma _B^2=E(b_t- Eb_t)^2$, respectively, are described under the special seasonal behaviour of $\sigma _t^2$. For both types of estimators strong consistency and asymptotic normality are proved.},
author = {Janečková, Hana},
journal = {Kybernetika},
keywords = {random coefficient autoregressive model},
language = {eng},
number = {4},
pages = {[405]-424},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Estimation of variances in a heteroscedastic RCA(1) model},
url = {http://eudml.org/doc/33592},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Janečková, Hana
TI - Estimation of variances in a heteroscedastic RCA(1) model
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 4
SP - [405]
EP - 424
AB - The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form $X_t=b_tX_{t-1}+Y_t$. Two different procedures for estimating $\sigma _t^2=EY_t^2, \sigma _b^2=Eb_t^2$ or $\sigma _B^2=E(b_t- Eb_t)^2$, respectively, are described under the special seasonal behaviour of $\sigma _t^2$. For both types of estimators strong consistency and asymptotic normality are proved.
LA - eng
KW - random coefficient autoregressive model
UR - http://eudml.org/doc/33592
ER -

References

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  2. Davidson J., Stochastic Limit Theory, Oxford University Press, New York 1994 Zbl0904.60002MR1430804
  3. Hwang S. Y., Basawa I. V., 10.1016/S0378-3758(97)00147-X, J. Statist. Plann. Inference 68 (1998), 2, 323–337 (1998) Zbl0942.62102MR1629591DOI10.1016/S0378-3758(97)00147-X
  4. Janečková H., RCA(1) model with heteroscedasticity, Preprint 13, Charles University, Prague 2000 
  5. Janečková H., RCA(1) model with heteroscedasticity, In: Proceedings of the Summer School of the Union of the Czech Mathematicians and Physicists Robust 2000 (J. Antoch and G. Dohnal, eds.), Union of the Czech Mathematicians and Physicists, Prague 2001, pp. 82–91 
  6. Janečková H., On the relation between heteroscedastic RCA and non-stationary ARCH processes, In: Proceedings of the Conference Mathematical Methods in Economics MME 2001 (M. Dlouhý, ed.), Czech Society for Operations Research, Hradec Králové 2001, pp. 87–92 
  7. Janečková H., Some generalizations in a heteroscedastic RCA(1) model, Acta Univ. Carolin.–Math. Phys. 1 (2002). To appear Zbl1186.62107MR1959860
  8. Janečková H., Time Series with Changing Parameters, Doctoral Thesis, Charles University, Prague 2002 
  9. Jürgens U., 10.1007/BF02932535, Statist. Hefte 26 (1985), 237–249 (1985) Zbl0573.62086MR0861799DOI10.1007/BF02932535
  10. Nicholls D. F., Quinn B. G., Random Coefficient Autoregressive Models: An Introduction (Lecture Notes in Statistics 11), Springer-Verlag, New York 1982 MR0671255
  11. Štěpán J., Teorie Pravděpodobnosti (The Theory of Probability), Academia, Prague 1987 
  12. Tsay R. S., Conditional heteroscedastic time series models, J. Amer. Statist. Assoc. 82 (1987), 398, 590–604 (1987) Zbl0636.62092MR0898364

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