| Title:
|
Estimation of variances in a heteroscedastic RCA(1) model (English) |
| Author:
|
Janečková, Hana |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
[405]-424 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
random coefficient autoregressive model |
| MSC:
|
62F10 |
| MSC:
|
62F12 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 1264.62069 |
| idMR:
|
MR1937137 |
| . |
| Date available:
|
2009-09-24T19:47:17Z |
| Last updated:
|
2015-03-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135474 |
| . |
| Reference:
|
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| Reference:
|
[2] Davidson J.: Stochastic Limit Theory.Oxford University Press, New York 1994 Zbl 0904.60002, MR 1430804 |
| Reference:
|
[3] Hwang S. Y., Basawa I. V.: Parameter estimation for generalized random coefficient autoregressive processes.J. Statist. Plann. Inference 68 (1998), 2, 323–337 Zbl 0942.62102, MR 1629591, 10.1016/S0378-3758(97)00147-X |
| Reference:
|
[4] Janečková H.: RCA(1) model with heteroscedasticity.Preprint 13, Charles University, Prague 2000 |
| Reference:
|
[5] Janečková H.: RCA(1) model with heteroscedasticity.In: Proceedings of the $11^{th}$ 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 |
| Reference:
|
[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 |
| Reference:
|
[7] Janečková H.: Some generalizations in a heteroscedastic RCA(1) model.Acta Univ. Carolin.–Math. Phys. 1 (2002). To appear Zbl 1186.62107, MR 1959860 |
| Reference:
|
[8] Janečková H.: Time Series with Changing Parameters.Doctoral Thesis, Charles University, Prague 2002 |
| Reference:
|
[9] Jürgens U.: The estimation of a random coefficient AR(1) process under moment conditions.Statist. Hefte 26 (1985), 237–249 Zbl 0573.62086, MR 0861799, 10.1007/BF02932535 |
| Reference:
|
[10] Nicholls D. F., Quinn B. G.: Random Coefficient Autoregressive Models: An Introduction (Lecture Notes in Statistics 11).Springer-Verlag, New York 1982 MR 0671255 |
| Reference:
|
[11] Štěpán J.: Teorie Pravděpodobnosti (The Theory of Probability).Academia, Prague 1987 |
| Reference:
|
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| . |
