# Article

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Keywords:
random coefficient autoregressive model
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.
References:
[1] Basu A. K., Roy S. Sen: On a rates of convergence in the central limit theorem for parameter estimation in random coefficient autoregressive models. J. Indian Statist. Assoc. 26 (1988), 19–25 MR 1002100
[2] Davidson J.: Stochastic Limit Theory. Oxford University Press, New York 1994 MR 1430804 | Zbl 0904.60002
[3] Hwang S. Y., Basawa I. V.: Parameter estimation for generalized random coefficient autoregressive processes. J. Statist. Plann. Inference 68 (1998), 2, 323–337 DOI 10.1016/S0378-3758(97)00147-X | MR 1629591 | Zbl 0942.62102
[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 $11^{th}$ 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
[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 MR 1959860 | Zbl 1186.62107
[8] Janečková H.: Time Series with Changing Parameters. Doctoral Thesis, Charles University, Prague 2002
[9] Jürgens U.: The estimation of a random coefficient AR(1) process under moment conditions. Statist. Hefte 26 (1985), 237–249 DOI 10.1007/BF02932535 | MR 0861799 | Zbl 0573.62086
[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
[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 MR 0898364 | Zbl 0636.62092

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