zbMATH — the first resource for mathematics

Some generalizations in a heteroscedastic RCA(1) model. (English) Zbl 1186.62107
From the text: In this paper results of the author [RCA(1) model with heteroscedasticity. Proc. 11th summer school Union Czech Mathematicians and Physicists “Robust 2000”(J. Antoch (ed.), G. Dohnal (ed.), Prague, 82–91 (2001)] are generalized. We are dealing here with two heteroscedastic RCA(1) models where the assumption of independence is weakened. In the first one the error process is supposed to be martingale differences, in the second one the same behavior is assumed for centered random coefficients. In the paper we show that all asymptotic results (strong consistency and asymptotic normality) derived in the paper cited above hold unchanged under these generalized conditions. Since all proofs of essential theorems are substantially based on several auxiliary lemmas we concentrate our attention to proofs of such lemmas. Because the proofs of the theorems can then be made analogously as in our Preprint 13 (Charles University, Prague (2000)), we present here only the main steps.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: EuDML