zbMATH — the first resource for mathematics

Wild bootstrap in RCA(1) model. (English) Zbl 1248.62155
Summary: A heteroskedastic autoregressive process of first order is considered where the autoregressive parameter is random and errors are allowed to be non-identically distributed. A wild bootstrap procedure to approximate the distribution of the least-squares estimator of the mean of the random parameter is proposed as an alternative to the approximation based on asymptotic normality; and the consistency of this procedure is established.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
Full Text: EuDML Link
[1] Anděl J.: Autoregressive series with random parameters. Math. Operationsforch. Statist. 7 (1976), 735-741 · Zbl 0346.62066
[2] Davidson J.: Stochastic Limit Theory. Oxford University Press, New York 1994 · Zbl 0904.60002
[3] Janečková H.: Time Series with Changing Parameters. Ph.D. Thesis, Charles University, Prague 2002
[4] Janečková H.: Some generalizations in a heteroscedastic RCA(1) model. Acta Univ. Carolin. - Math. Phys. 43 (2002), 21-47 · Zbl 1186.62107
[5] Jürgens U.: The estimation of a random coefficient AR(1) process under moment conditions. Statist. Hefte 16 (1985), 237-249 · Zbl 0573.62086
[6] Kreiss J. P.: Asymptotical properties of residual bootstrap for autoregression. Preprint, TU Braunschweig 1997
[7] Liu R. Y.: Bootstrap procedures under some non-i. i.d. models. Ann. Statist. 16 (1988), 1696-1708 · Zbl 0655.62031
[8] Nicolls D. F., Quinn B. G.: Random Coefficient Autoregressive Models: An Introduction (Lecture Notes in Statistics 11). Springer-Verlag, New York 1982
[9] Prášková Z.: Bootstrapping in nonstationary autoregression. Kybernetika 38 (2002), 389-404 · Zbl 1264.62072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.