zbMATH — the first resource for mathematics

Estimation of autoregressive models with ARCH errors. (English) Zbl 0639.62084
Summary: We consider a p-th order autoregressive process with autoregressive conditionally heteroscedastic (ARCH) errors. A series representation and some ergodic properties of the first order ARCH errors are derived. The consistency and the asymptotic normality of the maximum likelihood estimators are presented. Asymptotic distributions of the least squares estimator and an estimated generalized least squares estimator are also derived. The invariance of Dickey and Fuller test for nonstationarity of an autoregressive process is established under the ARCH errors.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
62J05 Linear regression; mixed models