STATIONARITY OF SQUARES SEQUENCES FROM
ARCH(1)

Zhiqiang Zhang (P. R. China), Riquan Zhang (P. R. China) and Jingyan Feng (P. R. China)

Received November 9, 2007

References:

[1] R. A. Davis and T. Mikosch, The sample autocorrelations of heavytailed processes with applications to ARCH, Appl. Statist. 26 (1998), 2049-2080. [2] R. F. Engel, Autoregressive conditional heteroskedasticity with estimates of the variance of U. K. inflation, Econometrica 50 (1982), 987-1008. [3] L. Giraitis, P. Kokoszka and R. Leipus, Stationary ARCH models: dependence structure and central limit theorem, Econometric Theory 16 (2000), 3-22. [4] S. G. Pantula, Estimation of Autoregressive Models with ARCH errors, Sankhya B 50 (1988), 119-138.

Keywords and phrases: ARCH, converges in distribution, Brownian motion, almost sure convergence, mean square convergence.