ON ALMOST SURE LIMIT THEOREM AND STRONG LAW OF LARGE NUMBERS FOR SQUARES SEQUENCE FROM ARCH(1)

Yang Shi (P. R. China), Zhiqiang Zhang (P. R. China) and Riquan Zhang (P. R. China)

Received May 26, 2008

References:

[1] R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50(4) (1982), 987-1007. [2] L. Giraitis, P. Kokoszka and R. Leipus, Stationary ARCH models: dependence structure and central limit theorem, Econometric Theory 16 (2000), 3-22. [3] E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. [4] Pan Jiazhu, Tail dependence of random variables from ARCH and heavytailed bilinear models, Science in China (Series A) 45 (2002), 749-760. [5] Przemyslaw Matula, On almost sure limit theorems for positively dependent random variables, Statist. Probab. Lett. 74 (2005), 59-66. [6] S. G. Pantula, Estimation of autoregressive models with ARCH errors, Sankhyā B 50 (1988), 119-138. [7] Alessio Sancetta, Strong law of large numbers for pairwise positive quadrant dependent random variables, Statist. Infer. Stoch. Processes (2008) (online at http://www.springerlink.com).

Keywords and phrases: ARCH, almost sure limit theorem, rate of convergence, strong law of large numbers, positive quadrant dependence.