How misleading can sample acf's of stable MAs be? (very!)

• 成果类型: Article
• 署名作者: Resnick, S; Samorodnitsky, G; Xue, F
• 署名单位: Cornell University; Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 797-817
• 关键词: statistical-analysis; tail

摘要

For the stable moving average process X-t = integral(-infinity)(infinity) f(t + x) M(dx), t= 1,2,...., we find the weak limit of its sample autocorrelation function as the sample size n increases to infinity. It turns out that, as a rule, this limit is random! This shows how dangerous it is to rely on sample correlation as a model fitting tool in the heavy tailed case. We discuss for what functions f this limit is nonrandom for all (or only some-this can be the case, too!) lags.