The asymptotic behavior of quadratic forms in -mixing random variables

✍ Scribed by Fuming Lin

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 649 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.07.044

✦ Synopsis

Let {Z i , i ≥ 1} be a linear process defined by Z t = ∞ j=0 d j ξ t-j with {d j , j ≥ 0} being a regular varying sequence of real numbers and {ξ t , -∞ < t < ∞} being a sequence of φ-mixing random variables. The present paper studies the asymptotic behavior of the quadratic form n k,l=1 µ(kl)Z k Z l under some mild assumptions on d j and ξ t . Meanwhile, the similar results of α-mixing random variables are presented.