The asymptotic behavior of the empirical process based on a linear process under some contiguous alternatives

✍ Scribed by Sangyeol Lee

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 529 KB
• Volume: 67
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00069-4

✦ Synopsis

Suppose that Xt = }-~,:0 ai~,t-i is a linear process, where {ag} is a sequence of absolutely summable real numbers and {~,} is a sequence of iid random variables with zero mean and finite variance. In this paper, motivated by Gaussian tests of {Xt }, we investigate the asymptotic behavior of the empirical process n

where 4) denotes the standard normal distribution and 62,, = n -I ~t"-l Xt2, under a sequence of contiguous altematives as well as the null where {X~} is Gaussian. Provided some regularity conditions hold, the corresponding limiting process under the alternatives is shown to be a Gaussian process with a drift. The result is useful for performing the local power study of a test statistic generated by ~.