ABSTRACT
Using this approach different classes of local al1,ernatives can be consitiered. For iristarice if we choose by, - 1 we arc in the casc of the so-called Pitman alternatives where the local alternatives approach . f0 ( . ) at the rate c ~ . Dcpcndirig on the particular form of LLI(.) these departures can be thought as being of more global nature ill the sense that they not become centered arouird ally particular frequency as the sarnplc increases. 0x1 the contrary, if t,he sequence b7, is also allowed to approach zcm its '1' + o then the departure of j'?~ froin the hypot,hcsizetl spectral de~lsity ,/b I~ecomes more and more ceritered around the frequency X* ils r , . 1 lIlcrcits(!s. This is the class of sharp pcak locitl ;tlternatives iiltrocllmxi by Rosenblatt (1975) in the context of clerlsity testing imsed on a sanlple of i.i.d. tlnta; see also Ghosh and Huarig ( 1 9 9 1 ) . The following theorem characterizcs the behavior of the ,5T,h test statistic for the class of local alternatives given in (21.2.5).
