ON THE ESTIMATION OF A HARMONIC COMPONENT IN A TIME SERIES WITH STATIONARY RESIDUALS. INDEPENDENT RESIDUALS

摘要

We then have a fairly general type of 'hidden periodicities' model9 the term "hidden periodicity' denoting a harmonic component in Dt whose frequency as well as its amplitude and phase is unknown* The restricted model obtained by taking the residual component to consist of 'white noise9, so that Yt = çt (the parameter Q_ thus disappearing) , has been quite widely used in analysing physical and economic data, underlying what is often referred to as 'Periodogram Analysis', although in recent years it has tended to "be regarded as unsatisfactory, mainly because of the misleading results that can, be obtained if the 'white noise' assumption is not a good approxi¬mation or because of doubts as to whether it is realistic to represent mt as the sum of harmonic components.