ON ESTIMATING THE HIDDEN PERIODICITIES IN LINEAR TIME SERIES MODELS

In this paper the tollowing modelX(n)=sum from j=1 to p αe+ξis considered,where p,λ,λ,…,λ,are constants α=(α,α,…,α) is a random vector and {ξ;n=0,±1,±2,…} is a wide-sense stationary sequence with zero means.In [4],theorem about thestrong consistent estimates of λ,λ.…,λand α are proved under the assumption that α is a constantvector and p and δ are known constants such that0<δ<(?){λ-λ}.The main purpose of the present paper is to prove theorems on the strong consistent estimates ofparameters p,λ,λ,…,λand random vector α without knowing p and δ.Numerical examples arealso given to illustrate our method of estimation.