BAYESIAN-ANALYSIS OF THE MODEL OF HIDDEN PERIODICITIES

Consider a model of hidden periodicities X(t) = Y(t) + SIGMA(i=1)k(a(i) cosomega(i)t + b(i) sin omega(i)t), t = 1,..., 2m + 1. It is assumed that Y(t) are i.i.d. N(0,sigma2) variables and that omega(i) is-an-element-of {lambda1,..., lambda(m)} where lambda(r) = 2pir/(2m + 1). Let a(i), b(i) and sigma have a vague prior distribution and let the vector (omega1,..., omega(k))' have a rectangular distribution. The posterior distribution of the parameters is derived and its asymptotic properties are investigated. The results can be used for estimating the number of periodical components k.