Kybernetika

Consider a model of hidden periodicities $X_t=Y_t+\sum_{i=1}^k (a_i\cos \omega_i t + b_i \sin \omega_i t)$, $t=1,\dots,2m+1$. It is assumed that $Y_t$ are i.i.d. $N(0,\sigma^2)$ variables and that $\omega _i \in \{\lambda_1,\dots, \lambda_m\}$ where $\lambda_r= 2\pi r/(2m +1)$. Let $a_i$, $b_i$ and $\sigma$ have a vague prior distribution and let the vector $(\omega_1, \dots, \omega_k)'$ 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 $k$.