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Zbl 0858.62081
Anděl, Jiří
Bayesian analysis of the model of hidden periodicities. (English)
[J] Kybernetika 31, No.1, 1-16 (1995). ISSN 0023-5954

Summary: 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 $k$.

MSC 2000:: *62M15 Spectral analysis of processes
62F15 Bayesian inference

Keywords: time series; model of hidden periodicities; vague prior; rectangular distribution; posterior distribution; number of periodical components

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Zentralblatt MATH Berlin [Germany]