# Bayesian approach for estimation of harmonic oscilations with fluctuating amplitude

### Abstract

*Abstract: Th**is** article **examines **cyclic components with **fluctuating **amplitude, **where** harmonic models are also used **for** description of the **fluctuating **amplitude. It is shown that a harmonic component with **fluctuating **amplitude can be represented as **a** sum of two harmonic components with constant amplitude. But since the overall model is a sum of several harmonic components with a constant amplitude, the question arises how **to understand **which pairs of harmonic components are simply **a** sum of two harmonic components with a constant amplitude and which pairs form harmonic components with **fluctuating **amplitude.** The first step in answering this question is to evaluate a model that is not a sum of separate harmonic components but a sum of pairs of harmonic components. But before that, the article shows how to evaluate any model. The second step is to define a rule that takes the form of a system of two inequalities. Only when both inequalities are satisfied only then we can argue that there is a cyclic component with a fluctuating amplitude. For illustration, the dynamics of the price level in Bulgaria is examined. There are revealed **4** harmonic components with a constant amplitude describing the trend, and **12** harmonic components that describe cycles. Of these, **3** are with fluctuating amplitude and **9** are with constant amplitude. The resulting model has a very good explanatory power – 99.8% of the variation of the price level is explained by the obtained model.*

### References

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4. Naydenov, G. and Haralampiev, K., 2014. Dulgite vulni na Kondratiev pri “sotsializma”. Sofia: Izdatelski kompleks – UNSS

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