Bayesian approach for estimation of harmonic oscilations with fluctuating amplitude
Abstract: This 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.
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