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Open AccessFeature PaperArticle

A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series

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Dpto. Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
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Dpto. Economía Financiera y Actuarial, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 844; https://doi.org/10.3390/math8050844
Received: 1 May 2020 / Revised: 17 May 2020 / Accepted: 19 May 2020 / Published: 23 May 2020
We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy. View Full-Text
Keywords: non-periodicity; scale index; wavelets; chaotic dynamical systems non-periodicity; scale index; wavelets; chaotic dynamical systems
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Bolós, V.J.; Benítez, R.; Ferrer, R. A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series. Mathematics 2020, 8, 844.

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