Vector wavelet coherence for multiple time series
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Vector wavelet coherence for multiple time series Tunc Oygur1 · Gazanfer Unal2 Received: 21 July 2020 / Revised: 14 September 2020 / Accepted: 27 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper introduces a new wavelet methodology to handle dynamic co-movements of multivariate time series via extending multiple and quadruple wavelet coherence methodologies. The primary motivation of our works is to measure wavelet coherence analytically for the specific dimension. Thanks to the analytical solution, both smoothed complex wavelet coherence (C d ) and vector wavelet coherence (V R 2 ) can be calculated for any dimensions. Two illustrative cases employ to explore the method. The first illustration designates that dynamic co-movement between VIX and stock indices over the period between January 2000 to November 2019. Vector wavelet coherence methodology employed to examine the structure of dynamic relationships. Empirical results revealed that the relationships detected are not significant for most time-frequencies. The second application aims to approve existing multiple, quadruple, five, and six wavelet coherences. In order to validate, we generate synthetic sine curves and employ vector wavelet coherence for both multivariate (y, x1 , x2 ), quadruple (y, x1 , x2 , x3 ), five (y, x1 , x2 , x3 , x4 ), and six (y, x1 , x2 , x3 , x4 , x5 ) coherencies. The results of VMC only capture the relational frequencies and verify the existing methodologies. Keywords Vector wavelet coherence · Multivariate wavelet coherence · Multiscale analysis · Multivariate time series
1 Introduction The wavelet analysis has increasingly become a standard econophysics tool for time-series studies. Wavelet transforms expand time series into the time-frequency domain. Also, it can discover localized cyclic periodicities. There are two kinds of wavelet transform; the Continuous Wavelet Transform (CWT) and its discrete equivalent (DWT). The DWT is especially helpful for noise reduction and data compression. On the other hand, the CWT is more suitable for feature extraction [1]. In literature, many studies have proposed new techniques and tools for continuous wavelet analysis to feature extraction. For example, Torrence and Compo [2] provided a very user-friendly toolkit for the wavelet transform. Maraun and Kurts [3] proposed a cross wavelet transform and developed a
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Gazanfer Unal [email protected] Tunc Oygur [email protected]
1
Financial Economics Programme, Yeditepe University, Istanbul 34755, Turkey
2
Faculty of Economics, Administrative and Social Sciences, Bahçe¸sehir University, Istanbul 34353, Turkey
wavelet coherence (WTC). Wavelet coherence is an excellent method when the co-movement between two (or more)-time series is considered. Contagion and spillover are also used in the literature in place of nco-movement. Grinsted et al. [1] incorporated WTC into the package by adding to the toolkit of Torrence and Compo [2]. Mihanovic et al. [4] introduced two new techniques,
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