On Some Problems in Discrete Wavelet Analysis of Bivariate Spectra with an Application to Business Cycle Synchronization in the Euro Zone

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract The paper considers some of the problems emerging from discrete wavelet analysis of popular bivariate spectral quantities like the coherence and phase spectra and the frequency-dependent time delay. The approach taken here, introduced by Whitcher and Craigmile (2004), is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, we point at a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme resembling the one applied in the context of the dual-tree complex wavelet transform of Kingsbury (see Selesnick et al., 2005). Secondly, via a broad set of simulation experiments we examine small and large sample properties of two wavelet estimators of the scaledependent time delay. The estimators are: the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for empirical examination of short-and medium-term lead-lag relations for octave frequency bands. Besides, we show how the MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss certain issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronization between 11 euro zone member countries. The study is supplemented with wavelet analysis of variance and covariance of the euro zone business cycles. The empirical examination underlines good localization properties and high computational efficiency of the wavelet transformations applied, and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as a wavelet evidence on dating the Great Moderation in the euro zone. Terms of use: Documents inJEL C19, E32, E58, O52

Amplitude and phase synchronization of European business cycles: a wavelet approach

“…See (Bruzda 2011). It is worth mentioning that in order to have good analytic properties of the Hilbert wavelet transform at the first several stages of the Mallat's pyramid algorithm we need a different couple of wavelet filters at the first stage (see Selesnick, Baraniuk, Kingsbury 2005, as well as Bruzda 2011.…”

“…The estimation was performed with the biased version of (24), which produced slightly better results in short samples in our companion simulation analysis than the unbiased wavelet cross-covariance estimator (see Bruzda 2011). Only nonboundary wavelet coefficients were used.…”

Geli̇şmekte Olan Ülkelere Ai̇t Msci Endeksleri̇ İle Abd Pi̇yasa Endeksi̇ Arasindaki̇ Çapraz Korelasyonlarin Wavelet Anali̇zi̇ İle İncelenmesi̇

“…And in this paper, wavelet cross correlation techniques and exchange rate expectations are analyzed. Bruzda (2011), analyzed interactions between the Polish business cycles and the euro zone cycles. Marius and Petre (2011) analyzed how stock markets in Germany and United Kingdom impacts Romanian stock market.…”