How hard is the euro are core? An evaluation of growth cycles using wavelet analysis

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles. The methodology uses the con-tinuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a non-decimated discrete wavelet transform in order to analyse bivariate time series in terms of conventional frequency domain measures from spectral analysis. The findings are that coherence and phasing between the three core members of the euro area (France, Germany and Italy) have increased since the launch of the euro.time-varying spectral analysis; coherence; phase; business cycles; EMU; growth cycles; Hilbert trans-form; wavelet analysis

A new statistical test based on the wavelet cross-spectrum to detect time–frequency dependence between non-stationary signals: Application to the analysis of cortico-muscular interactions

The study of the correlations that may exist between neurophysiological signals is at the heart of modern techniques for data analysis in neuroscience. Wavelet coherence is a popular method to construct a time-frequency map that can be used to analyze the time-frequency correlations be- tween two time series. Coherence is a normalized measure of dependence, for which it is possible to construct confidence intervals, and that is commonly considered as being more interpretable than the wavelet cross-spectrum (WCS). In this paper, we provide empirical and theoretical arguments to show that a significant level of wavelet coherence does not necessarily correspond to a significant level of dependence between random signals, especially when the number of trials is small. In such cases, we demonstrate that the WCS is a much better measure of statistical dependence, and a new statistical test to detect significant values of the cross-spectrum is proposed. This test clearly outperforms the limitations of coherence analysis while still allowing a consistent estimation of the time-frequency correlations between two non-stationary stochastic processes. Simulated data are used to investigate the advantages of this new approach over coherence analysis. The method is also applied to experimental data sets to analyze the time-frequency correlations that may exist between electroencephalogram (EEG) and surface electromyogram (EMG)

On the Co-movement of Crude, Gold Prices and Stock Index in Indian Market

This non-linear relationship in the joint time-frequency domain has been studied for the Indian National Stock Exchange (NSE) with the international Gold price and WTI Crude Price being converted from Dollar to Indian National Rupee based on that week's closing exchange rate. Though a good correlation was obtained during some period, but as a whole no such cointegration relation can be found out. Using the \textit{Discrete Wavelet Analysis}, the data was decomposed and the presence of Granger Causal relations was tested. Unfortunately no significant relationships are being found. We then studied the \textit{Wavelet Coherence} of the two pairs viz. NSE-Nifty \& Gold and NSE-Nifty \& Crude. For different frequencies, the coherence between the pairs have been studied. At lower frequencies, some relatively good coherence have been found. In this paper, we report for the first time the co-movements between Crude Oil, Gold and Indian Stock Market Index using Wavelet Analysis (both Discrete and Continuous), a technique which is most sophisticated and recent in market analysis. Thus for long term traders they can include gold and/or crude in their portfolio along with NSE-Nifty index in order to decrease the risk(volatility) of the portfolio for Indian Market. But for short term traders, it will not be effective, not to include all the three in their portfolio

How hard is the euro area core? A wavelet analysis of growth cycles in Germany, France and Italy

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles. The methodology uses the continuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a non-decimated discrete wavelet transform in order to analyse bivariate time series in terms of conventional frequency domain measures from spectral analysis. The findings are that coherence and phasing between the three core members of the euro area (France, Germany and Italy) have increased since the launch of the euro

Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case