Wavelet Co-movement Significance Testing with Respect to Gaussian White Noise Background

Abstract

The paper deals with significance testing of time series co-movement measured via time-frequency approach. We use the wavelet analysis for estimation of the co/cross-spectra for the co-movement analysis. This technique is very popular in the most of economic applications for its better time resolution compare to other techniques. Such approach put in evidence the existence of both long-run and short-run co-movement. In order to have better predictive power it is suitable to support and validate obtained results via some testing approach. We investigate the test of wavelet power co/cross-spectrum with respect to the Gaussian white noise background with the use of the Bessel function. Our experiment is performed on synthetic signal and real data. We use seasonally adjusted quarterly data of gross domestic product of the United Kingdom, Korea and G7 countries. To validate the test results we perform Monte Carlo simulation. We describe the advantages and disadvantages of both approaches and formulate recommendations for using time-frequency testing for wavelet co/cross-spectra.The paper deals with significance testing of time series co-movement measured via time-frequency approach. We use the wavelet analysis for estimation of the co/cross-spectra for the co-movement analysis. This technique is very popular in the most of economic applications for its better time resolution compare to other techniques. Such approach put in evidence the existence of both long-run and short-run co-movement. In order to have better predictive power it is suitable to support and validate obtained results via some testing approach. We investigate the test of wavelet power co/cross-spectrum with respect to the Gaussian white noise background with the use of the Bessel function. Our experiment is performed on synthetic signal and real data. We use seasonally adjusted quarterly data of gross domestic product of the United Kingdom, Korea and G7 countries. To validate the test results we perform Monte Carlo simulation. We describe the advantages and disadvantages of both approaches and formulate recommendations for using time-frequency testing for wavelet co/cross-spectra.