A Note on Wavelet Correlation and Cointegration

In a recent paper Leong-Huang:2010 {Journal of Applied Statistics 37, 215–233} proposed a wavelet-correlation-based approach to test for cointegration between two time series. However, correlation and cointegration are two different concepts even when wavelet analysis is used. It is known that statistics based on nonstationary integrated variables have non-standard asymptotic distributions. However, wavelet analysis offsets the integrating order of nonstationary series so that traditional asymptotics on stationary variables suffices to ascertain the statistical properties of wavelet-based statistics. Based on this, this note shows that wavelet correlations cannot be used as a test of cointegration.

Fluorescence cross-correlation spectroscopy to study hemodynamics

[EN] In the recent years a series of optical correlation techniques have been developed in order to be able to measure flow velocity with high spatial resolution while being non-invasive in order to be employed in-vivo on biological organisms. The technique employed in my thesis work, scanning laser image correlation (SLIC), is a powerful approach for the detection of flow motions because it overcomes some limitations of the classical spectroscopy techniques. SLIC method consists in repeated laser scans over a linear pattern and on the cross correlation of the signal emitted by the excited fluorophores in different positions along the scan line. Therefore, the resulting measurements for flow velocity are really accurate.