Analytic wavelets for multivariate time series analysis

Abstract : Many applications fields deal with multivariate long-memory time series. A challenge is to estimate the long-memory properties together with the coupling between the time series. Real wavelets procedures present some limitations due to the presence of phase phenomenons. A perspective is to use analytic wavelets to recover jointly long-memory properties, modulus of long-run covariance between time series and phases. Approximate wavelets Hilbert pairs of Selesnick (2002) fullfilled some of the required properties. As an extension of Selesnick (2002)’s work, we present some results about existence and quality of these approximately analytic wavelets.