Wavelet estimation of fractional cointegration vector for multivariate time series

Cointegration analysis is one of the most active areas in the econometrics and time series where different methods are introduced for identifying and estimating cointegration vectors in fractionally integrated time series. In this paper, we estimate the fractional cointegration vector by fully modified narrow band least squares method (FMNBLS) and a proposed method, depending on a linear regression model and wavelet theory, and assuming the errors of the model following ARFIMA model, also estimate the fractional parameter (long memory parameter) for each variable depending on the Wavelet Whittle method. These methods were applied on simulated multivariate data for functional magnetic resonance imaging (fMRI) using the R program and programming the proposed method by MATLAB program.