Estimate Long Memory Causality Relationship by Wavelet Method

The traditional causality relationship proposed by Granger (Econometrica 37(3):424---438, 1969) assumes the relationships between variables are short range dependence with the same integrated order.Chen (J Forecast 25(3):193---200, 2006, J Forecast 27:607---620, 2008) proposed a bivariate model which can catch the long-range dependence among the two variables and the series do not need to be fractionally co-integrated. A fractional integrated transfer function is introduced to catch the long-range dependence in this bivariate causality model and a pseudo spectrum based estimator is proposed to estimate the long memory parameter in the transfer function. In recent years, a wavelet domain-based method has gained popularity in estimations of long memory parameter in unit series. No extension to bi-series or multi-series has been made and this paper aims to fill this gap. We will construct an estimator for the long memory parameter in the bi-variable causality model in the wavelet domain. The theoretical background is derived and Monte Carlo simulation is used to investigate the performance of the estimator.