In this article, we consider the superposition (sum) of two independent Gaussian long-memory time series, potentially nonstationary or noninvertible. Our estimation for the two memory parameters is semiparametric. We formulate the nonlinear log-wavelet-variance regression (NLWVR) estimation with weighted least squares. In the sequel, we can establish theoretically consistency with convergence rate as well as asymptotic normality of the estimator, provided that basically the two memory parameters are unequal but their difference is not large, say, less than 1 for two independent Gaussian ARFIMA series. In addition, we show that the NLWVR estimator can ignore certain deterministic time trend and sustain consistency.
Xiaojiang Yu (Thu,) studied this question.