Let $\rho(h)=corr(X_i,X_{i+h})$ be the autocorrelation function of stationary time series $X_1,X_2,\dots$.
Any good estimator exists for the partial absolute sum of autocorrelation, i.e.,$\sum_{h=0}^{n-1}|\rho(h)|$, based on given finite observations $X_1,\dots,X_n$, even when the infinite sum $\sum_{h=0}^{\infty}|\rho(h)|=\infty$?
I see many kernal or window approaches only perform good for short memory time series.