On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root

In the autoregressive moving average (ARMA) model with one autoregressive unit root, limiting distribution of the residual autocorrelations depends only on parameters other than the parameter corresponding to the unit root and is the same as that in the corresponding stationary ARMA process. On the other hand, limiting distribution of the partial sum process of residuals does not depend on parameter other than the parameter corresponding to the unit root and is the same as that in AR(1) with autoregressive coefficient one.