We consider semiparametric estimation of the memory parameter in a model which includes as special cases both the long-memory stochastic volatility (LMSV) and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow for potential nonstationarity in volatility, by allowing the signal process to have a memory parameter $d^*\geq 1/2$. We show that the local Whittle estimator is consistent for $d^*\in(0,1)$. We also show that the local Whittle estimator is asymptotically normal for $d^*\in(0,3/4)$, and essentially recovers the optimal semiparametric rate of convergence for this problem. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility.