This article analyzes the performance of the Gaussian semiparametric or local Whittle estimate when applied to a (Seasonal or Cyclical) Long Memory in Stochastic Volatility model. We prove that this estimate preserves the consistency and asymptotic normality encountered in models with long memory in first moments and justify the use of existing inference techniques. Although these asymptotic properties do not depend on the signal-to-noise ratio the finite sample performance rely upon this magnitude and an appropriate choice of the bandwidth is important to minimize the effect of the added noise. We compare an appropriate version of the approximate mean square error optimal bandwidth proposed by Henry and Robinson (1996) with a Monte Carlo mean square error optimal bandwidth. An application to a Spanish stock index is finally included.