model. Roughly speaking, the standard way to estimate a time varying parameter $d(u)$ at rescaled time $u=t/T\in(0,1)$ of a locally stationary process is to use that, for a sample size $T$, $Tb$ observations around time index $t$ approximately behave as a stationary sample as the bandwidth parameter $b\to0$. In [@beran:2009 Theorems 1] the proposed estimator of the time varying long memory parameter $d$ is claimed to satisfy a central limit theorem at rate $(Tb)^{-1/2}$. On the other hand Theorem 2 in [@beran:2009] says that the bias is of order $b^2$ if $d$ is two times continuously differentiable. Such results are somewhat similar to that for estimating the time varying parameter of a locally stationary short memory process, see [@moulines-priouret-roueff-2005], or, in a more general fashion, Example 3.6 in [@dahlhaus-2009]. Hence the presence of long memory in [@beran:2009] seems not to affect the estimation rates. It can be explained by the parametric approach for the correlation structure of the observed locally stationary time series in that the filter in the linear (although infinite) locally autoregressive representation of the process is completely determined by a finite-dimensional parameter. It follows that only a finite number of local correlations are needed to determine the 