Let us consider a discrete moving average $(Z_i)_{i\in \mathbb Z}$ of the form $$\begin{aligned}
Z_i= \sum_{j=1}^{\infty} b_j \zeta_{i-j},\end{aligned}$$ where $(\zeta_i)_{i\in \mathbb Z}$ is a sequence of i.i.d. random variables with mean $0$ and variance $1$, and $(b_j)_{j\geq 1}$ are non-random coefficients. The innovation $\zeta_1$ is assumed to satisfy: There exists $K,\delta>0$ such that for all $u\in {\mathbb{R}}$, $|{\mathbb{E}}[ e^{ i u \zeta_1}]|\leq K(1+|u|)^{-\delta}$. For simplicity of exposition and comparison we assume that the distribution of $\zeta_1$ is symmetric. Now, we briefly review the results of [@s04]. The assumptions on the decay of the coefficients $(b_j)_{j\geq 1}$ and the tail behaviour of the innovations are as follows: $$\begin{aligned}
b_j \sim k_0 j^{-\gamma} \quad \text{as } j\rightarrow \infty, \qquad \mathbb P(|\zeta_1| >x) \sim q x^{-\beta} \quad \text{as } x\rightarrow \infty,\end{aligned}$$ for some $\gamma \in (1/2,1)$, $\beta \in (2,4)$ and $k_0,q\neq 0$. Surgailis [@s04] studies the asymptotic behaviour of the statistic $$\begin{aligned}
S_n = \sum_{i=1}^n h(Z_i),\end{aligned}$$ where $h:{\mathbb{R}}\to{\mathbb{R}}$ is a *bounded* measurable function with $\mathbb E[h(Z_1)]=0$. In this framework the most important ingredient is the *Appell rank* of the function $h$ (cf. [@at87]). It is defined as $$\begin{aligned}
k^{\star} := \min_{k\geq 1} \{h_\infty^{(k)} (0) \not= 0\} \qquad \text{with} \qquad h_\infty (x):= \mathbb E[h(Z_1+x)].  