We assume that the vectors x contains discrete observations from a diffusion process $x$ following the Ito stochastic differential equation $$dx(t)= \sigma(t) \ dW(t) + b(t) \ dt,$$ $$d\sigma^2(t)= \gamma(t) \ dZ(t) + a(t) \ dt,$$ where $W$ and $Z$ are two Brownian motions defined on the filtered probability space $(\Omega, (\mathcal{F}_t)_{t \in [0,T]}, P)$, with correlation $\rho$, while $\sigma, \gamma, b$ and $a$ are random processes, adapted to $\mathcal{F}_t$.

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The spot leverage at time $t \in [0,T]$ is defined as $$B(t):=\frac{d\langle x,\sigma^2 \rangle_t}{dt}=\rho\sigma(t)\gamma(t).$$ For any positive integer $n$, let $\mathcal{S}_{n}:=\{ 0=t_{0}\leq \cdots \leq t_{n}=T \}$ be the observation times. Moreover, let $\delta_l(x):= x(t_{l+1})-x(t_l)$ be the increments of $x$.

The Fourier estimator of the spot leverage at time $t \in [0,T]$ is given by $$\widehat B_{n,N,M,L}(\tau)= \sum_{|k|\leq L} \left(1-{|k|\over L}\right)c_k(B_{n,N,M}) \, e^{{\rm i}\frac{2\pi}{T}k\tau},$$ where: $$c_k(B_{n,N,M})= {T \over {2M+1}} \sum_{|s|\leq M} c_s(d\sigma_{{n},N})c_{k-s}(dx_{n}),$$ $$c_k(d\sigma_{{n},N})={\rm i} \, k\, \frac{2\pi}{T} c_k(\sigma_{{n},N}), \quad c_k(\sigma_{n,N})={T\over {2N+1}} \sum_{|s|\leq N} c_{s}(dx_{n})c_{k-s}(dx_{n}),$$ $$c_k(dx_{n}):= {1\over {T}} \sum_{l=0}^{n-1} e^{-{\rm i}\frac{2\pi}{T}kt_l}\delta_{l}(x).$$