Given a time series, $x_1$, $x_2$, ..., $x_t$, .... I want to solve for $$\mathrm{min}_{w_1, w_2, ..., w_m}\rho(x_t-\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t-m}; w_{t-1}, w_{t-2}, ..., w_{t-m}))\textrm{ for }q\in(0, 1)$$ Here, $\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t_m}; w_{t-1}, w_{t-2}, ..., w_{t-m})$ is the $q$-th quantile of samples, $x_{t-1}, x_{t-2}, ..., x_{t_m}$ with weights, $w_{t-1}, w_{t-2}, ..., w_{t-m}$. And $\rho(x)$ is defined to be $$\rho(x)=q\cdot\mathrm{max}(x, 0)-(1-q)\cdot\mathrm{min}(x, 0)$$


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