计算科学 - 分位数估计的最佳时间序列权重 - 吾爱随笔录

给定一个时间序列， $x_1$ , $x_2$ , ..., $x_t$ , .... 我想解决

{m i n}_{w_{1}, w_{2}, . . ., w_{m}} ρ (x_{t} - Q u a n t i l e (q; x_{t - 1}, x_{t - 2}, . . ., x_{t - m}; w_{t - 1}, w_{t - 2}, . . ., w_{t - m})) for q \in (0, 1)

$\mathrm{min}_{w_1, w_2, ..., w_m}\rho(x_t-\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t-m}; w_{t-1}, w_{t-2}, ..., w_{t-m}))\textrm{ for }q\in(0, 1)$ 这里，

Q u a n t i l e (q; x_{t - 1}, x_{t - 2}, . . ., x_{t_{m}}; w_{t - 1}, w_{t - 2}, . . ., w_{t - m})

$\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t_m}; w_{t-1}, w_{t-2}, ..., w_{t-m})$ 是个

q

$q$ -样本的分位数，

x_{t - 1}, x_{t - 2}, . . ., x_{t_{m}}

$x_{t-1}, x_{t-2}, ..., x_{t_m}$ 与重量，

w_{t - 1}, w_{t - 2}, . . ., w_{t - m}

$w_{t-1}, w_{t-2}, ..., w_{t-m}$ . 和

ρ (x)

$\rho(x)$ 被定义为

ρ (x) = q \cdot m a x (x, 0) - (1 - q) \cdot m i n (x, 0)

$\rho(x)=q\cdot\mathrm{max}(x, 0)-(1-q)\cdot\mathrm{min}(x, 0)$