Estimates Q-alpha using the first \(k\) elements of a time series.
Usage
Qalpha(x, alpha = 0.8)
Value
Numeric vector of \(Q^{\alpha}\)-s estimated using x[1], ..., x[k], \(k = 1, ..., n\), \(n\) being the length of x.
Arguments
x
numeric vector.
alpha
quantile. Numeric value in (0, 1]
Details
$$\hat{Q}^{\alpha}_{1:k} = U_{1:k}^{-1}(\alpha) = \inf\{x | \alpha \leq U_{1:k}(x)\},$$
where \(U_{1:k}\) is the empirical distribtion function of \(|x_i - x_j|, \, 1 \leq i < j \leq k\).