Computes Beta weighting curves as in Ghysels, Sinko and Valkanov (2007). Handy to self-select specific
time aggregation weighting schemes for input in ctr_agg using the weights argument.
weights_beta(n, a = 1:4, b = 1:4)a single numeric to indicate the lag length (cf., n).
a numeric as the first parameter (cf., a).
a numeric as the second parameter (cf., b).
A data.frame of beta weighting curves per combination of a and b. If n = 1,
all weights are set to 1.
The Beta weighting abides by following formula:
\(f(i/n; a, b) / \sum_{i}(i/n; a, b)\), where \(i\) is the lag index ordered
from 1 to \(n\), \(a\) and \(b\) are two decay parameters, and
\(f(x; a, b) = (x^{a - 1}(1 - x)^{b - 1}\Gamma(a + b)) / (\Gamma(a)\Gamma(b))\), where \(\Gamma(.)\) is
the gamma function.
Ghysels, Sinko and Valkanov (2007). ``MIDAS regressions: Further results and new directions''. Econometric Reviews 26, 53-90, https://doi.org/10.1080/07474930600972467.