Compute Beta weighting curves

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, do.normalize = TRUE)

Arguments

n	a single numeric to indicate the lag length (cf., n).
a	a numeric as the first parameter (cf., a).
b	a numeric as the second parameter (cf., b).
do.normalize	a logical, if TRUE weights are normalized to unity.

Value

A data.frame of beta weighting curves per combination of a and b. If n = 1, all weights are set to 1.

Details

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.

References

Ghysels, Sinko and Valkanov (2007). MIDAS regressions: Further results and new directions. Econometric Reviews 26, 53-90, doi: 10.1080/07474930600972467 .

See also

ctr_agg