gb: Gegenbauer polynomials shifted to [a,b]

In jstriaukas/midasml: Estimation and Prediction Methods for High-Dimensional Mixed Frequency Time Series Data

Gegenbauer polynomials shifted to [a,b]

Description

For a given set of points in X, computes the orthonormal Gegenbauer polynomials basis of L2 [a,b] for a given degree and α parameter. The Gegenbauer polynomials are a special case of more general Jacobi polynomials. In turn, you may get Legendre polynomials from Gegenbauer by setting α = 0, or Chebychev's polynomials by setting α = 1/2 or -1/2.

Usage

gb(degree, alpha, a = 0, b = 1, jmax = NULL, X = NULL)

Arguments

degree	polynomial degree.
alpha	Gegenbauer polynomials parameter.
a	lower shift value (default - 0).
b	upper shift value (default - 1).
jmax	number of high-frequency lags.
X	optional evaluation grid vector.

Value

Psi weight matrix with Gegenbauer functions upto degree.

Author(s)

Jonas Striaukas

Examples

degree <- 3
alpha <- 1
jmax <- 66
gb(degree = degree, alpha = alpha, a = 0, b = 1, jmax = jmax)

jstriaukas/midasml documentation built on Oct. 5, 2022, 12:18 a.m.