| d_to_coef {esemifar} | R Documentation |
Filter Coefficients of the Fractional Differencing Operator
Description
Output is with positive signs on the left-hand side of the equation.
Usage
d_to_coef(d, max_i = 1000)
Arguments
d |
the fractional differencing coefficient. |
max_i |
the maximum index up until which to return the coefficient series. |
Details
Consider the FARIMA model
(1-B)^d Y_t = ar_1 X_{t-1} + ... + ar_p X_{t-p}+ma_1 e_{t-1}+...+ma_q e_{t-q}+e_t,
where e_t are the innovations and where X_t=(1-B)^d Y_t.
d is the fractional differencing
coefficient.
The fractional differencing operator (1-B)^d can alternatively be expressed
as an infinite coefficient series, so that
(1-B)^d=\sum_{l=0}^{\infty}b_l B^k,
where B is the backshift operator and where b_l, l=0,1,2,...,
are the coefficients. Note that b_0=1 by definition.
The function returns the series of coefficients \{b_l, l =0,1,2,...\}.
Value
A numeric vector is returned.
Author(s)
Dominik Schulz (Scientific Employee) (Department of Economics, Paderborn University),
Author
Examples
d_to_coef(d = 0.3, max_i = 100)