farima_to_ma {esemifar}

MA Representation of a FARIMA Model

Description

Output has representation with positive signs (on the right-hand side of the equation); inputs are both with positive signs (on right-hand side of equation).

Usage

farima_to_ma(ar = numeric(0), ma = numeric(0), d = 0, max_i = 1000)

Arguments

ar

the AR-coefficient series ordered by lag.

ma

the MA-coefficient series ordered by lag.

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. ar_i, i=1, ..., p, are the AR-coefficients to pass to the argument ar, ma_j, j = 1, ..., q, are the MA-coefficients to pass to the argument ma. d is the fractional differencing coefficient. The function then returns the coefficients from the corresponding infinite-order AR-representation

Y_t = c_0 e_t + c_1 e_{t-1}+c_2 e_{t-2} + c_3 e_{t-3} + ...,

where c_l, l = 0, 1, 2, ..., are the coefficients. Following this notation, c_0 = 1 by definition.

Value

A numeric vector is returned.

Author(s)

• Dominik Schulz (Scientific Employee) (Department of Economics, Paderborn University),
  Author

Examples

farima_to_ma(ar = 0.75, ma = 0.5, d = 0.3, max_i = 100)