farima_to_ma function

MA Representation of a FARIMA Model

MA Representation of a FARIMA Model

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).

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.

Returns

A numeric vector is returned.

Details

Consider the FARIMA model

(1−B)dYt=ar1Xt−1+...+arpXt−p+ma1et−1+...+maqet−q+et, (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 ete_t are the innovations and where Xt=(1−B)dYtX_t=(1-B)^d Y_t. ariar_i, i=1,...,pi=1, ..., p, are the AR-coefficients to pass to the argument ar, majma_j, j=1,...,qj = 1, ..., q, are the MA-coefficients to pass to the argument ma. dd is the fractional differencing coefficient. The function then returns the coefficients from the corresponding infinite-order AR-representation

Yt=c0et+c1et−1+c2et−2+c3et−3+..., Y_t = c_0 e_t + c_1 e_{t-1}+c_2 e_{t-2} + c_3 e_{t-3} + ...,

where clc_l, l=0,1,2,...l = 0, 1, 2, ..., are the coefficients. Following this notation, c0=1c_0 = 1 by definition.

Examples

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

Author(s)

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

    Author

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