arma_to_ar function

AR Representation of an ARMA Model

AR Representation of an ARMA 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).

arma_to_ar(ar = numeric(0), ma = numeric(0), max_i = 1000)

Arguments

  • ar: the AR-coefficient series ordered by lag.
  • ma: the MA-coefficient series ordered by lag.
  • max_i: the maximum index up until which to return the coefficient series.

Returns

A numeric vector is returned.

Details

Consider the ARMA model

Xt=ar1Xt−1+...+arpXt−p+ma1et−1+...+maqet−q+et, X_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. 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.The function then returns the coefficients from the corresponding infinite-order AR-representation

−et=c0Xt+c1Xt−1+c2Xt−2+c3Xt−3+..., -e_t = c_0 X_t + c_1 X_{t-1}+c_2 X_{t-2} + c_3 X_{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

arma_to_ar(ar = 0.75, ma = 0.5, max_i = 100)

Author(s)

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

    Author

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