Solve ARMA system
solve_ARMA.RdCompute the outputs of ARMA(p, q) systems of the form $$y_t = a_1 y_{t-1} + ... + a_p y_{t-p} + b_0 u_t + \cdots + b_q u_{t-q}$$
Arguments
- a
\((m, mp)\) matrix \((a_p,...,a_1)\).
- b
\((m, n(q+1))\) matrix \((b_0,...,b_q\).
- u
\((n, N)\) matrix with the inputs \((u_1,...,u_N\).
- y
\((m, N)\) matrix with the outputs \((y_1,...,y_N\).
- t0
integer, start iteration at t=t0.
Value
The R implementation solve_ARMA_R returns the matrix y with the computed outputs.
The RcppArmadillo implementation returns NULL but overwrites the input argument y!
Details
Values \(y_t\), \(u_t\) for \(t\leq 0\) are implicitly set to be zero. However, if we start the iteration with some \(t_0>1\) we can enforce non-zero initial values.
The routines are used internally and hence do not check their arguments.
We require \(m > 0\), \(p \geq 0\), \(n \geq 0\), \((q+1) \geq 0\)
and \(1 \leq t_0 \leq N\).
Note also that the RcppArmadillo implementation overwrites the input argument y.
Use this procedure with care!
Note the non standard arguments: The order of the AR coefficients is reversed. The data matrices are organized column-wise (to avoid memory shuffling)!