random_coefmats2 generates random VAR model coefficient matrices.
random_coefmats2(p, d, ar_scale = 1)Returns \(((pd^2)x1)\) vector containing stationary vectorized coefficient matrices \((vec(A_{1}),...,vec(A_{p})\).
a positive integer specifying the autoregressive order
a positive real number. Larger values will typically result larger AR coefficients.
The coefficient matrices are generated using the algorithm proposed by Ansley
and Kohn (1986) which forces stationarity. It's not clear in detail how ar_scale
affects the coefficient matrices. Read the cited article by Ansley and Kohn (1986) and
the source code for more information.
Note that when using large ar_scale with large p or d, numerical
inaccuracies caused by the imprecision of the float-point presentation may result in errors
or nonstationary AR-matrices. Using smaller ar_scale facilitates the usage of larger
p or d.
Ansley C.F., Kohn R. 1986. A note on reparameterizing a vector autoregressive moving average model to enforce stationarity. Journal of statistical computation and simulation, 24:2, 99-106.