Generate a Random Model — r

This function may be used to generate random state space or VARMA models. The main argument is a model template, which defines the type of model to generate, see e.g. model structures(). If bounds for the poles and/or the zeroes are given, then the procedure simply generates random models until a model which satisfies the constraint is found. Of course this is a very crude method and it may need a large number of randomly generated model.

Usage

r_model(
  template,
  ntrials.max = 100,
  bpoles = NULL,
  bzeroes = NULL,
  rand.gen = stats::rnorm,
  ...
)

Arguments

template: A model template as computed e.g. by model2template().
ntrials.max: Maximum number of trials.
bpoles, bzeroes: Lower bounds on the poles and zeroes of the model (such that stability and invertibility assumptions are satisfied). If set to NA, then the corresponding test is skipped.
rand.gen: (optional) A function to generate the random, "free" parameters.
...: Additional parameters, passed on to rand.gen. In particular, if the "free" paramameters are generated by rnorm(), then the standard deviation sd may be set. Choosing small values for sd makes it easier to find a stable and miniphase model. Of course this "trick" only works if the reference model, which is obtained with a zero parameter vector, satisfies the constraints.

Value

Model object whose class depends on the template.

Examples

# Generate a random VARMA model in echelon form ############

# Compute the appropriate model template
tmpl = tmpl_arma_echelon(nu = c(1,2,1))

# Create a random model, which is stable but not necessarily miniphase
model = r_model(tmpl, bpoles = 1, sd = 0.5)
model
#> ARMA model [3,3] with orders p = 2 and q = 2
#> AR polynomial a(z):
#>      z^0 [,1]     [,2]  [,3]   z^1 [,1]        [,2]        [,3]   z^2 [,1]
#> [1,]        1 0.000000     0 -0.2230435 -0.09862739 -0.19911985 0.00000000
#> [2,]        0 1.000000     0  0.0000000  0.10891433  0.00000000 0.08518435
#> [3,]        0 0.418622     1  0.2510531  0.06956840  0.05433312 0.00000000
#>            [,2]      [,3]
#> [1,]  0.0000000 0.0000000
#> [2,] -0.3917393 0.8690266
#> [3,]  0.0000000 0.0000000
#> MA polynomial b(z):
#>      z^0 [,1]     [,2]  [,3]   z^1 [,1]        [,2]       [,3]   z^2 [,1]
#> [1,]        1 0.000000     0 -0.5002612 -0.26449849 -0.2369659  0.0000000
#> [2,]        0 1.000000     0  1.3306812  0.03203034 -0.2724562 -0.5397279
#> [3,]        0 0.418622     1  0.0840577 -0.12188649  0.1518820  0.0000000
#>           [,2]       [,3]
#> [1,] 0.0000000  0.0000000
#> [2,] 0.2843032 -0.8556644
#> [3,] 0.0000000  0.0000000
#> Left square root of noise covariance Sigma:
#>             u[1]       u[2]      u[3]
#> u[1]  0.13235178  0.0000000 0.0000000
#> u[2]  0.12266369 -0.5161338 0.0000000
#> u[3] -0.05594441 -0.2964049 0.6447166

# Check whether the poles satisfy the constraint
min(abs(poles(model)))
#> There are determinantal roots at (or close to) infinity.
#> Roots close to infinity got discarded.
#> [1] 1.10882
min(abs(zeroes(model)))
#> There are determinantal roots at (or close to) infinity.
#> Roots close to infinity got discarded.
#> [1] 1.118997