# random_regime: Create random regime parameters In uGMAR: Estimate Univariate Gaussian and Student's t Mixture Autoregressive Models

## Description

`random_regime` generates random regime parameters.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```random_regime( p, mu_scale, sigma_scale, restricted = FALSE, constraints = NULL, m, forcestat = FALSE ) ```

## Arguments

 `p` a positive integer specifying the autoregressive order of the model. `mu_scale` a real valued vector of length two specifying the mean (the first element) and standard deviation (the second element) of the normal distribution from which the μ_{m} mean-parameters are generated in random mutations in the genetic algorithm. Default is `c(mean(data), sd(data))`. Note that the genetic algorithm optimizes with mean-parametrization even when `parametrization=="intercept"`, but input (in `initpop`) and output (return value) parameter vectors may be intercept-parametrized. `sigma_scale` a positive real number specifying the standard deviation of the (zero mean, positive only by taking absolute value) normal distribution from which the component variance parameters are generated in the random mutations in the genetic algorithm. Default is `var(stats::ar(data, order.max=10)\$resid, na.rm=TRUE)`. `restricted` a logical argument stating whether the AR coefficients φ_{m,1},...,φ_{m,p} are restricted to be the same for all regimes. `constraints` specifies linear constraints imposed to each regime's autoregressive parameters separately. For non-restricted models:a list of size (pxq_{m}) constraint matrices C_{m} of full column rank satisfying φ_{m}=C_{m}ψ_{m} for all m=1,...,M, where φ_{m}=(φ_{m,1},...,φ_{m,p}) and ψ_{m}=(ψ_{m,1},...,ψ_{m,q_{m}}). For restricted models:a size (pxq) constraint matrix C of full column rank satisfying φ=Cψ, where φ=(φ_{1},...,φ_{p}) and ψ=ψ_{1},...,ψ_{q}. The symbol φ denotes an AR coefficient. Note that regardless of any constraints, the autoregressive order is always `p` for all regimes. Ignore or set to `NULL` if applying linear constraints is not desired. `m` which regime? This is required for models with constraints for which a list of possibly differing constraint matrices is provided. `forcestat` use the algorithm by Monahan (1984) to force stationarity on the AR parameters (slower)? Not supported for constrained models.

## Details

If `forcestat==TRUE`, then the AR coefficients are relatively large, otherwise they are usually relatively small.

## Value

Regular models:

υ_{m}=(φ_{m,0},φ_{m},σ_{m}^2) where φ_{m}=(φ_{m,1},...,φ_{m,p}).

Restricted models:

Not supported!

Constrained models:

Replace the vectors φ_{m} with vectors ψ_{m}.

## References

• Monahan J.F. 1984. A Note on Enforcing Stationarity in Autoregressive-Moving Average Models. Biometrica 71, 403-404.

uGMAR documentation built on Jan. 24, 2022, 5:10 p.m.