FOR INTERNAL USE. isStationary_int checks the stationary condition and isIdentifiable checks the identification conditions
of the specified GMAR or StMAR model.
isStationary_int(p, M, params, restricted = FALSE)isIdentifiable(p, M, params, restricted = FALSE, StMAR = FALSE)
a positive integer specifying the order of AR coefficients.
a positive integer specifying the number of mixture components or regimes.
a real valued parameter vector specifying the model.
Size \((M(p+3)-1x1)\) vector \(\theta\)\(=\)(\(\upsilon_{1}\),...,\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1}\)), where \(\upsilon_{m}\)\(=(\phi_{m,0},\)\(\phi_{m}\)\(, \sigma_{m}^2)\) and \(\phi_{m}\)=\((\phi_{m,1},...,\phi_{m,p}), m=1,...,M\).
Size \((M(p+4)-1x1)\) vector (\(\theta, \nu\))\(=\)(\(\upsilon_{1}\),...,\(\upsilon_{M}\), \(\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M}\)).
Size \((3M+p-1x1)\) vector \(\theta\)\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1})\), where \(\phi\)=\((\phi_{1},...,\phi_{M})\).
Size \((4M+p-1x1)\) vector (\(\theta, \nu\))\(=(\phi_{1,0},...,\phi_{M,0},\)\(\phi\)\(, \sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1}, \nu_{1},...,\nu_{M})\).
Symbol \(\phi\) denotes an AR coefficient, \(\sigma^2\) a variance, \(\alpha\) a mixing weight and \(v\) a degrees of freedom parameter. Note that in the case M=1 the parameter \(\alpha\) is dropped, and in the case of StMAR model the degrees of freedom parameters \(\nu_{m}\) have to be larger than \(2\).
an (optional) logical argument stating whether the AR coefficients \(\phi_{m,1},...,\phi_{m,p}\) are restricted
to be the same for all regimes. Default is FALSE.
an (optional) logical argument stating whether StMAR model should be considered instead of GMAR model. Default is FALSE.
Returns TRUE or FALSE accordingly.
These functions don't have any argument checks!
These functions don't support models parametrized with general linear constraints.
Kalliovirta L., Meitz M. and Saikkonen P. (2015) Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36, 247-266.
References regarding the StMAR model will be updated after they are published.