params |
a real valued parameter vector specifying the model.
- For non-restricted models:
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Size (M(p+3)+M-M1-1x1) vector \theta=(\upsilon_{1},...,\upsilon_{M},
\alpha_{1},...,\alpha_{M-1},\nu) where
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\upsilon_{m}=(\phi_{m,0},\phi_{m},\sigma_{m}^2)
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\phi_{m}=(\phi_{m,1},...,\phi_{m,p}), m=1,...,M
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\nu=(\nu_{M1+1},...,\nu_{M})
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M1 is the number of GMAR type regimes.
In the GMAR model, M1=M and the parameter \nu dropped. In the StMAR model, M1=0.
If the model imposes linear constraints on the autoregressive parameters:
Replace the vectors \phi_{m} with the vectors \psi_{m} that satisfy
\phi_{m}=C_{m}\psi_{m} (see the argument constraints).
- For restricted models:
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Size (3M+M-M1+p-1x1) vector \theta=(\phi_{1,0},...,\phi_{M,0},\phi,
\sigma_{1}^2,...,\sigma_{M}^2,\alpha_{1},...,\alpha_{M-1},\nu), where \phi=(\phi_{1},...,\phi_{p})
contains the AR coefficients, which are common for all regimes.
If the model imposes linear constraints on the autoregressive parameters:
Replace the vector \phi with the vector \psi that satisfies
\phi=C\psi (see the argument constraints).
Symbol \phi denotes an AR coefficient, \sigma^2 a variance, \alpha a mixing weight, and \nu a degrees of
freedom parameter. If parametrization=="mean", just replace each intercept term \phi_{m,0} with the regimewise mean
\mu_m = \phi_{m,0}/(1-\sum\phi_{i,m}). In the G-StMAR model, the first M1 components are GMAR type
and the rest M2 components are StMAR type.
Note that in the case M=1, the mixing weight parameters \alpha are dropped, and in the case of StMAR or G-StMAR model,
the degrees of freedom parameters \nu have to be larger than 2.
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