Description Usage Arguments Details Value Author(s) References See Also
View source: R/Mstep.hh.MSAR.VM.R
M step of the EM algorithm for fitting homogeneous Markov switching auto-regressive models, called in fit.MSAR.VM.
1 | Mstep.hh.MSAR.VM(data, theta, FB, constr = 0)
|
data |
array of univariate or multivariate series with dimension T*N.samples*d. T: number of time steps of each sample, N.samples: number of realisations of the same stationary process, d: dimension. |
theta |
model's parameter; object of class MSAR. See also init.theta.MSAR. |
FB |
Forward-Backward results, obtained by calling Estep.MSAR function |
constr |
constraints are added to the κ parameter (A preciser) |
The homogeneous MSAR model is labeled "HH" and it is written
P(X_t|X_{t-1}=x_{t-1}) = Q_{x_{t-1},x_t}
with X_t the hidden univariate process defined on \{1,\cdots,M \}
Y_t|X_t=x_t,y_{t-1},...,y_{t-p}
has a von Mises distribution with density
p_2(y_t|x_t,y_{t-s}^{t-1}) = \frac {1}{b(x_t,y_{t-s}^{t-1})} \exp≤ft(κ_0^{(x_t)} \cos(y_t-φ_0^{(x_t)})+ ∑_{\ell=1}^sκ_\ell^{(x_t)} \cos(y_t-y_{t-\ell}-φ_\ell^{(x)})\right)
which is equivalent to
p_2(y_t|x_t,y_{t-s}^{t-1}) = \frac {1}{b(x_t,y_{t-s}^{t-1})} ≤ft|\exp≤ft([γ_0^{(x_t)} + ∑_{\ell=1}^sγ_\ell^{(x_t)} e^{iy_{t-\ell}}]e^{-iy_t}\right)\right|
b(x_t,y_{t-s}^{t-1}) is a normalisation constant.
Both the real and the complex formulation are implemented. In practice, the complex version is used if the initial κ is complex.
List containing
mu |
intercepts |
kappa |
von Mises AR coefficients |
prior |
prior probabilities |
transmat |
transition matrix |
Valerie Monbet, valerie.monbet@univ-rennes1.fr
Ailliot P., Bessac J., Monbet V., Pene F., (2014) Non-homogeneous hidden Markov-switching models for wind time series. JSPI.
fit.MSAR.VM, Estep.MSAR.VM
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