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Multivariate AR-1 State-space Model
MARSS_marss.Rd
The form of MARSS models for users is "marxss", the MARSS models with inputs. See MARSS.marxss
. In the internal algorithms (e.g. MARSSkem
), the "marss" form is used and the \(\mathbf{D}\mathbf{d}_t\) are incorporated into the \(\mathbf{a}_t\) matrix and \(\mathbf{C}\mathbf{c}_t\) are incorporated into the \(\mathbf{u}_t\). The \(\mathbf{a}\) and \(\mathbf{u}\) matrices then become time-varying if the model includes \(\mathbf{d}_t\) and \(\mathbf{c}_t\).
This is a MARSS(1) model of the marss form: $$\mathbf{x}_{t} = \mathbf{B} \mathbf{x}_{t-1} + \mathbf{u}_t + \mathbf{G} \mathbf{w}_t, \textrm{ where } \mathbf{W}_t \sim \textrm{MVN}(0,\mathbf{Q})$$ $$\mathbf{y}_t = \mathbf{Z} \mathbf{x}_t + \mathbf{a}_t + \mathbf{H} \mathbf{v}_t, \textrm{ where } \mathbf{V}_t \sim \textrm{MVN}(0,\mathbf{R})$$ $$\mathbf{X}_1 \sim \textrm{MVN}(\mathbf{x0}, \mathbf{V0}) \textrm{ or } \mathbf{X}_0 \sim \textrm{MVN}(\mathbf{x0}, \mathbf{V0}) $$Note, by default \(\mathbf{V0}\) is a matrix of all zeros and thus \(\mathbf{x}_1\) or \(\mathbf{x}_0\) is treated as an estimated parameter not a diffuse prior. To remove clutter, the rest of the parameters are shown as time-constant (no \(t\) subscript) but all parameters can be time-varying.
Note, "marss" is a model form. A model form is defined by a collection of form functions discussed in marssMODEL
. These functions are not exported to the user, but are called by MARSS()
using the argument form
. These internal functions convert the users model list into the vec form of a MARSS model and do extensive error-checking.
Usage
MARSS(y,
inits = NULL,
model = NULL,
miss.value = as.numeric(NA),
method = "kem",
form = "marxss",
fit = TRUE,
silent = FALSE,
control = NULL,
fun.kf = "MARSSkfas",
...)
Details
See the help page for the MARSS.marxss
form for details.
Value
A object of class marssMLE
.
Examples
if (FALSE) {
# See the MARSS man page for examples
?MARSS
# and the Quick Examples chapter in the User Guide
RShowDoc("UserGuide", package = "MARSS")
}