Infer `VARMAX`

model innovations

[W,logL] = vgxinfer(Spec,Y) [W,logL] = vgxinfer(Spec,Y,X,Y0,W0)

`vgxinfer`

infers the innovations from observations
of a multivariate time series process specified by a `VARMAX`

model.

`Spec` | A model specification structure for a multidimensional `VARMAX` time
series process, as produced by `vgxset` or `vgxvarx` . |

`Y` | Response data. `Y` is a matrix or a 3-D array.
If `Y` is a numObs-by-numDims matrix,
it represents numObs observations of a single path
of a numDims-dimensional time series. If `Y` is
a numObs-by-numDims-by-numPaths array,
it represents numObs observations of numPaths paths
of a numDims-dimensional time series. Observations
across paths are assumed to occur at the same time. The last observation
is assumed to be the most recent. |

`X` | Exogenous data. `X` is a cell vector or a
cell matrix. Each cell contains a numDims-by-numX design
matrix `X(` so that, for some b,
`X(` *b is
the regression component of a single numDims-dimensional
observation `Y(` at time t.
If `X` is a numObs-by-1 cell vector,
it represents one path of the explanatory variables. If `X` is
a numObs- by-numXPaths cell
matrix, it represents numXPaths paths of the explanatory
variables. If `Y` has multiple paths, `X` must
contain either a single path (applied to all paths in `Y` )
or at least as many paths as in `Y` (extra paths
are ignored). |

`Y0` | Presample response data. `Y0` is a matrix
or a 3-D array. If `Y0` is a numPresampleYObs-by-numDims matrix,
it represents numPresampleYObs observations of
a single path of a numDims-dimensional time series.
If `Y0` is a numPresampleYObs-by-numDims-by-numPreSampleYPaths array,
it represents numPresampleYObs observations of numPreSampleYPaths
paths of a numDims-dimensional time series. If `Y0` is
empty or if numPresampleYObs is less than the
maximum `AR` lag in `Spec` , presample
values are padded with zeros. If numPresampleYObs is
greater than the maximum `AR` lag, the most recent
samples from the last rows of each path of `Y0` are
used. If `Y` has multiple paths, `Y0` must
contain either a single path (applied to all paths in `Y` )
or at least as many paths as in `Y` (extra paths
are ignored). |

`W0` | Presample innovations data. `W0` is a matrix
or a 3-D array. If `W0` is a numPresampleWObs-by-numDims matrix,
it represents numPresampleWObs observations of
a single path of a numDims-dimensional time series.
If W0 is a numPresampleWObs-by-numDims-by-numPreSampleWPaths array,
it represents numPresampleWObs observations of numPreSampleWPaths
paths of a numDims-dimensional time series. If `W0` is
empty or if numPresampleWObs is less than the
maximum MA lag in Spec, presample values are padded with zeros. If numPresampleWObs is
greater than the maximum `MA` lag, the most recent
samples from the last rows of each path of `W0` are
used. If `Y` has multiple paths, `W0` must
contain either a single path (applied to all paths in `Y` )
or at least as many paths as in `Y` (extra paths
are ignored). |

`W` | Inferred innovations process, the same size as `Y` . |

`LogL` | 1-by-numPaths vector containing the total
loglikelihood of the response data in each path of `Y` . |

Y = vgxproc(Spec,W1,X,Y0,W0); W2 = vgxinfer(Spec,Y,X,Y0,W0); `W2` that is identical to `W1` .
Differences can appear if the process in `Spec` fails
to be either stable or invertible. |

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