## Documentation Center |

Infer `VARMAX` model innovations

`[W,logL] = vgxinfer(Spec,Y)`

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

Given a `VARMAX` model specification, `vgxinfer`
infers the innovations from observations of a multivariate time series
process.

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 t)b,
X(*t)b is
the regression component of a single numDims-dimensional
observation Y( at time t)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); produces an innovations
process |

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