vgxinfer

Infer VARMAX model innovations

Synopsis

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

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

Description

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

Input Arguments

SpecA model specification structure for a multidimensional VARMAX time series process, as produced by vgxset or vgxvarx.
YResponse 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.

Optional Input Arguments

XExogenous data. X is a cell vector or a cell matrix. Each cell contains a numDims-by-numX design matrix X(t) so that, for some b, X(t)*b is the regression component of a single numDims-dimensional observation Y(t) 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).
Y0Presample 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).
W0Presample 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).

Output Arguments

WInferred innovations process, the same size as Y.
LogL1-by-numPaths vector containing the total loglikelihood of the response data in each path of Y.

    Note:   The functions vgxinfer and vgxproc are complementary. For example, given a specification structure Spec for a stable and invertible process and an innovations process W1, the code

    Y = vgxproc(Spec,W1,X,Y0,W0);
    W2 = vgxinfer(Spec,Y,X,Y0,W0);

    produces an innovations process W2 that is identical to W1. Differences can appear if the process in Spec fails to be either stable or invertible.

See Also

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