Documentation |
Generate VARMAX model responses from innovations
[Y,logL] = vgxproc(Spec,W)
[Y,logL] = vgxproc(Spec,W,X,Y0,W0)
Given a VARMAX model specification and an innovations process, vgxproc generates model responses using known innovations. To generate responses with simulated innovations, use vgxsim. To generate responses with zero-valued innovations, use vgxpred.
Spec | A model specification structure for a multidimensional VARMAX time series process, as produced by vgxset or vgxvarx. |
W | Innovations data, as produced by vgxinfer. W is a matrix or a 3-D array. If W is a numObs-by-numDims matrix, it represents numObs observations of a single path of a numDims-dimensional time series. If W 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(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 W has multiple paths, X must contain either a single path (applied to all paths in W) or at least as many paths as in W (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 W has multiple paths, Y0 must contain either a single path (applied to all paths in W) or at least as many paths as in W (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 W has multiple paths, W0 must contain either a single path (applied to all paths in W) or at least as many paths as in W (extra paths are ignored). |
Y | Response data, the same size as W. |
LogL | 1-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. |