Documentation |
Simulate VARMAX model responses
Y = vgxsim(Spec,numObs)
[Y,W] = vgxsim(Spec,numObs,X,Y0,W0,numPaths)
vgxsim simulates sample paths and innovations of a multidimensional VARMAX time series process.
Spec | A model specification structure for a multidimensional VARMAX time series process, as produced by vgxset or vgxvarx. |
numObs | Positive integer indicating the number of observations generated for each path of output arguments Y and W. |
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 response 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). |
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). |
numPaths | Number of simulated paths. The default is 1. It is necessary to specify numPaths to generate multiple paths. If numPaths > 1 and X, Y, and W are single paths, all forecasts are identical. |