A varm model object is a MATLAB® variable containing properties that describe the model, such as AR polynomial degree p, response dimensionality n, and coefficient values. varm must be able to infer n and p from your specifications; n and p are not estimable.

The varm function returns a varm object specifying the functional form and storing the parameter values of a p-order, stationary, multivariate vector autoregression model (VAR(p)) model.

numseries = 3; dnan = diag(nan(numseries,1)); VAR2diag = varm(AR={dnan dnan},SeriesNames=seriesnames); VAR2full = varm(numseries,2); VAR2full.SeriesNames = seriesnames; VAR4diag = varm(AR={dnan dnan dnan dnan},SeriesNames=seriesnames); VAR4full = varm(numseries,4); VAR4full.SeriesNames = seriesnames; The matrix dnan is a diagonal matrix with NaN values along its main diagonal. In general, missing values specify the presence of the parameter in the model, and indicate that the parameter needs to be fit to data. MATLAB® holds the off diagonal elements, 0, fixed during estimation.

This MATLAB function displays a summary of the VAR(p) model Mdl.

This MATLAB function returns the fully specified, estimated VAR(p) model EstMdl.

Mdls is an 8-by-1 vector of varm objects containing estimable parameters. Mdls(4) matches the structure of the fourth model in the table. Lags 4 and 8 of the model contain coefficient matrices of NaN values, which indicates that they are estimable. All other lags have coefficient matrices of zeros, which means that they are effectively absent from the model. The Beta property is an empty matrix; MATLAB® populates Beta during estimation when you specify predictor data.

Enter Mdl.PropertyName at the MATLAB command line, where PropertyName is the name of the property you want to examine or reassign. You can change any writable property of a model object using dot notation: ... Create a VAR(2) model object for three response variables.

Given a fully specified varm model, you must supply the autoregression coefficients to armairf. By default, armairf sends a unit shock through the system, which results in the forecast error impulse response. You can optionally supply the innovations covariance matrix and choose whether to generate generalized or orthogonalized impulse responses.

Stationary multivariate linear models including exogenous predictor variables

This MATLAB function returns the numeric array Y containing a random numobs-period path of multivariate response series from performing an unconditional simulation of the fully specified VAR(p) model Mdl.

A fully-specified model (for example, EstMdl in what follows) The number of periods for the forecast (for example, numperiods in what follows) A presample time series (e.g., Y(end-3:end,:) in what follows) ... Load the Data_USEconModel data set. This example uses two time series: the logarithm of real GDP, and the real 3-month T-bill rate, both differenced to be approximately stationary. Suppose that a VAR(4) model is appropriate to describe the time series.

This MATLAB function returns a numeric array containing paths of minimum mean squared error (MMSE) multivariate response forecasts Y over a length numperiods forecast horizon, using the fully specified VAR(p) model Mdl.

This MATLAB function returns a random vector of coefficients Coeff and a random innovations covariance matrix Sigma drawn from the prior Bayesian VAR(p) model PriorMdl.

This example simulates data from an arbitrary 3-D VAR(2) model, and fits a VAR(2) model to the simulated data.

Mdl is a varm model object. It serves as a template for model estimation. MATLAB� considers any NaN values as unknown parameter values to be estimated. For example, the Constant property is a 2-by-1 vector of NaN values.

This MATLAB function creates a Bayesian VAR(p) model object for the input number of response time series variables, which specifies dimensionalities and prior assumptions for all model coefficients Λ and the innovations covariance Σ.

This MATLAB function returns a numeric array E containing the series of multivariate inferred innovations from evaluating the fully specified VAR(p) model Mdl at the numeric array of response data Y.

Create a default VAR(4) model using shorthand syntax.

YIRF is a 15-by-2-by-2 array of impulse responses. Each row corresponds to a time in the forecast horizon (0,...,14), column j corresponds to a shock to variable Y(:,j) at time 0, and page k contains the impulse responses of a variable Y(:,k).