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.

Mdl = varm(2,4); Mdl.SeriesNames = {'Transformed real GDP','Transformed real 3-mo T-bill rate'}; EstMdl = estimate(Mdl,Y); ... numperiods = 21; FDates = dateshift(DataTimeTable.Time(end),'end','quarter',1:numperiods); [Forecast,ForecastMSE] = forecast(EstMdl,numperiods,Y(end-3:end,:));

Create and estimate a VAR(4) model for the CPI growth rate and unemployment rates. Treat the last ten periods as the forecast horizon. load Data_USEconModel cpi = DataTimeTable.CPIAUCSL; unrate = DataTimeTable.UNRATE; rcpi = price2ret(cpi); unrate = unrate(2:end); Y = [rcpi unrate]; Mdl = varm(2,4); EstMdl = estimate(Mdl,Y(1:(end-10),:));

The fevd function returns the forecast error variance decomposition (FEVD) of the variables in a VAR(p) model attributable to shocks to each response variable in the system.

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.

Forecast Multivariate Model Responses Using Econometric Modeler App Interactively estimate a multivariate model and generate forecasts from the model. Create and Adjust VAR Model Using Shorthand Syntax This example shows how to create a three-dimensional VAR(4) model with unknown parameters using varm and the shorthand syntax.

EstMdl is an estimated varm model object. It is fully specified because all parameters have known values.

This MATLAB function returns optimal one-step-ahead point forecasts YF of a fully specified threshold-switching dynamic regression model Mdl over a forecast horizon of length numPeriods.

For the two VAR(4) models, the presample period is the first four rows of Data. Use the same presample period for the VAR(2) models so that all the models are fit to the same data. This is necessary for model fit comparisons. For both models, the forecast period is the final 10% of the rows of Data.

Mdl = varm with properties: Description: "2-Dimensional VAR(4) Model" SeriesNames: "Y1" "Y2" NumSeries: 2 P: 4 Constant: [2×1 vector of NaNs] AR: {2×2 matrices of NaNs} at lags [1 2 3 ...

VAR model, specified as a varm model object created by varm or estimate.

This MATLAB function returns optimal point forecasts YF of a fully specified Markov-switching dynamic regression model Mdl over a forecast horizon of length numPeriods.

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. Use the shorthand syntax. ... Display the VAR(2) model. ... Mdl = varm with properties: Description: "3-Dimensional VAR(2) Model" SeriesNames: "Y1" "Y2" "Y3" NumSeries: 3 P: 2 Constant: [3×1 vector of NaNs] AR: {3×3 matrices of NaNs} at lags [1 2] Trend: [3×1 vector of zeros] Beta: [3×0 matrix] Covariance: [3×3 matrix of NaNs]

Mdl = varm(2,4); Mdl.SeriesNames = {'Transformed real GDP','Transformed real 3-mo T-bill rate'}; EstMdl = estimate(Mdl,Y); Define the forecast horizon.

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.

%% set forecast horizon h = 16; % save 16 observations for out-of-sample analysis Y0 = y(1:end-16,:); var_f = estimate(model,Y0); % Forecast based on Y0 [Y_fore, YMSE] = forecast(var_f,h,Y0); % Calculate confidence bands extractMSE = @(x)diag(x)'; MSE = cellfun(extractMSE,YMSE,'UniformOutput',false); SE = sqrt(cell2mat(MSE)); YFI = zeros(h,var_est.NumSeries,2); YFI(:,:,1) = Y_fore - 2*SE; YFI(:,:,2) = Y_fore + 2*SE; % re-scale time-series and forecasts y_scale = m_y + y.*s_y; Y_fore_scale = m_y + Y_fore.*s_y; YFI_scale = m_y + YFI.*s_y; Y1 = y_scale(end-15:end,:); % Now plot forecasts fh = dat

This MATLAB function converts the VEC(p – 1) model Mdl to its equivalent VAR(p) model representation VARMdl.

Forecast CPI growth rates given known values of the unemployment rate using Monte Carlo simulation.