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Forecast VAR Model Using Monte Carlo Simulation

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This example shows how to use Monte Carlo simulation viasimulateto forecast a VAR model.

simulateenables you to generate simulations of time series based on your model. If you have a trustworthy VAR model object, you can use these simulations as sample forecasts.

simulaterequires:

  • A model (EstMdlin what follows)

  • The number of periods for the forecast (numobsin what follows)

simulateoptionally takes:

  • An exogenous data series

  • A presample time series (Y(end-3:end,:)in what follows)

  • Future sample responses for conditional simulation

  • The number of realizations, or paths, to simulate (2000in what follows)

Load theData_USEconModeldata 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. For illustration, a VAR(4) model describes the time series.

loadData_USEconModelDEF = log(DataTable.CPIAUCSL); GDP = log(DataTable.GDP); rGDP = diff(GDP - DEF);% Real GDP is GDP - deflationTB3 = 0.01*DataTable.TB3MS; dDEF = 4*diff(DEF);% ScalingrTB3 = TB3(2:end) - dDEF;% Real interest is deflatedY = [rGDP,rTB3];

Fit a VAR(4) model specification.

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

Define the forecast horizon.

numobs = 21; FDates = dateshift(DataTable.Time(end),'end','quarter',1:numobs);

Simulate the model fornumobssteps ahead, and generate 2000 paths. Specify presample observations from the end of the data.

rng(1);%For reproducibilityYsim = simulate(EstMdl,numobs,'Y0',Y(end-3:end,:),'NumPaths', 2000);

Calculate the mean and standard deviation of the simulated series:

Ymean = mean(Ysim,3);% Calculate meansYstd = std(Ysim,0,3);% Calculate std deviations

Plot the means +/- 1 standard deviation for the simulated series:

figure; subplot(2,1,1) plot(DataTable.Time(end-10:end),Y(end-10:end,1),'k') hold('on') plot([DataTable.Time(end) FDates],[Y(end,1);Ymean(:,1)],'r') plot([DataTable.Time(end) FDates],[Y(end,1);Ymean(:,1)]+[0;Ystd(:,1)],'b') plot([DataTable.Time(end) FDates],[Y(end,1);Ymean(:,1)]-[0;Ystd(:,1)],'b') title('Transformed real GDP') subplot(2,1,2) plot(DataTable.Time(end-10:end),Y(end-10:end,2),'k') hold('on') plot([DataTable.Time(end) FDates],[Y(end,2);Ymean(:,2)],'r') plot([DataTable.Time(end) FDates],[Y(end,2);Ymean(:,2)]+[0;Ystd(:,2)],'b') plot([DataTable.Time(end) FDates],[Y(end,2);Ymean(:,2)]-[0;Ystd(:,2)],'b') title('Transformed real 3-mo T-bill rate')

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