Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

Simulate Conditional Variance Model

This example shows how to simulate a conditional variance model using simulate.

Step 1. Load the data and specify the model.

Load the Deutschmark/British pound foreign exchange rate data included with the toolbox, and convert to returns. Specify and fit a GARCH(1,1) model.

load Data_MarkPound
r = price2ret(Data);
T = length(r);
Mdl = garch(1,1);
EstMdl = estimate(Mdl,r);
v0 = infer(EstMdl,r);
 
    GARCH(1,1) Conditional Variance Model:
    ----------------------------------------
    Conditional Probability Distribution: Gaussian

                                  Standard          t     
     Parameter       Value          Error       Statistic 
    -----------   -----------   ------------   -----------
     Constant    1.05333e-06   3.50465e-07        3.00552
     GARCH{1}       0.806592      0.012908        62.4878
      ARCH{1}       0.154345     0.0115735        13.3361

Step 2. Simulate foreign exchange rate returns.

Use the fitted model to simulate 25 realizations of foreign exchange rate returns and conditional variances over a 1000-period forecast horizon. Use the observed returns and inferred conditional variances as presample innovations and variances, respectively.

rng default; % For reproducibility
[V,Y] = simulate(EstMdl,1000,'NumPaths',25,...
    'E0',r,'V0',v0);

figure
subplot(2,1,1)
plot(v0)
hold on
plot(T+1:T+1000,V)
xlim([0,T+1000])
title('Conditional Variances')
hold off

subplot(2,1,2)
plot(r)
hold on
plot(T+1:T+1000,Y)
xlim([0,T+1000])
title('Returns')
hold off

Step 3. Plot the returns distribution at a future time.

Use simulations to generate a forecast distribution of foreign exchange returns 500 days into the future. Generate 1000 sample paths to estimate the distribution.

rng default; % For reproducibility
[V,Y] = simulate(EstMdl,500,'NumPaths',1000,...
    'E0',r-EstMdl.Offset,'V0',v0);

figure
histogram(Y(500,:),10)
title('Return Distribution in 500 Days')

See Also

| | |

Related Examples

More About

Was this topic helpful?