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    %% Forecast GJR Model Conditional Variances
% Forecast conditional variances from a fully specified |gjr|
% model object. That is, forecast from an estimated |gjr| model
% or a known |gjr| model in which you specify all parameter values. This
% example follows from <docid:econ_ug.bupeold-1>.
%%
% Load the Nelson-Plosser data set. Convert the yearly stock price indices
% (|SP|) to returns.

% Copyright 2015 The MathWorks, Inc.

load Data_NelsonPlosser;
sp = price2ret(DataTable.SP);
%%
% Create a GJR(1,1) model and fit it to the return series.
Mdl = gjr('GARCHLags',1,'ARCHLags',1,'LeverageLags',1);
EstMdl = estimate(Mdl,sp);
%%
% Forecast the conditional variance of the nominal return series 10 years
% into the future using the estimated GJR model.  Specify the entire
% return series as presample observations. The software infers presample
% conditional variances using the presample observations and the model.
numPeriods = 10;
vF = forecast(EstMdl,numPeriods,'Y0',sp);
%%
% Plot the forecasted conditional variances of the nominal returns. Compare
% the forecasts to the observed conditional variances.
v = infer(EstMdl,sp);
nV = size(v,1);
dates = dates((end - nV + 1):end);

figure;
plot(dates,v,'k:','LineWidth',2);
hold on;
plot(dates(end):dates(end) + 10,[v(end);vF],'r','LineWidth',2);
title('Forecasted Conditional Variances of Returns');
ylabel('Conditional variances');
xlabel('Year');
axis tight;
legend({'Estimation Sample Cond. Var.','Forecasted Cond. var.'},...
    'Location','NorthWest');