MATLAB实现VAR向量自回归时间序列区间预测（完整源码和数据）

clc clear load Data_USEconModel DEF = log(DataTable.CPIAUCSL); GDP = log(DataTable.GDP); rGDP = diff(GDP - DEF); % Real GDP is GDP - deflation TB3 = 0.01*DataTable.TB3MS; dDEF = 4*diff(DEF); % Scaling rTB3 = TB3(2:end) - dDEF; % Real interest is deflated Y = [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); % Predict the evolution of the time series: numperiods = 21; FDates = dateshift(DataTable.Time(end),'end','quarter',1:numperiods); [Forecast,ForecastMSE] = forecast(EstMdl,numperiods,Y(end-3:end,:)); % Extract the main diagonal elements from the matrices in each cell of ForecastMSE. Apply the square root of the result to obtain standard errors. extractMSE = @(x)diag(x)'; MSE = cellfun(extractMSE,ForecastMSE,'UniformOutput',false); SE = sqrt(cell2mat(MSE)); % Estimate approximate 95% forecast intervals for each response series. ForecastFI = zeros(numperiods,Mdl.NumSeries,2); ForecastFI(:,:,1) = Forecast - 2*SE; ForecastFI(:,:,2) = Forecast + 2*SE; % Plot the forecasts and the data. figure h1 = plot(DataTable.Time((end-49):end),Y((end-49):end,1)); hold on h2 = plot(FDates,Forecast(:,1)); h3 = plot(FDates,ForecastFI(:,1,1),'k--'); plot(FDates,ForecastFI(:,1,2),'k--'); title('Real GDP Growth Rate') h = gca; fill([FDates(1) h.XLim([2 2]) FDates(1)],h.YLim([1 1 2 2]),'k',... 'FaceAlpha',0.1,'EdgeColor','none'); legend([h1 h2 h3],'True','Forecast','95% Forecast interval',... 'Location','northwest') hold off figure h1 = plot(DataTable.Time((end-49):end),Y((end-49):end,2)); hold on h2 = plot(FDates,Forecast(:,2)); h3 = plot(FDates,ForecastFI(:,2,1),'k--'); plot(FDates,ForecastFI(:,2,2),'k--'); title('3-month T-bill rate') h = gca; fill([FDates(1) h.XLim([2 2]) FDates(1)],h.YLim([1 1 2 2]),'k',... 'FaceAlpha',0.1,'EdgeColor','none'); legend([h1 h2 h3],'True','Forecast','95% Forecast interval',... 'Location','northwest') hold off %此示例使用两个时间序列：实际 GDP 的对数和实际 3 个月国库券利率，两者的差异近似平稳。 假设 VAR(4) 模型适合描述时间序列。