matlab預測ARMA-GARCH 條件均值和方差模型

原文連接：http://tecdat.cn/?p=2841

此示例顯示MATLAB如何從複合條件均值和方差模型預測 和條件差別。

步驟1加載數據並擬合模型 

加載工具箱附帶的納斯達克數據。將條件均值和方差模型擬合到數據中。

nasdaq = DataTable.NASDAQ;
r = price2ret(nasdaq);
N = length(r);

model = arima('ARLa gs' 1,'Variance',garch(1,1),...
              'Distrib ution','t');
fit = estimate(mode ,r,'Variance0',{'Constant0',0.001});
 
    ARIMA(1,0,0) Model (t Distribution):
 
                  Value      StandardError    TStatistic      PValue  
                _________    _____________    __________    __________

    Constant    0.0012326     0.00018163         6.786      1.1528e-11
    AR{1}        0.066389       0.021398        3.1026       0.0019182
    DoF            14.839         2.2588        6.5693      5.0539e-11

 
 
    GARCH(1,1) Conditional Variance Model (t Distribution):
 
                  Value       StandardError    TStatistic      PValue  
                __________    _____________    __________    __________

    Constant    3.4488e-06     8.3938e-07        4.1087      3.9788e-05
    GARCH{1}       0.82904       0.015535        53.365               0
    ARCH{1}        0.16048       0.016331        9.8268      8.6333e-23
    DoF             14.839         2.2588        6.5693      5.0539e-11
[E0,V0] = infer(fit,r);

第2步預測收益和條件差別 

使用forecast計算回報狀語從句：條件方差爲1000週期的將來視界的MMSE預測。使用觀察到的回報和推斷殘差以及條件方差做爲預採樣數據。

[Y,YMS E,V] = forecast(fit, 100 0,'Y 0',r,'E0', E0, 'V0' ,V0);
upper = Y + 1.96*sqrt(YMSE);
lower = Y - 1.96*sqrt(YMSE);

figure
subplot(2,1,1)
plot(r,'Color',[.75,.75,.75])
hold on
plot(N+1:N+1000,Y,'r','LineWidth',2)
plot(N+1:N+1000,[upper,lower],'k--','LineWidth',1.5)
xlim([0,N+1000])
title('Forecasted Returns')
hold off
subplot(2,1,2)
plot(V0,'Color',[.75,.75,.75])
hold on
plot(N+1:N+1000,V,'r','LineWidth',2);
xlim([0,N+1000])
title('Forecasted Conditional Variances')
hold off

​

條件方差預測收斂於GARCH條件方差模型的漸近方差。預測的收益收斂於估計的模型常數（AR條件均值模型的無條件均值）。