Creating a probability distribution from GARCH model

How do I simulate a GARCH model forecast in order to create a probability distribution?

Answer 1

[Karanjot]

Hi Todd,

I understand that you want to simulate a GARCH model forecast to create a probability distribution.

To simulate a GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model forecast and create a probability distribution using MathWorks products, you can use the Econometrics Toolbox in MATLAB. Here's a step-by-step guide:

• Load the necessary data: Prepare your time series data that you want to model using the GARCH model.
• Specify a GARCH model. For example:

Mdl = garch('Constant',0.01,'GARCH',0.7,'ARCH',0.25) 

• To simulate future returns based on the GARCH model, you can use the ‘simulate’ function. You may choose to simulate from the model with or without using presample data.

rng default; 
[Vw,Yw] = simulate(Mdl,100,'NumPaths',5,... 
    'E0',0.05,'V0',0.001); 
Vw(1,:) 

• You can create a probability distribution from the simulated returns using the ‘fitdist’ function. This function fits a parametric distribution to the data and returns an object that represents the estimated distribution. You can choose a distribution that best fits your data based on statistical criteria

pd = fitdist(Vw, 'Normal'); 

To learn more about simulating GARCH models, please refer to the below documentation:

https://www.mathworks.com/help/econ/unconditional-variance.html

I hope this helps!