Moments of GARCH(1,1) 

The value of a generalized autoregressive conditionally heteroscedastic process GARCHProcess has a heavy-tailed distribution with only a few finite moments of low order.

Fourth moment of a GARCHProcess with orders (1,1).

In[1]:=
Click for copyable input
X
Out[1]=

Define the function to extract moment finiteness conditions.

In[2]:=
Click for copyable input
X

Visualize the parameter conditions for moments to exist.

In[3]:=
Click for copyable input
X
Out[3]=

Values of the first few even moments for a weakly stationary GARCHProcess.

show complete Wolfram Language input
In[5]:=
Click for copyable input
X
Out[5]=

Compare to the values of the even moments for a non-weakly stationary GARCH with process initial values set to zero.

In[6]:=
Click for copyable input
X
Out[6]=
de es ja pt-br zh