Identify Conditional Heteroscedacity 

TimeSeriesModelFit automatically checks for conditional heteroscedacity in data and fits ARCH/GARCH models to data.

Create a time series of daily returns on Starbucks Corp. stock.

show complete Wolfram Language input
In[2]:=
Click for copyable input
X
In[3]:=
Click for copyable input
X
Out[3]=

Compute the autocorrelation function.

In[4]:=
Click for copyable input
X
show complete Wolfram Language input
Out[5]=

Test for autocorrelation in the sequence of returns.

In[6]:=
Click for copyable input
X
Out[6]=

The returned time series is not autocorrelated, but its square is.

In[7]:=
Click for copyable input
X
In[8]:=
Click for copyable input
X
Out[8]=
In[9]:=
Click for copyable input
X
Out[9]=

TimeSeriesModelFit determines the GARCH family as the best fit for the data.

In[10]:=
Click for copyable input
X
Out[10]=

Find the fitted process.

In[11]:=
Click for copyable input
X
Out[11]=

The model residuals appear uncorrelated.

In[12]:=
Click for copyable input
X
Out[12]=
In[13]:=
Click for copyable input
X
Out[13]=

Use TimeSeriesModel to compute confidence intervals of future forecast.

In[14]:=
Click for copyable input
X
In[15]:=
Click for copyable input
X
Out[15]=