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Ordinary Least Squares Regression

This example illustrates an ordinary least squares regression, by simulating a return series that scales the daily return values of the New York Stock Exchange Composite Index. It also provides an example of a constant conditional variance model.

1. Load the NYSE data set and convert the price series to a return series:

   load garchdata
   nyse = price2ret(NYSE);

2. Create a specification structure. Set the Display flag to 'off' to suppress the optimization details that garchfit usually displays:

   spec = garchset('P',0,'Q',0,'C',0,...
                   'Regress',1.2,...
                   'K',0.00015,...
                   'Display','off')
   spec = 
             Comment: 'Mean: ARMAX(0,0,?); Variance: GARCH(0,0)'
        Distribution: 'Gaussian'
                   C: 0
             Regress: 1.2000
       VarianceModel: 'GARCH'
                   K: 1.5000e-004
             Display: 'off'
   

3. Simulate a single realization of 2000 observations, fit the model, and examine the results:

   strm = RandStream('mt19937ar','Seed',2269);
   RandStream.setDefaultStream(strm);
   [e,s,y]        = garchsim(spec,2000,1,[],nyse);
   [coeff,errors] = garchfit(spec,y,nyse);
   garchdisp(coeff,errors)
    
       Mean: ARMAX(0,0,1); Variance: GARCH(0,0)
    
     Conditional Probability Distribution: Gaussian
     Number of Model Parameters Estimated: 3
   
                                  Standard          T     
     Parameter       Value          Error       Statistic 
    -----------   -----------   ------------   -----------
              C    -0.00022331    0.00028146      -0.7934
     Regress(1)    1.2084         0.03006         40.2005
              K    0.0001581      5.1417e-006     30.7479

   These estimation results are just the ordinary least squares (OLS) regression results. In fact, in the absence of GARCH effects and assuming Gaussian innovations, maximum likelihood estimation and least squares regression are the same thing.

   Note   This example appears purely for illustrative purposes. Although you can use the Econometrics Toolbox software to perform OLS, to do so is computationally inefficient and not recommended.

Regression in Monte Carlo

Multiple Time Series for Linear Models

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