title: Coefficient matching for GARCH model and R-program output
body: <p>I have the following output for my garch model using R-program.</p>
  
  <pre><code> Call:
   garch(x = cyber3, order = c(1, 1))
  
   Model:
   GARCH(1,1)
  
   Residuals:
         Min        1Q    Median        3Q       Max 
   -13.77455  -0.35905   0.07161   0.49866   9.55536 
  
   Coefficient(s):
       Estimate  Std. Error  t value Pr(&gt;|t|)    
   a0 2.610e-06   1.076e-07    24.25   &lt;2e-16 ***
   a1 1.564e-01   4.098e-03    38.17   &lt;2e-16 ***
   b1 8.460e-01   3.936e-03   214.94   &lt;2e-16 ***
   ---
   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
   Diagnostic Tests:
           Jarque Bera Test
  
   data:  Residuals
   X-squared = 160230, df = 2, p-value &lt; 2.2e-16
  
  
           Box-Ljung test
  
   data:  Squared.Residuals
   X-squared = 0.01052, df = 1, p-value = 0.9183
  </code></pre>
  
  <p>Then just to be safe and confirm, may I know how the a0, a1 and b1 correspond to the actual GARCH mathematical formula? For my guess, they should be constant, coefficient for the past return and coefficient for the past variance if I am correct. May I confirm this?</p>