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I'm using GARCH() function (tseries package) to fit garch model.

I tried it with random numbers: g <- garch(rnorm(750), order = c(1,1))

I know in this case the variance is constant BUT how to understand it reading the output of that function?

summary(g)
Call:
garch(x = rnorm(750), order = c(1, 1))

Model:
GARCH(1,1)

Residuals:
     Min       1Q   Median       3Q      Max 
-3.34115 -0.68029  0.07071  0.71918  3.31074 

Coefficient(s):
    Estimate  Std. Error  t value Pr(>|t|)
a0 9.454e-01   4.789e+00    0.197    0.843
a1 9.102e-03   4.535e-02    0.201    0.841
b1 2.448e-12   5.028e+00    0.000    1.000

Diagnostic Tests:
        Jarque Bera Test

data:  Residuals 
X-squared = 0.0373, df = 2, p-value = 0.9815


        Box-Ljung test

data:  Squared.Residuals 
X-squared = 2e-04, df = 1, p-value = 0.9879
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A hint in the output is that neither a1 nor b1 are significantly different from zero. Another way to tell would be to do a Ljung-Box test on the squares of the original data.

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  • $\begingroup$ are you referring to the (P-value) column? why only a1 and b1? qhat a0 represent? In the output I already see the Ljung-Box test in the output. Do i have to do it again on the original squared values? $\endgroup$
    – Dail
    Commented Nov 21, 2011 at 9:40
  • $\begingroup$ a0 is the intercept and doesn't indicate garchness. The Ljung-Box in the output is the test on the residuals from the model, and asks if the model captured all the garchness. Testing on the original data asks if there is any garchness in the first place. $\endgroup$
    – Patrick Burns
    Commented Nov 21, 2011 at 17:43
  • $\begingroup$ so I need to see A1 and B1 the other are information are not important to understand if the series is heteroscedastic or not, right?.... Patrick probably an ARCH model is better then Garch ? $\endgroup$
    – Dail
    Commented Nov 21, 2011 at 18:18
  • $\begingroup$ Yes, a1 and b1 are what control changes in volatility. No, garch models are better than arch models. Also 750 observations is really too short (assuming daily data). You really want to have at least 1000, and 2000 is much better. $\endgroup$
    – Patrick Burns
    Commented Nov 21, 2011 at 20:45
  • $\begingroup$ wow 2000? is not too much? we are talking about many years $\endgroup$
    – Dail
    Commented Nov 21, 2011 at 20:58

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