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 Quantlet: archest Description: estimates a GARCH process with mean zero by QMLE

Reference(s):
See e.g. Christian Gourieroux (1997), ARCH Models and Financial Applications, New York, Springer-Verlag.

 Usage: y = archest(xx,q,p) Input: xx vector q 1 or 2 (can be extended) p 1 or 2 (can be extended) Output: y list containing 1. parameter estimates, 2. standard errors, 3. likelihood value, 4. volatility estimate

Example:
```library("times")             ; loads the quantlets from times library
randomize(0)
daxreturn=tdiff(log(dax))   ; generates the monthly return
z=archest(daxreturn,1,1)
z{1}{1}                      ; Parameter Estimates
z{2}                         ; Standard Errors
z{3}                         ; Likelihood
timeplot(z{4}, 261)         ; Plot of Volatility Estimate

```
Result:
```Contents of minimum
[1,]  0.0024817
[2,]  0.13412
[3,]  0.10404

Contents of stderr
[1,]  0.0014225
[2,]  0.10998
[3,]  0.42943

Contents of lik
[1,]  381.48

"For reading convenience the graphical output has been omitted."
```
Example:
```library("times")             ; loads the quantlets from times library
randomize(0)                ; Seeding Initial Values
x=normal(100)                ; Generates normal distributed values
z=archest(x,1,1)
z{1}{1}                      ; Parameter Estimates

```
Result:
```Contents of minimum
[1,]  0.48528
[2,]  0.0026728
[3,]  0.53451
```

Author: C. Hafner, W. Haerdle, 19960814, G. Aydinli, 20010419 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006