methods-coef: GARCH Coefficients Methods In fGarch: Rmetrics - Modelling Autoregressive Conditional Heteroskedasticity

Description

Coefficients methods for GARCH Modelling.

Methods

object = "ANY"

Generic function.

object = "fGARCH"

Extractor function for coefficients from a fitted GARCH model.

object = "fGARCHSPEC"

Extractor function for coefficients from a GARCH specification structure.

Note

`coef` is a generic function which extracts coefficients from objects returned by modeling functions.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## garchSpec - # Use default parameters beside alpha: spec = garchSpec(model = list(alpha = c(0.05, 0.05))) spec coef(spec) ## garchSim - # Simulate an univariate "timeSeries" series x = garchSim(spec, n = 200) x = x[,1] ## garchFit - fit = garchFit( ~ garch(1, 1), data = x) ## coef - coef(fit) ```

Example output

```Loading required package: timeDate

Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org

Formula:
~ garch(2, 1)
Model:
omega: 1e-06
alpha: 0.05 0.05
beta:  0.8
Distribution:
norm
Presample:
time          z     h y
1   -1 -0.1891135 1e-05 0
2    0  0.9539806 1e-05 0
omega alpha1 alpha2 gamma1 gamma2   beta     mu     ar     ma  delta
1e-06  5e-02  5e-02  0e+00  0e+00  8e-01  0e+00  0e+00  0e+00  2e+00
attr(,"distribution")
[1] "norm"

Series Initialization:
ARMA Model:                arma
Formula Mean:              ~ arma(0, 0)
GARCH Model:               garch
Formula Variance:          ~ garch(1, 1)
ARMA Order:                0 0
Max ARMA Order:            0
GARCH Order:               1 1
Max GARCH Order:           1
Maximum Order:             1
Conditional Dist:          norm
h.start:                   2
llh.start:                 1
Length of Series:          200
Recursion Init:            mci
Series Scale:              0.00269998

Parameter Initialization:
Initial Parameters:          \$params
Limits of Transformations:   \$U, \$V
Which Parameters are Fixed?  \$includes
Parameter Matrix:
U         V    params includes
mu     -0.70857998   0.70858 -0.070858     TRUE
omega   0.00000100 100.00000  0.100000     TRUE
alpha1  0.00000001   1.00000  0.100000     TRUE
gamma1 -0.99999999   1.00000  0.100000    FALSE
beta1   0.00000001   1.00000  0.800000     TRUE
delta   0.00000000   2.00000  2.000000    FALSE
skew    0.10000000  10.00000  1.000000    FALSE
shape   1.00000000  10.00000  4.000000    FALSE
Index List of Parameters to be Optimized:
mu  omega alpha1  beta1
1      2      3      5
Persistence:                  0.9

--- START OF TRACE ---
Selected Algorithm: nlminb

R coded nlminb Solver:

0:     282.38824: -0.0708580 0.100000 0.100000 0.800000
1:     282.34888: -0.0708678 0.103307 0.100856 0.801437
2:     282.32332: -0.0708880 0.104692 0.0982103 0.799257
3:     282.28048: -0.0709352 0.111795 0.0962744 0.798637
4:     282.19787: -0.0710776 0.120712 0.0886228 0.789806
5:     282.14785: -0.0713446 0.130534 0.0937502 0.780690
6:     282.11579: -0.0717825 0.134943 0.0980785 0.768702
7:     282.08666: -0.0726737 0.140839 0.0929116 0.769373
8:     282.03083: -0.0778534 0.152405 0.113158 0.741753
9:     281.98650: -0.0835615 0.157682 0.109197 0.730925
10:     281.91453: -0.0893262 0.162398 0.111801 0.729407
11:     281.82330: -0.112436 0.162726 0.115049 0.725113
12:     281.81378: -0.118987 0.166201 0.111863 0.725878
13:     281.81375: -0.119188 0.166127 0.112549 0.725384
14:     281.81375: -0.119141 0.166205 0.112523 0.725336
15:     281.81375: -0.119142 0.166179 0.112520 0.725368

Final Estimate of the Negative LLH:
LLH:  -901.0885    norm LLH:  -4.505442
mu         omega        alpha1         beta1
-3.216815e-04  1.211429e-06  1.125203e-01  7.253682e-01

R-optimhess Difference Approximated Hessian Matrix:
mu         omega        alpha1         beta1
mu     -3.040187e+07  1.733435e+09 -1.650372e+04  3.575789e+03
omega   1.733435e+09 -2.767849e+13 -1.568200e+08 -1.933172e+08
alpha1 -1.650372e+04 -1.568200e+08 -1.124447e+03 -1.159680e+03
beta1   3.575789e+03 -1.933172e+08 -1.159680e+03 -1.421235e+03
attr(,"time")
Time difference of 0.009485722 secs

--- END OF TRACE ---

Time to Estimate Parameters:
Time difference of 0.1381474 secs
mu         omega        alpha1         beta1
-3.216815e-04  1.211429e-06  1.125203e-01  7.253682e-01
```

fGarch documentation built on May 31, 2017, 4:02 a.m.