# methods-summary: GARCH Summary Methods In fGarch: Rmetrics - Modelling Autoregressive Conditional Heteroskedasticity

## Description

Summary methods for GARCH Modelling.

## Methods

object = "ANY"

Generic function

object = "fGARCH"

Summary function for objects of class `"fGARCH"`.

## How to read a diagnostic summary report?

The first five sections return the title, the call, the mean and variance formula, the conditional distribution and the type of standard errors:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ``` Title: GARCH Modelling Call: garchFit(~ garch(1, 1), data = garchSim(), trace = FALSE) Mean and Variance Equation: ~arch(0) Conditional Distribution: norm Std. Errors: based on Hessian ```

The next three sections return the estimated coefficients, and an error analysis including standard errors, t values, and probabilities, as well as the log Likelihood values from optimization:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` Coefficient(s): mu omega alpha1 beta1 -5.79788e-05 7.93017e-06 1.59456e-01 2.30772e-01 Error Analysis: Estimate Std. Error t value Pr(>|t|) mu -5.798e-05 2.582e-04 -0.225 0.822 omega 7.930e-06 5.309e-06 1.494 0.135 alpha1 1.595e-01 1.026e-01 1.554 0.120 beta1 2.308e-01 4.203e-01 0.549 0.583 Log Likelihood: -843.3991 normalized: -Inf ```

The next section provides results on standardized residuals tests, including statistic and p values, and on information criterion statistic including AIC, BIC, SIC, and HQIC:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ``` Standardized Residuals Tests: Statistic p-Value Jarque-Bera Test R Chi^2 0.4172129 0.8117146 Shapiro-Wilk Test R W 0.9957817 0.8566985 Ljung-Box Test R Q(10) 13.05581 0.2205680 Ljung-Box Test R Q(15) 14.40879 0.4947788 Ljung-Box Test R Q(20) 38.15456 0.008478302 Ljung-Box Test R^2 Q(10) 7.619134 0.6659837 Ljung-Box Test R^2 Q(15) 13.89721 0.5333388 Ljung-Box Test R^2 Q(20) 15.61716 0.7400728 LM Arch Test R TR^2 7.049963 0.8542942 Information Criterion Statistics: AIC BIC SIC HQIC 8.473991 8.539957 8.473212 8.500687 ```

## Author(s)

Diethelm Wuertz for the Rmetrics R-port.

## Examples

 ```1 2 3 4 5 6``` ```## garchSim - x = garchSim(n = 200) ## garchFit - fit = garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE) summary(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

Title:
GARCH Modelling

Call:
garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE)

Mean and Variance Equation:
data ~ garch(1, 1)
<environment: 0x1c5e458>
[data = x]

Conditional Distribution:
norm

Coefficient(s):
mu        omega       alpha1        beta1
-6.4040e-05   1.2383e-11   8.8709e-04   1.0000e+00

Std. Errors:
based on Hessian

Error Analysis:
Estimate  Std. Error  t value Pr(>|t|)
mu     -6.404e-05   2.473e-04   -0.259    0.796
omega   1.238e-11   1.389e-07    0.000    1.000
alpha1  8.871e-04   1.394e-02    0.064    0.949
beta1   1.000e+00   6.466e-03  154.655   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Log Likelihood:
847.0734    normalized:  4.235367

Description:
Tue Jul  4 05:44:55 2017 by user: anon

Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test   R    Chi^2  1.712507  0.4247504
Shapiro-Wilk Test  R    W      0.9917929 0.320692
Ljung-Box Test     R    Q(10)  7.711915  0.6569533
Ljung-Box Test     R    Q(15)  17.65768  0.2810895
Ljung-Box Test     R    Q(20)  24.6037   0.2170152
Ljung-Box Test     R^2  Q(10)  4.991155  0.8917681
Ljung-Box Test     R^2  Q(15)  10.18916  0.8076755
Ljung-Box Test     R^2  Q(20)  11.26092  0.9391733
LM Arch Test       R    TR^2   6.153837  0.9081293

Information Criterion Statistics:
AIC       BIC       SIC      HQIC
-8.430734 -8.364768 -8.431514 -8.404039
```

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