# methods-summary: GARCH summary methods In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

 summary-methods R Documentation

## GARCH summary methods

### Description

Summary methods for GARCH modelling.

### Methods

Methods for `summary` defined in package fGarch:

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:

```
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:

```        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:

```
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

``````## garchSim -
x = garchSim(n = 200)

## garchFit -
fit = garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE)
summary(fit)
``````

fGarch documentation built on May 29, 2024, 8:30 a.m.