Garch fitting of financial data in R programming

Feb 3rd, 2012
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Manchester College
Course: Mathematics
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This document provides a simple example of how to fit Garch models in a financial data. The paper calculates log returns of the data before fitting and testing the data using L-jung Box test. The student should enhance understanding of the codes by trying the process using a different set of data.

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library(fBasics)library(moments)library(fGarch)setwd("C:/Users/D/Desktop/project")eabll=read.csv("Book1.csv",header=TRUE);eablleabl=na.omit(eabll);eableablrt=eabl$EABL;eablrtlogrt=log(eablrt);logrt#a#mean of the log returnsmean(logrt) [1] 5.035465Mean not equal to zero#b#skewness of log returnsskewness(logrt)[1] 0.6705608The data is positively skewed.#c#kurtosis of log returnskurtosis(logrt)[1] 4.862654#since kurtosis is greater than three hence it is a leptokurtic showing it has an excess kurtosis with a fat tail.#dBox.test(logrt,lag=10,type='Ljung') Box-Ljung testdata: logrtX-squared = 21327.56, df = 10, p-value < 2.2e-16#commentP value is small hence heteroscedastic with no dependency.#e#acf plotacf(logrt)acf(logrt^2)#(f)#fitting GARCH(1,1) model with Gaussian inovationsfitmodel=garchFit(~garch(1,1),data=logrt,cond.dist ="norm",trace=F)summary(fitmodel)#outputStandardised Residuals Tests: Statistic p-Value Jarque-Bera Test R Chi^2 5419785 0 Shapiro-Wilk Test R W 0.5737438 0 Ljung-Box Test R Q(10) 6767.593 0 Ljung-Box Test R Q(15) 9797.003 0 Ljung-Box Test R Q(20) 12652.83 0 Ljung-Box Test R^2 Q(10) 0.05045615 1 Ljung-Box Test R^2 Q(15) 0.07463037 1 Ljung-Box Test R^2 Q(20) 0.1045167 1 LM Arch Test R TR^2 0.05965995 1 Information Criterion Statistics:

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