CODEWITHSUNDEEP
statisticstime-seriesfinance
sonlobo
sonlobo

Reputation: 1

ARCH effect in GARCH model

After fitting GARCH model in R and obtain the output, how do I know whether there is any evidence of ARCH effect?

I am not toosure whether I have to check in optimal parameters, Information criteria, Q-statistics on standardized residuals, ARCM LM Tests, Nyblom stability test, Sign Bias Test or Adjusted Pearson Goodness-of-fit test?

I assume I have to check under ARCH LM Tests, and if the p-value is rather high, there is an ARCH effect, am I right?

Thank you

Upvotes: 0

Views: 2513

Answers (1)

Hanjo Odendaal
Hanjo Odendaal

Reputation: 1441

You need to start by looking for second order persistence in the return series itself before going on to fit a GARCH model. Lets work through a quick example of how this will work

Start by getting the return series. Here I will use the quantmod library to load in the data for SPDR S&P 500 ETF or SPY

library(quantmod)
library(PerformanceAnalytics) 

rtn<-getSymbols(c('SPY'),return.class='ts')

Next, calculate the return series either yourself or using the Return.calculate function as provided by the PerformanceAnalytics library

Rtn <- diff(log(SPY[,"SPY.Close"])) * 100

#OR

Rtn <- Return.calculate(SPY[,"SPY.Close"], method = c("compound","simple")[2]) * 100

Now, lets have a look at the persistence of the first and second order moments of the series. For second order moments, lets use the squared return series as a proxy. 

Plotdata<-cbind(Rtn, Rtn^2)
plot.zoo(Plotdata)

ACF_plots

There remains strong first persistence in returns and there is clearly periods of strong second order persistence as seen in the squared returns.

We can now formally start testing for ARCH-effects. A formal test for ARCH effects is LBQ stats on squared returns:

Box.test(coredata(Rtn^2), type = "Ljung-Box", lag = 12)

    Box-Ljung test

data:  coredata(Rtn^2)
X-squared = 2001.2, df = 12, p-value < 2.2e-16

We can clearly reject the null hypothesis of independence in a given time series. (ARCH-effects)

Fin.Ts also provides the ARCH-LM test for conditional heteroskedasticity in the returns:

library(FinTS)
ArchTest(Rtn)
    ARCH LM-test; Null hypothesis: no ARCH effects

data:  Rtn
Chi-squared = 722.19, df = 12, p-value < 2.2e-16

This supports the conclusion of the LBQ test that ARCH-effects are present.

Upvotes: 0

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