**Timely Portfolio**, and kindly contributed to R-bloggers)

I returned from Scotland to find a wonderful new blog from Ireland http://timeseriesireland.wordpress.com. To highlight his work, I thought I would apply his most recent post AIB Stock Price, EGARCH-M, and rgarch to the S&P 500. Clearly the author of TimeSeriesIreland has a much better grasp of time series statistics than I do, so I will not attempt to change lag orders or perfect the model. Rather I will use his model specifications for AIB daily data for S&P 500 weekly data. This should be fun; maybe this will provoke some comments.

From TimelyPortfolio |

From TimelyPortfolio |

From TimelyPortfolio |

From TimelyPortfolio |

From TimelyPortfolio |

And, it is a shame that I need to disclaim, but **THIS IS FOR ILLUSTRATIVE PURPOSES ONLY AND SHOULD NOT BE CONSIDERED INVESTMENT ADVICE. YOU ARE RESPONSIBLE FOR YOU OWN GAINS AND LOSSES.** I built a very basic system around the fittedmodel$z just for fun. Here are the results.

From TimelyPortfolio |

R code:

#all credit for this code goes to the very insightful author

#of http://timeseriesireland.wordpress.com

#based on the first couple of posts I look forward to following him

#for explanation of the statistics and their use, please see

#http://timeseriesireland.wordpress.com/2011/05/17/aib-stock-price-egarch-m-and-rgarch/#more-295

#I change the code to use SP500 weekly xts data instead of AIB daily tseries data

require(rgarch)

require(urca)

require(ggplot2)

require(quantmod)

#define start and end dates

start<-“1929-01-01″

end<- format(Sys.Date(),”%Y-%m-%d”) # yyyy-mm-dd

tckr<-“^GSPC”

#use quantmod to get SP500 data

getSymbols(tckr,from=start,to=end)

GSPC<-to.weekly(GSPC)

#get log returns, could also use ROC with type = “continuous”

LGSPC<-log(GSPC[,4])

retGSPC<-diff(LGSPC)

#data frame allows us to use ggplot with date data from xts

#I have not found any better way to ggplot xts data

df1<-data.frame(index(GSPC),coredata(GSPC[,4]))

colnames(df1)<-c(“dates”,”sp500″)

### Plot sp500 price:

gg1.1<-ggplot(df1,aes(dates,sp500)) + xlab(NULL) + ylab(“SP500 log Price”) + scale_y_log10()

gg1.2<-gg1.1+geom_line(colour=”darkblue”) + opts(title=”Weekly SP500 Price 1950-current”)

gg1.2

#set first return to 0

retGSPC[1]<-0

df2<-data.frame(index(retGSPC),coredata(retGSPC))

colnames(df2)<-c(“dates”,”sp500″)

gg2.1<-ggplot(df2,aes(dates,sp500)) + xlab(NULL) + ylab(“Log Changes”)

gg2.2<-gg2.1+geom_line(colour=”darkred”) + opts(title=”Weekly SP500 Price Return”)

gg2.2

### ACFs and PACFs

par(mfrow=c(2,1))

acf(retGSPC, main=”ACF of SP500 Log Returns”, lag = 50)

pacf(retGSPC, main=”PACF of SP500 Log Returns”, lag = 50)

ar9<-arima(retGSPC, order=c(9,0,0))

acf(ar9$residuals)

ressq<-(ar9$residuals)^2

Box.test(ressq, lag = 8, type = “Ljung-Box”)

pacf(ressq, main=”PACF of Squared Residuals”, lag = 30)

# Note that the GARCH order is revered from what I have discussed above

specm1 <- ugarchspec(variance.model=list(model=”eGARCH”, garchOrder=c(2,4), submodel = NULL),

mean.model=list(armaOrder=c(9,0), include.mean=TRUE, garchInMean = TRUE))

#this might take a while

fitm1 <- ugarchfit(data = retGSPC, spec = specm1)

fitm1

#plot(fitm1) #use option 8

fittedmodel <- [email protected]

sigma1<-fittedmodel$sigma

df2<-data.frame(index(retGSPC),coredata(retGSPC),sigma1)

colnames(df2)<-c(“dates”,”sp500″,”sigma1″)

gg3.1<-ggplot(df2,aes(dates)) + xlab(NULL) + ylab(“Log Changes”)

gg3.2<-gg3.1+geom_line(aes(y = sp500, colour=”Log Returns”)) + opts(title=”Weekly Log Return with 2 Conditional Standard Deviations”)

gg3.3<-gg3.2 + geom_line(aes(y = sigma1*2, colour=”2 S.D.”)) + geom_line(aes(y = sigma1*-2, colour=”2 S.D.”)) + scale_colour_hue(“Series:”) + opts(legend.position=c(.18,0.8))

gg3.3

fitm2 <- ugarchfit(data = retGSPC,out.sample = 10, spec = specm1)

fitm2

pred <- ugarchforecast(fitm2, n.ahead = 10,n.roll = 0)

pred.fpm <- fpm(pred)

pred.fpm

#just because I cannot stand it

#I’ll play with a system

#not something I would bet my money on

signal<-runMean(as.xts(fittedmodel$z,order.by=index(retGSPC)),50)

#chartSeries(signal)

signal<-lag(signal,k=1)

signal[is.na(signal)]<-0

ret<-ifelse(signal > 0,ROC(GSPC[,4],1,type=”discrete”),0)

returnCompare<-merge(ret,ROC(GSPC[,4],1,type=”discrete”))

colnames(returnCompare)<-c(“ZSystem”,”SP500″)

charts.PerformanceSummary(returnCompare,ylog=TRUE,main=”Just for Fun Z System”)

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**Timely Portfolio**.

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