o3<-rts(sqrt(Sjf.data$O3),frequency=12,units="hours")
CO<-rts(sqrt(Sjf.data$CO),frequency=12,units="hours")
HCHO<-rts(sqrt(Sjf.data$HCHO),frequency=12,units="hours")

graphsheet()
pairs(cbind(o3,CO,HCHO))

graphsheet()
lag.plot(cbind(o3,CO,HCHO),lags=36,layout=c(6,6))

#Subtract mean and replace missing values with 0

o3m<-mean(o3,na.rm=T)
o3c<-o3-o3m
o3c[is.na(o3c)==T]<-0
	
COm<-mean(CO,na.rm=T)
COc<-CO-COm
COc[is.na(COc)==T]<-0

HCHOm<-mean(HCHO,na.rm=T)
HCHOc<-HCHO-HCHOm
HCHOc[is.na(HCHOc)==T]<-0

graphsheet()
par(mfrow=c(3,1),omi=c(.5,1,.5,1))
tsplot(o3c)
title("Mean Corrected sqrt(o3) \n NA's set to zero")
tsplot(COc)
title("Mean Corrected sqrt(CO) \n NA's set to zero")
tsplot(HCHOc)
title("Mean Corrected sqrt(HCHO) \n Na's set to zero")

graphsheet()
par(mfrow=c(2,1),omi=c(.5,1,.5,1))
acf(cbind(o3c,COc,HCHOc))
acf(cbind(o3c,COc,HCHOc),type="partial")

#Let's try "prewhitening" each series and then look
#at the cross-correlations

o3f<-ar(o3c,aic=T,order.max=12,method="burg")
COf<-ar(COc,aic=T,order.max=12,method="burg")
HCHOf<-ar(HCHOc,aic=T,order.max=24,method="burg")

# Align series and combine

n<-length(o3c)
Aresid<-rts(cbind(o3f$resid[25:n],COf$resid[25:n],HCHOf$resid[25:n]),
	frequency=12,units="hours")
graphsheet()
par(mfrow=c(3,1),omi=c(.5,1,.5,1))
ts.plot(o3f$resid[25:n])
title("Prewhitened o3 Series")
ts.plot(COf$resid[25:n])
title("Prewhitened CO Series")
ts.plot(HCHOf$resid[25:n])
title("Prewhitened HCHO Series")

graphsheet()
par(mfrow=c(2,1),omi=c(.5,1,.5,1))
acf(Aresid)
acf(Aresid,type="partial")