| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 22 seconds |
| R Server | 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 |
| ARIMA Parameter Estimation and Backward Selection | |||||||
| Iteration | ar1 | ar2 | ar3 | ma1 | sar1 | sar2 | sma1 |
| Estimates ( 1 ) | -0.4931 | -0.0412 | 0.1123 | 0.7681 | 0.7921 | 0.1923 | -0.9248 |
| (p-val) | (0.007 ) | (0.757 ) | (0.3525 ) | (0 ) | (0.0013 ) | (0.16 ) | (0.0476 ) |
| Estimates ( 2 ) | -0.4841 | 0 | 0.123 | 0.7754 | 0.7775 | 0.2065 | -0.9247 |
| (p-val) | (0.004 ) | (NA ) | (0.2777 ) | (0 ) | (0 ) | (0.1039 ) | (1e-04 ) |
| Estimates ( 3 ) | -0.5302 | 0 | 0 | 0.8312 | 0.7779 | 0.2101 | -0.9363 |
| (p-val) | (1e-04 ) | (NA ) | (NA ) | (0 ) | (0 ) | (0.0941 ) | (0 ) |
| Estimates ( 4 ) | -0.4997 | 0 | 0 | 0.7861 | -0.18 | 0 | 0.0966 |
| (p-val) | (0.0019 ) | (NA ) | (NA ) | (0 ) | (0.7743 ) | (NA ) | (0.8781 ) |
| Estimates ( 5 ) | -0.4978 | 0 | 0 | 0.7845 | -0.0831 | 0 | 0 |
| (p-val) | (0.0021 ) | (NA ) | (NA ) | (0 ) | (0.4669 ) | (NA ) | (NA ) |
| Estimates ( 6 ) | -0.5242 | 0 | 0 | 0.8069 | 0 | 0 | 0 |
| (p-val) | (4e-04 ) | (NA ) | (NA ) | (0 ) | (NA ) | (NA ) | (NA ) |
| Estimated ARIMA Residuals |
| Value |
| 1.90269307527953 |
| -198.661083862078 |
| -2.49442230550271 |
| -73.39814573819 |
| 87.660409690833 |
| -66.5619029214113 |
| 86.1984189874349 |
| -144.544591838291 |
| 24.4464291857329 |
| -34.7347452991774 |
| -162.607626620642 |
| -37.684576287412 |
| 99.5693110958048 |
| 29.7364233236420 |
| -72.48180311868 |
| -45.5987149852892 |
| 66.0065955478389 |
| -153.135517726305 |
| -19.6290763890155 |
| -41.1755023488961 |
| -36.5817763534200 |
| -9.32157492039132 |
| 120.307876901022 |
| 9.03341236496523 |
| 43.3694712895595 |
| -6.92706948484032 |
| 157.611029521724 |
| -61.0230661092392 |
| -3.47661857692318 |
| -50.5164100668766 |
| 130.616208314738 |
| -50.6464582641845 |
| 308.758802665199 |
| 19.7308179128116 |
| -50.7894638830553 |
| 32.1313097830279 |
| 162.815154271249 |
| 64.9709458506573 |
| -295.773701785384 |
| 56.198578017442 |
| -129.798234320702 |
| -173.423901539597 |
| 93.1820343152865 |
| -15.1258459522640 |
| 102.761889659667 |
| -172.221027474123 |
| 28.4892464930404 |
| 69.099437882474 |
| 176.100240082615 |
| -52.5592808860096 |
| 51.1034605726193 |
| -107.118827027150 |
| 60.456081589946 |
| 59.5112352216435 |
| 6.38060591268215 |
| 51.4559572096124 |
| 13.3568595193785 |
| -3.83209082238179 |
| 231.591318818224 |
| 196.266075329032 |
| -24.5881558513141 |
| 327.333401898415 |
| 327.090488324119 |
| -298.003577087949 |
| 101.765221141730 |
| -119.272264501629 |
| -131.707046359030 |
| -58.7172114087587 |
| -86.0901908494055 |
| 151.542615793627 |
| 50.0273977957049 |
| 240.462317606687 |
| 545.950239388185 |
| -73.2682474972284 |
| -82.5092195359293 |
| 16.2365088420361 |
| -110.080470147505 |
| -198.993466787667 |
| 210.372304488266 |
| -116.146103271992 |
| -61.7277472078595 |
| -56.0805141269316 |
| 296.385511659688 |
| 154.499260284687 |
| -75.5983286220535 |
| 34.6226909310094 |
| -109.660554936656 |
| 15.7556038236912 |
| -27.7986799594387 |
| 196.356341543694 |
| 99.4094954100378 |
| -141.546949795743 |
| 216.344165114456 |
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if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc, ncol=nrc)
pval <- matrix(NA, nrow=nrc, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval <- arimaSelect.out[[2]][1:k,]
aic <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01) symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1) & (pval[j,i]>=.05)) symb = 'red'
else symb = 'black'
polygon(c(i+.5 ,i+.2 ,i+.5 ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix) {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i ,1+2*i ,1+2*i-.5 ,1+2*i),
c(.4 ,.7 , .4 , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated ARIMA Residuals', 1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Value', 1,TRUE)
a<-table.row.end(a)
for (i in (par4*par5+par3):length(resid)) {
a<-table.row.start(a)
a<-table.element(a,resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
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