Workshop 5: Q2
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 5 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 ) | 1.1428 | -0.3732 | -0.197 | -0.9607 | -0.147 | -0.2447 | -0.9607 |
| (p-val) | (7e-04 ) | (0.4677 ) | (0.4926 ) | (0 ) | (0.6454 ) | (0.0823 ) | (0 ) |
| Estimates ( 2 ) | 1.0049 | -0.1709 | -0.2981 | -0.9611 | 0 | -0.2791 | -0.9611 |
| (p-val) | (0 ) | (0.2816 ) | (0.0132 ) | (0 ) | (NA ) | (0.031 ) | (0 ) |
| Estimates ( 3 ) | 0.9324 | 0 | -0.4109 | -0.9586 | 0 | -0.3591 | -0.9586 |
| (p-val) | (0 ) | (NA ) | (0 ) | (0 ) | (NA ) | (1e-04 ) | (0 ) |
| Estimates ( 4 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 5 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 6 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 7 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 8 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 9 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 10 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 11 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 12 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimates ( 13 ) | NA | NA | NA | NA | NA | NA | NA |
| (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
| Estimated ARIMA Residuals |
| Value |
| -0.136846644743055 |
| 5.4667493877268 |
| -10.7713683953540 |
| -5.1065079240981 |
| 12.7382281344519 |
| 1.1199434317353 |
| -6.80694174924182 |
| -11.1487406966319 |
| -11.6209138249603 |
| -8.85434872619538 |
| 13.3724728867581 |
| -12.7379436768417 |
| 7.16262397476902 |
| 5.59422261985806 |
| -11.2863539608069 |
| -4.90640349891731 |
| 25.4397244846922 |
| 13.6460243707999 |
| 1.16515431154108 |
| -2.74469259834954 |
| -14.4278096104339 |
| -8.77238026112592 |
| 25.7875803113664 |
| -8.50832462223939 |
| 0.969130838788997 |
| 21.8164383143843 |
| -21.8367706092113 |
| 18.3801781941699 |
| 6.52990273608348 |
| 24.4937904781679 |
| 3.95585346552291 |
| -3.73310746623237 |
| -9.66330007610214 |
| -8.5924148711724 |
| 18.4535684650934 |
| -7.70291725066488 |
| 2.35105436444450 |
| 4.90881133369898 |
| -17.5749638237206 |
| 4.9722668119885 |
| 31.5238187431581 |
| 6.17629886430256 |
| 20.3010113004674 |
| -22.4052016715638 |
| 1.05458533958350 |
| -12.1107758240031 |
| 21.5154687828848 |
| -11.0185143557838 |
| -7.17968926001762 |
| 30.8115712123986 |
| -14.6488342778704 |
| 0.343235794090967 |
| 19.3620186669950 |
| 22.3519678682566 |
| 15.3617280540961 |
| -20.8278438107744 |
| -7.00965974421249 |
| -25.8236530753554 |
| 16.9439185861605 |
| -19.1117851256522 |
| -32.7963833980471 |
| 29.7284090757051 |
| -37.6554253699458 |
| 2.08043110378836 |
| 20.3461568593737 |
| 29.1388211527646 |
| -4.47254087311537 |
| -12.9391373822432 |
| -10.2556364283197 |
| -17.5459430761444 |
| 23.3790806247905 |
| -7.38328154599442 |
| -22.9755207712301 |
| 23.2543876476621 |
| -16.6294077397935 |
| 0.452418182855431 |
| 45.2853427565136 |
| 45.4961902970217 |
| -2.4426021263369 |
| 1.57866717311925 |
| -7.22510552275124 |
| -16.7042912920498 |
| 46.9671074503568 |
| -13.6353977401984 |
| -13.8292779696149 |
| 31.4211761365979 |
| -20.7130402880036 |
| 10.1541101082951 |
| 57.9867130918549 |
| 38.2267981559099 |
| 14.9780599733333 |
| -11.2091525002652 |
| -10.4135643792438 |
| -12.9636938067361 |
| 36.6358892142617 |
| -13.544903533712 |
| -28.3858024156121 |
| 40.2993084107085 |
| -34.9568516584571 |
| 9.14622547968767 |
| 64.3281531395407 |
| 37.9053818809498 |
| 26.5853091637665 |
| -21.9407912529329 |
| -10.1534296872204 |
| -16.4104203337118 |
| 33.3402697466117 |
| -20.7685037616465 |
| -41.5555345066807 |
| 21.7666641301317 |
| -51.5425042080953 |
| 2.14076611130209 |
| 51.1206433684914 |
| 36.0082728498236 |
| 24.9681453312179 |
| -67.6666872147266 |
| 4.38912780701314 |
| -37.857246775149 |
| 23.0311003940391 |
| -10.9346992354661 |
| -52.0207782421399 |
| 37.3055687476342 |
| -51.8717237700231 |
| 16.5121019267543 |
| 39.3256827887376 |
| 70.6902487362703 |
| 26.9305756686884 |
| -48.4341919232925 |
| 4.88955092698196 |
| -20.8865462033567 |
| 47.2866706040831 |
| -14.103390517921 |
| -44.8239287232602 |
| 10.5044591473250 |
| 8.79112124990451 |
| -8.39855741515234 |
| 61.7445759867994 |
| 83.8911385351213 |
| 5.12246741009614 |
| -34.7266210582844 |
| 15.8923092744175 |
| -45.8713831503159 |
| 52.8507682221234 |
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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*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, 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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