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ARIMA Roebel

*The author of this computation has been verified*
R Software Module: /rwasp_arimabackwardselection.wasp (opens new window with default values)
Title produced by software: ARIMA Backward Selection
Date of computation: Tue, 28 Dec 2010 22:11:35 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc.htm/, Retrieved Tue, 28 Dec 2010 23:10:31 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
40.7819 39.5915 38.8859 39.9068 41.47 41.5613 41.6005 41.4113 41.84 42.2892 43.1521 43.5998 43.116 42.4185 42.3687 42.2975 42.8528 43.535 44.7265 45.7293 45.7585 46.1685 46.5075 46.527 46.601 46.4607 46.7135 46.4113 45.55 44.6081 44.4395 44.9847 45.7558 45.3942 45.697 45.5664 46.0205 45.9195 45.8005 45.535 45.4977 45.5782 45.7697 45.2445 45.0615 45.2865 44.791 44.7625 44.7644 44.9973 44.7265 45.1465 44.7465 45.1795 45.6515 45.492 45.2775 45.2115 45.411 45.4005 44.7692 44.8913 45.032 44.879 44.833 44.8257 44.7815 44.479 44.6317 44.5043 44.3217 44.1005 44.047 43.6835 43.7864 44.1807 43.9595 43.937 43.991 43.865 43.671 43.93 43.863 43.7095 43.9435 43.736 43.6295 43.598 43.8726 43.8935 43.5957 43.7155 43.528 43.3415 43.3374 43.332 43.3869 43.5016 43.4875 43.6023 43.3886 43.3105 43.4455 43.5185 43.5755 43.6217 43.644 43.5789 43.5215 43.5033 43.632 43.263 43.3717 43.2745 43.2647 43.324 43.4455 43.409 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.1415-0.1462-0.10390.17520.41820.0958-0.4662
(p-val)(0.8704 )(0.6044 )(0.5827 )(0.8402 )(0.3606 )(0.0598 )(0.31 )
Estimates ( 2 )0-0.1013-0.1330.31710.45510.0947-0.5013
(p-val)(NA )(0.0425 )(0.0054 )(0 )(0.3466 )(0.0601 )(0.3031 )
Estimates ( 3 )0-0.0932-0.12990.319300.0644-0.0482
(p-val)(NA )(0.0581 )(0.0062 )(0 )(NA )(0.1972 )(0.3253 )
Estimates ( 4 )0-0.0891-0.12960.318700.06170
(p-val)(NA )(0.0696 )(0.0064 )(0 )(NA )(0.2144 )(NA )
Estimates ( 5 )0-0.0871-0.12310.3178000
(p-val)(NA )(0.0758 )(0.0091 )(0 )(NA )(NA )(NA )
Estimates ( 6 )00-0.1250.3482000
(p-val)(NA )(NA )(0.0079 )(0 )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )


Estimated ARIMA Residuals
Value
1.26228765295085e-06
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-2.85511069775669e-06
3.12833858399572e-06
3.67416664640821e-06
2.37047594522912e-05
1.71193197680947e-06
8.21643318935626e-06
2.16656857692094e-05
5.77043668072434e-06
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/1lw8l1293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/1lw8l1293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/2lw8l1293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/2lw8l1293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/3w5p61293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/3w5p61293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/4w5p61293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/4w5p61293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/5w5p61293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/5w5p61293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/6w5p61293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/6w5p61293574286.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/7w5p61293574286.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t12935742311u7ahene9kovdrc/7w5p61293574286.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = -1.8 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
Parameters (R input):
par1 = FALSE ; par2 = -1.8 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
R code (references can be found in the software module):
library(lattice)
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 <- 5 #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]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$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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