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*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: Fri, 11 Dec 2009 12:24:39 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p.htm/, Retrieved Fri, 11 Dec 2009 20:26:23 +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/2009/Dec/11/t1260559575rhs89oanpb2ch3p.htm/},
    year = {2009},
}
@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 = {2009},
    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 «
285 574 865 1147 1516 1789 2087 2372 2669 2966 3270 3652 329 658 988 1303 1603 1929 2235 2544 2872 3198 3544 3903 332 665 1001 1329 1639 1975 2304 2640 2992 3330 3690 4063 368 738 1103 1474 1846 2224 2608 2984 3351 3736 4122 4558 378 749 1113 1500 1867 2244 2621 2988 3349 3723 4108 4514
 
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'Gwilym Jenkins' @ 72.249.127.135


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ar4ar5ar6ar7ar8ar9ar10ar11
Estimates ( 1 )-0.9764-0.976-0.9768-0.9753-0.9758-0.9759-0.9751-0.977-0.976-0.9764-0.9772
(p-val)(0 )(0 )(0 )(0 )(0 )(0 )(0 )(0 )(0 )(0 )(0 )
Estimates ( 2 )0-0.4196-0.4034-0.3909-0.3886-0.3838-0.3738-0.3602-0.3391-0.3392-0.3817
(p-val)(NA )(8e-04 )(6e-04 )(8e-04 )(0.0014 )(0.0011 )(0.001 )(8e-04 )(6e-04 )(4e-04 )(3e-04 )
Estimates ( 3 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 14 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 15 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 16 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 17 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 18 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 19 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 20 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 21 )NANANANANANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )(NA )


Estimated ARIMA Residuals
Value
0.284994273615572
45.5890065425846
50.2875525044442
54.0621988500435
74.2923489226002
68.9720608179456
83.4064360271006
96.6496884644352
119.836255440659
155.116876367669
219.911240657658
393.745168411275
-36.140070854924
88.9228143325668
128.667741756691
157.333984473629
95.1406891945042
145.901907419492
152.764954770989
178.985998951740
202.997062281451
234.903798093063
275.083092647464
249.792059727137
-82.1722844391611
13.8760969121508
21.3983620195179
30.4928954668385
45.8567932637482
54.479720396588
76.3582113916914
105.701040174896
122.377921009507
137.654869548209
150.374739540010
161.015684729548
-52.9429703198698
79.1252370922898
108.989822398150
147.582320455987
214.402606179085
253.705636604033
307.122160892040
348.893895776216
355.861973776586
406.244124927371
430.09334398828
489.314574087758
-89.841998913521
18.4631545775246
19.2964105104095
31.4728176111503
33.1141730824782
30.3910257712696
23.0447728511299
17.3297227154458
2.96694744814658
-2.90825063933107
-5.34814490676672
-38.0370063735754
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/1ohh11260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/1ohh11260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/2rb5x1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/2rb5x1260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/3zctp1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/3zctp1260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/4zexp1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/4zexp1260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/5glta1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/5glta1260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/6c1be1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/6c1be1260559472.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/743gj1260559472.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/11/t1260559575rhs89oanpb2ch3p/743gj1260559472.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;
 
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;
 
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 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
par6 <- 11
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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