| | *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: Wed, 29 Dec 2010 13:29:25 +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/29/t1293629242ila6y1ke7t9r61k.htm/, Retrieved Wed, 29 Dec 2010 14:27:31 +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/29/t1293629242ila6y1ke7t9r61k.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 « | 09,166456
07,970589
07,104091
06,621064
07,529215
08,170938
08,157450
07,378962
07,921496
08,156740
08,856365
08,817177
08,734347
09,345927
08,992970
10,785120
08,886867
08,818847
08,823744
09,165298
08,652657
08,173054
07,563416
07,595809
08,381467
07,216432
06,540178
06,238914
05,487288
05,759462
05,993215
07,474726
07,348907
07,303379
07,119314
06,993780
06,958153
07,595706
08,088153
07,555753
07,315433
07,893427
08,858794
08,839367
08,014733
07,873465
08,930377
10,500550
12,611440
11,417870
11,872490
11,060820
12,043310
09,776299
09,557194
09,202590
10,224020
09,350807
08,300913
08,365779
08,133595
07,660470
08,074839
07,848597
07,998220
07,396895
07,900419
08,100500
07,899453
07,599783
08,100929
09,002175
10,298900
10,101520
10,699150
09,698140
09,800951
10,900470
10,697850
09,297252
10,397440
10,900720
12,901270
13,099060
11,698280
11,099870
11,301570
10,702110
10,099310
09,591119 | | Output produced by software: |
ARIMA Parameter Estimation and Backward Selection | Iteration | ar1 | ar2 | ar3 | ma1 | sma1 | Estimates ( 1 ) | -0.2535 | -0.0722 | -0.3183 | 0.2208 | -1 | (p-val) | (0.313 ) | (0.5226 ) | (0.0045 ) | (0.3771 ) | (2e-04 ) | Estimates ( 2 ) | -0.2325 | 0 | -0.3007 | 0.2178 | -1 | (p-val) | (0.3314 ) | (NA ) | (0.0066 ) | (0.3941 ) | (2e-04 ) | Estimates ( 3 ) | -0.0493 | 0 | -0.2977 | 0 | -1 | (p-val) | (0.652 ) | (NA ) | (0.0083 ) | (NA ) | (0 ) | Estimates ( 4 ) | 0 | 0 | -0.2951 | 0 | -1 | (p-val) | (NA ) | (NA ) | (0.0088 ) | (NA ) | (1e-04 ) | Estimates ( 5 ) | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 6 ) | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 7 ) | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 8 ) | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 9 ) | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
Estimated ARIMA Residuals | Value | -0.0300982735885726 | 1.22298266251403 | 0.41387319748961 | 1.54387399639625 | -1.53964013191776 | -0.493236268648726 | 0.440083417118872 | 0.252686574099731 | -0.847052898280759 | -0.456242848166602 | -0.896627238098687 | -0.261854109793551 | 0.219864663055287 | -0.9779226761178 | -0.0867016177166793 | -0.678866299050055 | -0.465733190296306 | -0.0396743577778399 | -0.0495355677349007 | 1.35498725719903 | -0.0444759779428794 | 0.148953761491016 | 0.160575913275671 | -0.168625333159360 | -0.407579824466851 | 0.960072971375945 | 0.987333145919615 | -0.820052517015471 | 0.566436984258222 | 0.557681492467188 | 0.552465669873931 | -0.172701908413452 | -0.614626482191682 | 0.178373123496878 | 0.778735266867344 | 1.20221435805525 | 1.63692598710485 | -0.490167976131893 | 1.07073957847363 | -0.338493219545373 | 1.03379574190024 | -2.06988849197775 | -0.829741508411483 | -0.163801886756705 | 0.406412608493574 | -0.754870422291202 | -1.39461157098429 | -0.0302944040908478 | -1.0817730080454 | -0.40294821528359 | 0.461244194857348 | -0.369108249175352 | 0.305933191414510 | -0.218332916532732 | 0.216255660584083 | 0.178742809516831 | -0.30529414440598 | 0.0483928981625587 | 0.455699624201397 | 0.472695482242856 | 0.709257301632355 | 0.407991218702275 | 0.797020493677451 | -0.60378372688973 | 0.255782509542629 | 1.43808608462927 | -0.606526575305287 | -1.37568953057968 | 1.34384842485443 | 0.6476258082823 | 1.36871455066589 | 0.169711290969969 | -1.70595814635105 | 0.26277500687437 | 0.105902453416176 | -0.904303962607227 | -0.531598576602556 | -0.40130853627356 |
| | Charts produced by software: | | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/14fy61293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/14fy61293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/24fy61293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/24fy61293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/3xpxr1293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/3xpxr1293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/4xpxr1293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/4xpxr1293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/5xpxr1293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/5xpxr1293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/6xpxr1293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/6xpxr1293629355.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/78ywc1293629355.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629242ila6y1ke7t9r61k/78ywc1293629355.ps (open in new window) |
| | Parameters (Session): | par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; | | Parameters (R input): | par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; 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 <- 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]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$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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