| | *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 13:27:55 +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/t1293629143era9lmutrkpq1vk.htm/, Retrieved Wed, 29 Dec 2010 14:25:43 +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/t1293629143era9lmutrkpq1vk.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 « | 00,521505
00,424828
00,425031
00,477194
00,828021
00,615619
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00,577905
00,566115
00,507758
00,750718
00,680840
00,766109
00,456147
00,497750
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00,159271 | | Output produced by software: |
ARIMA Parameter Estimation and Backward Selection | Iteration | ar1 | ar2 | ar3 | ma1 | sma1 | Estimates ( 1 ) | -0.0697 | -0.0072 | -0.1484 | -0.4838 | -0.9998 | (p-val) | (0.838 ) | (0.9726 ) | (0.2879 ) | (0.1522 ) | (0.0109 ) | Estimates ( 2 ) | -0.0601 | 0 | -0.1459 | -0.4936 | -1 | (p-val) | (0.7638 ) | (NA ) | (0.2238 ) | (0.0073 ) | (0.0109 ) | Estimates ( 3 ) | 0 | 0 | -0.1366 | -0.5371 | -1 | (p-val) | (NA ) | (NA ) | (0.25 ) | (0 ) | (0.0088 ) | Estimates ( 4 ) | 0 | 0 | 0 | -0.5686 | -1 | (p-val) | (NA ) | (NA ) | (NA ) | (0 ) | (0.0277 ) | 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 | -0.00153114388569615 | 0.0236463220552320 | 0.175675912059170 | -0.000708837657806076 | -0.18292816937981 | -0.142834560943860 | 0.116960891769420 | -0.0635235427815574 | 0.198501498504479 | -0.102027880939527 | 0.148236635746575 | -0.275578126403471 | -0.154974834476709 | 0.167915705100931 | -0.334328157496473 | -0.169777751352397 | -0.216709267150459 | 0.177001139001560 | 0.132246580692336 | 0.0641768967981246 | 0.0925875994432078 | 0.0266033277449047 | -0.0780386338075724 | -0.140075220224058 | 0.133633125220587 | 0.104871850679567 | -0.0449953460338595 | 0.0603856282607498 | -0.112409985755576 | -0.0410154063993668 | 0.226906041594393 | 0.129043753696515 | 0.0503195265291195 | 0.0135566462510629 | 0.102808525125445 | 0.109272032936057 | -0.0756891744082951 | -0.0376361112739818 | -0.0247928338514970 | -0.000925119475960507 | -0.0860103053181701 | 0.169552521373445 | -0.112258743937076 | 0.0368614365488567 | 0.0591811792006121 | -0.0976173188319573 | 0.108943013807139 | 0.0508088429358086 | -0.0183642213908830 | -0.0382526404539456 | 0.124619173506123 | -0.156815641589332 | 0.028519075755306 | 0.0908962779023131 | -0.0107668967858278 | 0.0697010100078719 | -0.06535809921504 | 0.177686283466744 | -0.0683416966772466 | -0.0667219973540245 | -0.0619954010717523 | 0.0203546611721316 | -0.145812315676226 | -0.0651593982463147 | -0.129850963549040 | 0.0527416216375101 | -0.149785389397084 | -0.187845831304919 | -0.0385968475863136 | 0.151689598629019 | -0.0165449047543406 | -0.120762314068000 | -0.0515469126239142 | -0.078667113981391 | -0.0552371504666414 | -0.0531029489677188 | -0.150547624750731 | -0.0772318559326222 |
| | Charts produced by software: | | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/15njr1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/15njr1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/2gwjc1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/2gwjc1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/3gwjc1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/3gwjc1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/4gwjc1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/4gwjc1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/5gwjc1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/5gwjc1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/6qoix1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/6qoix1293629268.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/7qoix1293629268.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/29/t1293629143era9lmutrkpq1vk/7qoix1293629268.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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