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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: Wed, 22 Dec 2010 14:37:14 +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/22/t1293028517bo9jbdnej16rmmj.htm/, Retrieved Wed, 22 Dec 2010 15:35:17 +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/22/t1293028517bo9jbdnej16rmmj.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 «
300 302 400 392 373 379 303 324 353 392 327 376 329 359 413 338 422 390 370 367 406 418 346 350 330 318 382 337 372 422 428 426 396 458 315 337 386 352 383 439 397 453 363 365 474 373 403 384 364 361 419 352 363 410 361 383 342 369 361 317 386 318 407 393 404 498 438
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )-1.3647-0.6488-0.03670.78710.79230.1758-0.8069
(p-val)(0 )(0 )(0 )(0 )(0 )(0 )(0 )
Estimates ( 2 )00.23270.1392-0.95360.7310.2069-0.7048
(p-val)(NA )(0.0916 )(0.3056 )(0 )(0.0077 )(0.2567 )(0.0489 )
Estimates ( 3 )00.22860-1.06580.73040.2211-0.7405
(p-val)(NA )(0.1083 )(NA )(0 )(0.0072 )(0.2195 )(0.0541 )
Estimates ( 4 )00.21190-0.93510.99240-0.9157
(p-val)(NA )(0.1374 )(NA )(0 )(0 )(NA )(0 )
Estimates ( 5 )000-0.84140.9920-0.9192
(p-val)(NA )(NA )(NA )(0 )(0 )(NA )(0 )
Estimates ( 6 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(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
0.299999591336684
1.21199233356701
75.4639797610251
51.8090123934091
10.3709114726381
14.9363265003291
-45.8963239567809
-23.8459253555833
16.6540572050692
43.615630330657
-17.9998241807339
17.7626600419157
-1.83686172329133
16.3095321745741
40.4310491777242
-32.9020923203062
46.4546718560895
26.6029330228096
12.4559403579264
9.1501303438064
34.2648480827087
33.1275776464389
-18.4830819516073
-27.8262414444688
-13.8016290347782
-29.1274212596908
-3.34492138406453
-21.6583166784908
-8.0666195130188
49.6964158806386
70.3882304484306
48.6210111029793
-3.8015627933975
43.5545748899729
-50.2014851484081
-48.1722435368535
42.5657093267597
1.94747365822287
-23.1998794996642
62.9958583118668
2.37745726905263
34.1152131535184
-24.2307750466742
-33.8432122019551
79.3323863089495
-42.6725703258637
22.0249725213098
13.1358833090987
-16.3519703647422
-8.78447570609995
11.0253146899665
-42.8971104780076
-41.7646403725663
4.32617856051018
-14.6407563110333
-2.10438360686061
-60.7865653625676
-35.8640122898727
12.1397297717034
-44.7357230536979
27.9840186152965
-26.3959600820902
4.01516011072297
22.5198993389735
13.0143963522460
83.8828435924023
51.2747027702898
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/15fac1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/15fac1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/25fac1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/25fac1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/35fac1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/35fac1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/4f69w1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/4f69w1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/5f69w1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/5f69w1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/6f69w1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/6f69w1293028619.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/7f69w1293028619.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028517bo9jbdnej16rmmj/7f69w1293028619.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
Parameters (R input):
par1 = TRUE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; 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 <- 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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