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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, 15 Dec 2010 16:58:59 +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/15/t1292432802u8fnkcaxj988vgf.htm/, Retrieved Wed, 15 Dec 2010 18:06:49 +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/15/t1292432802u8fnkcaxj988vgf.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 «
186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )-0.3350.18120.41280.29340.08170.0715-0.52
(p-val)(0.3331 )(0.1597 )(0.0028 )(0.3981 )(0.9016 )(0.8147 )(0.4008 )
Estimates ( 2 )-0.30940.18780.40680.266700.0455-0.4524
(p-val)(0.3873 )(0.1356 )(0.0038 )(0.4597 )(NA )(0.7934 )(0.0241 )
Estimates ( 3 )-0.34170.18050.41930.295100-0.4263
(p-val)(0.2548 )(0.1448 )(0.001 )(0.3367 )(NA )(NA )(0.0104 )
Estimates ( 4 )-0.0650.20050.3607000-0.5076
(p-val)(0.5729 )(0.0776 )(0.0036 )(NA )(NA )(NA )(1e-04 )
Estimates ( 5 )00.20220.3483000-0.5241
(p-val)(NA )(0.0746 )(0.0044 )(NA )(NA )(NA )(0 )
Estimates ( 6 )000.3466000-0.4955
(p-val)(NA )(NA )(0.0053 )(NA )(NA )(NA )(1e-04 )
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
-61398500.5306697
-50170611.9562072
-90565242.3431427
2653177045.91264
-2240570914.00404
-1232077483.96963
1434769069.68265
-503925110.791992
-441606639.171465
-806580533.67542
328047613.778977
777660397.812968
657513330.759815
-1137852092.56682
-663863370.100012
-67293422.6658567
645011450.626913
-1040638954.92127
15793563.3341636
-886162268.658963
602962795.193745
-201086674.733709
-418148793.272082
-1675015562.27364
-745620116.626504
-690534638.565388
163320490.376713
1269520643.44274
-58110473.7662917
-861093950.997105
92664086.567032
-214211552.342320
317649949.333784
-451883945.697547
-248879651.292323
912651044.394715
63227286.3049204
-318165453.381839
260054904.379655
245357176.591509
117481657.674422
892451276.686886
-7398296.94498098
105818380.505839
297403504.764255
-488496011.354148
-224972474.820311
-1951065502.94437
-529099586.961479
228942286.280969
189889880.479415
-1319879704.97439
4752300427.61518
-610229360.088148
-379906262.719908
-1314423426.44209
-561597353.278516
882142389.544464
-1340545143.42955
-179957577.963141
211952544.212539
-45274107.0990954
693776841.059231
-13618584.4804789
404154241.684562
555486531.794982
809841819.862022
2536415337.41736
1813856891.86413
2626113622.68319
-1680366322.26436
25889643.0143246
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/1257w1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/1257w1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/2257w1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/2257w1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/3257w1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/3257w1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/4257w1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/4257w1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/5ceph1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/5ceph1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/6ceph1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/6ceph1292432333.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/7ceph1292432333.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432802u8fnkcaxj988vgf/7ceph1292432333.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
Parameters (R input):
par1 = FALSE ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$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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