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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: Mon, 29 Nov 2010 20:17:08 +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/Nov/29/t1291062047jm2mc8qt1s6kx1e.htm/, Retrieved Mon, 29 Nov 2010 21:20:55 +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/Nov/29/t1291062047jm2mc8qt1s6kx1e.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 «

15086 20559 39383 68032 42346 40184 29183 18049 24377 48033 61410 40637 37914 22481 17061 21921 34043 36152 38929 36713 27928 14178 19331 35030 37834 45257 39650 33001 22268 34283 63733 54548 31666 32654 28409 16234 19544 33375 30839 27581 28596 28542 14285 20799 28729 30278 31266 38341 24938 15700 17382 34229 29584 33909 29397 24644 14124 18770 32681 30518 34310 24217 15806 12362 13751 25312 23549 30305 30411 15593 17382 15806 29183 33348 33589 30198 23469 15593 16474 27341 26673 33268 26406 23656 15086 18316 27528 30305 34550 34710 23843 12362 21200 27261 31586 33322 32814 21974 17115 14445 26673 31746 28249 29103 21974 17622 21066 28382 32147 35885 40824 28622 24297 30465 47927 51665 57058 48407 30011 21413 30518 41171 37487 44456 41465 28409 34870 29557 44936 44028 45310 39302 28516 19865 30091 38101 44402 52359 71182 60796 43735 63947 89071 86321 90967 54441 36 etc...

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	24 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ar2	ar3	sar1	sar2
Estimates ( 1 )	0.7592	0.0404	0.0545	-0.5699	-0.2491
(p-val)	(0 )	(0.2575 )	(0.0557 )	(0 )	(0 )
Estimates ( 2 )	0.7788	0	0.0741	-0.57	-0.2483
(p-val)	(0 )	(NA )	(0.0011 )	(0 )	(0 )
Estimates ( 3 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
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
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Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/1ymt11291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/1ymt11291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/2rvsm1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/2rvsm1291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/3rvsm1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/3rvsm1291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/4rvsm1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/4rvsm1291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/52m9p1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/52m9p1291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/62m9p1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/62m9p1291061803.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/72m9p1291061803.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062047jm2mc8qt1s6kx1e/72m9p1291061803.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

Parameters (R input):

par1 = FALSE ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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 <- 7 #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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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