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Shwws10_v1

*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: Fri, 11 Dec 2009 12:50:24 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk.htm/, Retrieved Fri, 11 Dec 2009 20:51:41 +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/2009/Dec/11/t1260561093c02weemcl80khpk.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

102.1 102.86 102.99 103.73 105.02 104.43 104.63 104.93 105.87 105.66 106.76 106 107.22 107.33 107.11 108.86 107.72 107.88 108.38 107.72 108.41 109.9 111.45 112.18 113.34 113.46 114.06 115.54 116.39 115.94 116.97 115.94 115.91 116.43 116.26 116.35 117.9 117.7 117.53 117.86 117.65 116.51 115.93 115.31 115

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

ARIMA Parameter Estimation and Backward Selection
Iteration	ma1	ma2	ma3
Estimates ( 1 )	2.6287	2.5922	0.947
(p-val)	(0 )	(0 )	(0 )
Estimates ( 2 )	0	0.7699	0.5636
(p-val)	(NA )	(3e-04 )	(0.0117 )
Estimates ( 3 )	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )
Estimates ( 5 )	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )

Estimated ARIMA Residuals
Value

25.9114593025249
9.72573174778178
19.7403176309267
11.5225742858671
18.5976418127997
11.0760540962296
19.0919945739626
10.5453731852632
19.5740407507266
9.98255812768702
20.0764874094902
9.15749069275822
21.6057083123133
7.8392697358571
21.8877171168885
10.4491035277594
16.3245777614363
17.1612980892749
11.0982119383041
19.0582016737469
13.3180717577881
15.1305950198631
19.0867576595925
10.1762217416065
22.8440269928784
8.90188241907991
21.8831182770903
13.2057361817320
16.5955953796708
17.4605641404216
15.5184314306774
14.3732246226578
21.3418776066799
8.41343245143028
25.2662585788938
7.83421022122246
23.9089287917346
10.6049443572494
20.283170662554
14.4114903058861
17.1616280940458
14.9339363166836
18.535716240155
11.6893755558937
22.0793614239128

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/18fnf1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/18fnf1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/28jkx1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/28jkx1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/3mjmw1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/3mjmw1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/4wf2d1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/4wf2d1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/5vf6z1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/5vf6z1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/61aer1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/61aer1260561021.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/7i7qe1260561021.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260561093c02weemcl80khpk/7i7qe1260561021.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; 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 <- as.numeric(par5) #seasonal period

par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial

par7 <- as.numeric(3) #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,par3,3), 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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