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ARIMA Backward Selection

*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: Sat, 25 Dec 2010 11:07:36 +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/25/t12932751780yj5yvl4nppb2ni.htm/, Retrieved Sat, 25 Dec 2010 12:06:25 +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/25/t12932751780yj5yvl4nppb2ni.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 «

716 677 710 839 886 891 917 820 793 932 906 844 801 957 1159 1264 1097 1240 1411 1535 1862 1894 2239 2465 2423 2692 2856 3450 4162 4260 4225 4092 4160 3896 3628 3754 3749 3907 4449 5272 6197 6446 7157 7559 7674 6929 7156 6805 7095 7222 7593 7910 7878

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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ar2	ar3	sar1	sar2	sma1
Estimates ( 1 )	-0.3698	0.3097	0.0603	0.2505	0.0839	0.5172
(p-val)	(0.8603 )	(0.8019 )	(0.8749 )	(0.886 )	(0.8908 )	(0.6529 )
Estimates ( 2 )	0.1822	0.422	-0.1148	-0.2712	0	0.4881
(p-val)	(0.796 )	(0.3855 )	(0.7468 )	(0.8684 )	(NA )	(0.7594 )
Estimates ( 3 )	0.0712	0.4042	-0.0473	0	0	0.3283
(p-val)	(0.9355 )	(0.2086 )	(0.8665 )	(NA )	(NA )	(0.7089 )
Estimates ( 4 )	0	0.4273	-0.0262	0	0	0.3981
(p-val)	(NA )	(0.0018 )	(0.8353 )	(NA )	(NA )	(0.0053 )
Estimates ( 5 )	0	0.4259	0	0	0	0.3928
(p-val)	(NA )	(0.002 )	(NA )	(NA )	(NA )	(0.0048 )
Estimates ( 6 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 8 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 9 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 10 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 11 )	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )

Estimated ARIMA Residuals
Value
0.715999498755167
-32.9599343280933
49.653572684612
125.394337086746
-17.5801021620334
-42.2613318352843
26.1091639773621
-108.299827543883
5.13224105822928
179.085396179223
-88.2893080847088
-86.9554591237869
6.36008487620421
179.281055931487
147.385007547526
-21.4544695405241
-240.694976178237
199.231013178644
165.796615026504
-7.47171842743773
260.645247686401
-120.270246291145
256.391392461961
118.814925901356
-235.88033082693
275.350537036238
78.246763976058
446.808665286172
471.093319889779
-339.060513892973
-188.733398600491
-81.1245189975589
117.812386462277
-254.982291812452
-199.032553416901
319.816773871602
-24.6985096266076
106.982620383998
504.844531439206
554.388511853246
476.844508422258
-278.316661285384
448.059234002561
141.431036116887
-238.601253742175
-803.199798217676
508.108505089714
-231.917137348519
265.838824844377
177.096170444308
167.404391030173
203.677038532303
-268.287305205124

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/19qwe1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/19qwe1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/29qwe1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/29qwe1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/3k0wz1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/3k0wz1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/4k0wz1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/4k0wz1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/5k0wz1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/5k0wz1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/6k0wz1293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/6k0wz1293275249.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/7u9v21293275249.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932751780yj5yvl4nppb2ni/7u9v21293275249.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 0 ; 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')

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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