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Q5: Backword

*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: Sun, 07 Dec 2008 09:06:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t1228666035ietr04x8zvqu5qv.htm/, Retrieved Sun, 07 Dec 2008 16:07:15 +0000

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/2008/Dec/07/t1228666035ietr04x8zvqu5qv.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

95.683 99.203 113.535 92.475 101.142 107.631 84.561 80.716 103.28 105.514 101.861 88.216 98.413 102.336 107.946 102.893 105.134 106.076 97.074 81.035 109.826 118.369 105.175 98.105 103.748 108.553 116.713 119.012 108.464 119.175 113.628 93.145 126.059 128.151 112.545 111.118 112.829 115.545 129.356 121.463 116.153 132.148 117.355 95.223 126.948 123.176 114.5 113.809 106.046 109.722 133.315 117.331 112.847 132.958 118.814 103.742 138.28 134.905 130.922 131.844 123.984 138.823 158.615 132.861 156.349 142.11 136.468 122.246 159.164 165.359 157.96 144.186 150.445 149.442 167.548 142.54 154.549 156.448 145.683 125.202 148.03 158.732 147.553 128.751 142.911 142.053 158.594 152.589 154.986 151.065 150.236 120.83 157.613 169.43 150.703 136.596 147.689 147.251 159.981 153.706 149.569 154.697 151.018 117.037 162.836 167.265 149.689 148.61 145.833 153.058 179.039 163.794 154.203 178.705 159.128 138.665 178.232 178.72 174.204 167.044 159.912 165.836 191.235 178.387 172.094 185.865 162.581 151.416 192.021 177.465 190.901 180.403 175.155 177.518 210.724 171.7 194.395 197.954 175.749 161.654 194.646 199.321 199.612 173.434 189.242 185.741 213.506 185.946 198.231 208.444 196.402 177.354 198.136 222.385 206.822 178.186 218.721 221.17 218.659 234.513 209.537 224.973

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	8 seconds
R Server	'George Udny Yule' @ 72.249.76.132
R Engine error message	Error in optim(init[mask], armafn, method = "BFGS", hessian = TRUE, control = optim.control, : non-finite finite-difference value [1] Calls: arimaSelect -> arima -> optim In addition: Warning message: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean, : some AR parameters were fixed: setting transform.pars = FALSE Execution halted

Charts produced by software:

Parameters (Session):

par1 = 0.5 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = FALSE ; par2 = 0.3 ; par3 = 0 ; par4 = 1 ; 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)

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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