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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationThu, 10 Dec 2009 15:32:11 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/10/t1260484383xi9wat1yhzvmxh8.htm/, Retrieved Fri, 29 Mar 2024 11:59:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65839, Retrieved Fri, 29 Mar 2024 11:59:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsverbetering 2
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [Workshop 9: ARIMA...] [2009-12-04 20:22:30] [3cb427d596a5d2eb77fa64560dc91319]
-         [ARIMA Backward Selection] [workshop 9] [2009-12-10 22:32:11] [682632737e024f9e62885141c5f654cd] [Current]
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Dataseries X:
0.51
0.51
0.51
0.51
0.52
0.52
0.52
0.53
0.53
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.53
0.53
0.53
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.53
0.53
0.53
0.53
0.53
0.54
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.56
0.56
0.56
0.56
0.56
0.55
0.56
0.55
0.55
0.56
0.55
0.55
0.55
0.55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65839&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65839&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65839&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1sar1
Estimates ( 1 )-0.12650.0696
(p-val)(0.3446 )(0.6741 )
Estimates ( 2 )-0.14050
(p-val)(0.276 )(NA )
Estimates ( 3 )00
(p-val)(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & sar1 \tabularnewline
Estimates ( 1 ) & -0.1265 & 0.0696 \tabularnewline
(p-val) & (0.3446 ) & (0.6741 ) \tabularnewline
Estimates ( 2 ) & -0.1405 & 0 \tabularnewline
(p-val) & (0.276 ) & (NA ) \tabularnewline
Estimates ( 3 ) & 0 & 0 \tabularnewline
(p-val) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65839&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]ar1[/C][C]sar1[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]-0.1265[/C][C]0.0696[/C][/ROW]
[ROW][C](p-val)[/C][C](0.3446 )[/C][C](0.6741 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]-0.1405[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.276 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65839&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65839&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ARIMA Parameter Estimation and Backward Selection
Iterationar1sar1
Estimates ( 1 )-0.12650.0696
(p-val)(0.3446 )(0.6741 )
Estimates ( 2 )-0.14050
(p-val)(0.276 )(NA )
Estimates ( 3 )00
(p-val)(NA )(NA )







Estimated ARIMA Residuals
Value
0.000509999739866717
7.236118630238e-08
0
0
0.01
0.00140477866702138
0
0.01
0.00140477866702138
-0.01
-0.00140477866702138
0
0
0
0
0
0
0
0
0.01
0.00140477866702138
0
0.01
0.00140477866702138
0
0
0
0
0
0
0
0
-0.01
-0.00140477866702138
0
0
0
0.01
0.0114047786670214
0.00140477866702138
0
0
0
0
0
0
0.01
0.00140477866702138
0
0
0
-0.01
0.00859522133297863
-0.00859522133297863
-0.00140477866702138
0.01
-0.00859522133297863
-0.00140477866702138
0
0

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.000509999739866717 \tabularnewline
7.236118630238e-08 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.00140477866702138 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.00140477866702138 \tabularnewline
-0.01 \tabularnewline
-0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.00140477866702138 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
-0.01 \tabularnewline
-0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.0114047786670214 \tabularnewline
0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0.01 \tabularnewline
0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
0 \tabularnewline
-0.01 \tabularnewline
0.00859522133297863 \tabularnewline
-0.00859522133297863 \tabularnewline
-0.00140477866702138 \tabularnewline
0.01 \tabularnewline
-0.00859522133297863 \tabularnewline
-0.00140477866702138 \tabularnewline
0 \tabularnewline
0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65839&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.000509999739866717[/C][/ROW]
[ROW][C]7.236118630238e-08[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]-0.01[/C][/ROW]
[ROW][C]-0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]-0.01[/C][/ROW]
[ROW][C]-0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.0114047786670214[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]-0.01[/C][/ROW]
[ROW][C]0.00859522133297863[/C][/ROW]
[ROW][C]-0.00859522133297863[/C][/ROW]
[ROW][C]-0.00140477866702138[/C][/ROW]
[ROW][C]0.01[/C][/ROW]
[ROW][C]-0.00859522133297863[/C][/ROW]
[ROW][C]-0.00140477866702138[/C][/ROW]
[ROW][C]0[/C][/ROW]
[ROW][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65839&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65839&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated ARIMA Residuals
Value
0.000509999739866717
7.236118630238e-08
0
0
0.01
0.00140477866702138
0
0.01
0.00140477866702138
-0.01
-0.00140477866702138
0
0
0
0
0
0
0
0
0.01
0.00140477866702138
0
0.01
0.00140477866702138
0
0
0
0
0
0
0
0
-0.01
-0.00140477866702138
0
0
0
0.01
0.0114047786670214
0.00140477866702138
0
0
0
0
0
0
0.01
0.00140477866702138
0
0
0
-0.01
0.00859522133297863
-0.00859522133297863
-0.00140477866702138
0.01
-0.00859522133297863
-0.00140477866702138
0
0



Parameters (Session):
par1 = TRUE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 1 ; par9 = 0 ;
Parameters (R input):
par1 = TRUE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 1 ; 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(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')