| Paper Statistiek | *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: Tue, 28 Dec 2010 16:09:56 +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/28/t1293552542hwr0i922cz7qn7k.htm/, Retrieved Tue, 28 Dec 2010 17:09:10 +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/28/t1293552542hwr0i922cz7qn7k.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: | ARIMA Backward Selection - Handelsbalans BelgiĆ« (1995-2009) | | Dataseries X: | » Textbox « » Textfile « » CSV « | 13363
12530
11420
10948
10173
10602
16094
19631
17140
14345
12632
12894
11808
10673
9939
9890
9283
10131
15864
19283
16203
13919
11937
11795
11268
10522
9929
9725
9372
10068
16230
19115
18351
16265
14103
14115
13327
12618
12129
11775
11493
12470
20792
22337
21325
18581
16475
16581
15745
14453
13712
13766
13336
15346
24446
26178
24628
21282
18850
18822
18060
17536
16417
15842
15188
16905
25430
27962
26607
23364
20827
20506
19181
18016
17354
16256
15770
17538
26899
28915
25247
22856
19980
19856
16994
16839
15618
15883
15513
17106
25272
26731
22891
19583
16939
16757
15435
14786
13680
13208
12707
14277
22436
23229
18241
16145
13994
14780
13100
12329
12463
11532
10784
13106
19491
20418
16094
14491
13067 | | Output produced by software: |
ARIMA Parameter Estimation and Backward Selection | Iteration | ar1 | ar2 | ar3 | ma1 | sar1 | sar2 | sma1 | Estimates ( 1 ) | -0.9222 | -0.8893 | -0.8729 | 0.768 | -1.0026 | -0.9422 | 0.6316 | (p-val) | (0 ) | (0 ) | (0 ) | (0 ) | (0 ) | (0 ) | (0 ) | Estimates ( 2 ) | 0 | -0.8452 | -0.0119 | -0.0505 | -0.9903 | -0.9136 | 0.7703 | (p-val) | (NA ) | (0 ) | (0.8168 ) | (0.478 ) | (0 ) | (0 ) | (0 ) | Estimates ( 3 ) | 0 | -0.8453 | 0 | -0.0543 | -0.9902 | -0.9139 | 0.7696 | (p-val) | (NA ) | (0 ) | (NA ) | (0.4325 ) | (0 ) | (0 ) | (0 ) | Estimates ( 4 ) | 0 | -0.8423 | 0 | 0 | -0.9877 | -0.9082 | 0.7782 | (p-val) | (NA ) | (0 ) | (NA ) | (NA ) | (0 ) | (0 ) | (0 ) | Estimates ( 5 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 6 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 7 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 8 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 9 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 10 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 11 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 12 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | Estimates ( 13 ) | NA | NA | NA | NA | NA | NA | NA | (p-val) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) | (NA ) |
Estimated ARIMA Residuals | Value | 3994.33960645376 | -156026.677739507 | -203655.688937884 | -164519.357806146 | -227965.016394317 | -60492.5306917827 | 1067176.84637888 | 1019206.55572076 | 11956.4361744015 | -183986.489882733 | -167806.528852016 | 123326.498714172 | -911594.448197265 | -122501.002126966 | -425806.344506969 | 296281.162374462 | -337858.441810153 | 153819.88979484 | 179703.510053426 | 516147.01466307 | -732726.381720797 | 240778.917720083 | -669636.130001004 | 320012.253343144 | -356349.259344542 | 141486.695245220 | -28556.9214395694 | 353148.223430309 | -556551.513072333 | 103474.334457168 | 196791.292123624 | 294175.070486228 | 1190579.16331394 | 44139.6326755661 | 725704.629881903 | 369961.095605750 | -518355.455539228 | 59384.5749953241 | -20543.0070769703 | 39647.380181377 | 627424.127242953 | 141139.091539164 | 2533482.30328322 | 130638.256087288 | 1180567.56759998 | -852165.585395445 | 159100.534844990 | -399619.547048739 | 486053.790206742 | -435968.068186157 | 1396507.53441604 | -247752.050728865 | 546995.940300292 | 35459.3168150662 | 1925707.24246206 | 649010.94334377 | 1338740.61124873 | -665964.716614855 | 684867.240123247 | -715999.587769227 | 326017.645031143 | 36517.3568875824 | 953150.250945275 | 88073.271118795 | 443587.806657745 | -726825.280230295 | 1123290.60276338 | 362728.271564528 | 815334.359389505 | 280090.274333219 | 758549.942162887 | -226654.654125261 | -99226.2068068231 | -1135260.94400324 | 493982.141170909 | -646664.530820415 | 522603.202304362 | -132377.135655287 | 2098347.37884476 | -143766.796214979 | -563093.46303453 | -589826.240264432 | -918626.222093755 | -84817.4805676693 | -883894.22960092 | 294009.816216827 | -69608.2055147296 | 770467.909299455 | -966726.327559156 | 185165.555778518 | -723383.695659279 | -127787.616019429 | -1214262.91273119 | -627096.759767233 | -196921.981562650 | 2582.6995479337 | -82814.845130645 | -295976.057479382 | -226317.294923320 | -764716.80792742 | -1113475.67489537 | -792245.01588731 | 46170.3998204871 | -465993.232461732 | -837638.127470281 | -30702.955707484 | -378441.930213011 | 432180.323581405 | -878264.229097746 | -286495.853485259 | 71282.6346752365 | -589891.228022714 | -544805.026943553 | 152239.924879994 | -931866.605691542 | 593116.969065609 | -1035738.06903276 | 104096.352652099 | 480757.986712893 |
| | Charts produced by software: | | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/1s2in1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/1s2in1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/2ktiq1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/2ktiq1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/3ktiq1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/3ktiq1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/4ktiq1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/4ktiq1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/5ktiq1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/5ktiq1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/6ktiq1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/6ktiq1293552589.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/7d2ht1293552589.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/28/t1293552542hwr0i922cz7qn7k/7d2ht1293552589.ps (open in new window) |
| | Parameters (Session): | par1 = FALSE ; par2 = 1.6 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; | | Parameters (R input): | par1 = FALSE ; par2 = 1.6 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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')
| |
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