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ARIMA werkloosheid laatste 20 jaar

*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: Wed, 10 Dec 2008 14:18:41 -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/10/t122894400950ty7gfrldg5qhz.htm/, Retrieved Wed, 10 Dec 2008 21:20:09 +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/10/t122894400950ty7gfrldg5qhz.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 «
451 450 444 429 421 400 389 384 432 446 431 423 416 416 413 399 386 374 365 365 418 428 424 421 417 423 423 419 406 398 390 391 444 460 455 456 452 459 461 451 443 439 430 436 488 506 502 501 501 515 521 520 512 509 505 511 570 592 594 586 586 592 594 586 572 563 555 554 601 622 617 606 595 599 600 592 575 567 555 555 608 631 629 624 610 616 621 604 584 574 555 545 599 620 608 590 579 580 579 572 560 551 537 541 588 607 599 578 563 566 561 554 540 526 512 505 554 584 569 540 522 526 527 516 503 489 479 475 524 552 532 511 492 492 493 481 462 457 442 439 488 521 501 485 464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time26 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.8362-0.00970.0954-0.790.42680.111-1
(p-val)(0 )(0.9127 )(0.2079 )(0 )(0 )(0.1475 )(0 )
Estimates ( 2 )0.829600.0916-0.78830.42760.1119-1.0006
(p-val)(0 )(NA )(0.1632 )(0 )(0 )(0.1417 )(0 )
Estimates ( 3 )0.949500-0.85840.42380.0932-1
(p-val)(0 )(NA )(NA )(0 )(0 )(0.211 )(0 )
Estimates ( 4 )0.944900-0.85520.45250-1.0054
(p-val)(0 )(NA )(NA )(0 )(0 )(NA )(0.0093 )
Estimates ( 5 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )


Estimated ARIMA Residuals
Value
-3.00527908604529
1.72469455576527
5.05495620938419
1.30471173119608
-9.10605665788978
15.8034294586408
2.44100414029581
7.39692603802547
6.62545158410508
-8.96900447553863
18.0517384889719
6.37532710510506
2.66624768255153
8.46018304759938
3.68254474927447
15.1214796351642
-7.87568088212899
8.94726113913649
-1.26815330124188
1.04675689102338
-0.046236452082505
5.40778730559648
1.42432672686451
7.13855581265847
-1.77043802293004
2.94542042197912
3.21368663856381
-7.37184717243795
4.61219330114677
10.2273299819625
-4.28826958985893
8.7263112455488
-2.5141713490715
4.2029870845734
1.68176112601366
-2.06179872569404
6.00680588800507
13.9703837577348
7.14040284411369
12.2714057546114
-3.23231705360705
4.49459041851388
4.58187808331331
1.13085079499364
11.5339768333095
6.32983391353182
9.55077439793081
-17.8465049013706
0.207695429386536
-10.2767683551064
-4.2689524681982
-7.47528458705837
-12.2587883901581
-5.37617361898788
-3.09602106036782
-8.55913218380403
-13.4124543574090
7.17518864637833
-3.73145930960860
-7.90825093700573
-15.7214194905453
-0.304448843542789
3.12598953836499
2.97886727959828
-7.47822536095032
5.74135226101986
-5.54840522906376
2.79422713083168
9.82628653906975
9.93886477331556
6.6835424753141
7.0746457529153
-13.5140128827842
4.18416625625279
9.42831625708179
-17.3265284953501
-10.4812316531365
0.484873357555866
-15.243405707868
-16.2890599200525
9.82567357765924
5.24279394388881
-12.9806420042428
-20.1679072946878
4.41296266892829
-3.42156754062714
-2.0798603149566
17.2223405214724
11.6619586074938
4.02050867730939
2.46516149260564
19.2789845027709
-11.7067622026348
-0.595748634112559
2.1116098876354
-17.5529994063480
-8.96363422818156
2.95046025287098
-7.72862161334343
7.39963073148416
-0.203523163723161
-6.3596857226252
0.594030000935188
-12.6930277355986
2.33639006449999
25.8181054894872
-13.4614966658500
-25.3798389526121
-8.9777718650864
6.0371199075578
11.0460423512270
-2.91113362462896
2.99527167913361
-1.15786425357424
7.68683451365179
0.319715931214822
-0.143586371626055
9.34281866724277
-16.9889276743827
0.418229029994595
-8.60465917546177
-5.15333112549864
5.3436048779143
-1.29682169827796
-9.58529779963682
18.5243006166673
-6.83739555071405
2.20823295634603
-0.723771547726678
18.2518801086466
-10.7268661673532
4.02241608825356
-11.7576567474980
-10.4037044977438
15.2877648681444
8.96156609458448
7.51325676191607
6.2005615873562
10.3358856546959
-6.97696946118616
4.69740929306865
-3.63139477988859
35.439783840506
4.66849938575454
-35.9781321328664
-0.196422619832023
2.26274345908775
14.2732147597612
13.6358956630674
-6.60122497520954
4.29735746810083
5.71421283805859
15.6484910494855
-36.9437568282871
4.10192344178067
13.2023660167493
21.2864868096588
0.0390740147284768
3.76104741765904
2.47480211459205
-0.214288265457192
12.3580629204088
-4.55977308248681
9.396389364973
8.6118449794161
-13.1092370511295
0.882416302402577
-14.4250583463793
-12.5231601847739
9.89463518190465
4.28445197931607
5.88606959618533
3.54337000203584
-13.4169503750635
2.37190617896013
6.07471691046414
-13.7051447661486
5.03066301410891
12.5172181022253
16.6105582417601
-8.63824208586666
-11.1569972198859
-18.2614884472428
5.23740741350184
7.16222660250904
-3.95662287618629
4.68773823881476
-2.58587758883235
-0.286041680927866
-19.1124056565189
4.61384750594928
-17.6745081612410
-1.68335794044838
1.31799715679281
-4.40215687450401
5.79179288100287
-2.36727720827297
11.0241065841648
14.8039885682367
-2.87357571550315
-9.201954527014
-14.6017988250528
-3.31015299984411
-37.8967374587891
-8.54964929348537
-16.9219991151268
19.2303143639784
-8.8539800986798
-8.19233572844141
10.5442965666254
-14.4480793295574
-17.9004461301639
19.6603619689034
1.97556373661521
-29.6421902104645
20.4475439107596
6.28160875853782
17.7536270486673
4.78754140905823
2.50812840826281
-0.666176446767118
10.7309164700546
-18.8129776567913
31.8653102624263
-7.85361979605564
-14.3072928562265
-1.81409992403110
8.30674704315858
24.3745282048484
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/211jr1228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/211jr1228943891.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/32chn1228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/32chn1228943891.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/4dakn1228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/4dakn1228943891.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/5rf3e1228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/5rf3e1228943891.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/6eyjx1228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/6eyjx1228943891.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/7oay61228943891.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t122894400950ty7gfrldg5qhz/7oay61228943891.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = 1.1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
Parameters (R input):
par1 = FALSE ; par2 = 1.1 ; par3 = 1 ; 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')
 





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