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Paper DMA ARIMA-aandelen

*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, 15 Dec 2010 19:38:10 +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/15/t12924418897j4aq5gi4dbznca.htm/, Retrieved Wed, 15 Dec 2010 20:38:09 +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/15/t12924418897j4aq5gi4dbznca.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:
Paper DMA
 
Dataseries X:
» Textbox « » Textfile « » CSV «
3030,29 2803,47 2767,63 2882,6 2863,36 2897,06 3012,61 3142,95 3032,93 3045,78 3110,52 3013,24 2987,1 2995,55 2833,18 2848,96 2794,83 2845,26 2915,03 2892,63 2604,42 2641,65 2659,81 2638,53 2720,25 2745,88 2735,7 2811,7 2799,43 2555,28 2304,98 2214,95 2065,81 1940,49 2042 1995,37 1946,81 1765,9 1635,25 1833,42 1910,43 1959,67 1969,6 2061,41 2093,48 2120,88 2174,56 2196,72 2350,44 2440,25 2408,64 2472,81 2407,6 2454,62 2448,05 2497,84 2645,64 2756,76 2849,27 2921,44 2981,85 3080,58 3106,22 3119,31 3061,26 3097,31 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,1 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,4 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,4 3857,62 3801,06 3504,37 3032,6 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.9818-0.2440.1833-0.7517-0.3675-0.12640.3495
(p-val)(0 )(0.0782 )(0.0886 )(0 )(0.5645 )(0.359 )(0.5784 )
Estimates ( 2 )0.9711-0.2410.1863-0.7441-0.0201-0.11110
(p-val)(0 )(0.0812 )(0.0844 )(0 )(0.8672 )(0.4199 )(NA )
Estimates ( 3 )0.9716-0.24120.1852-0.74580-0.11220
(p-val)(0 )(0.0811 )(0.0851 )(0 )(NA )(0.415 )(NA )
Estimates ( 4 )0.9733-0.23610.1811-0.7437000
(p-val)(0 )(0.0882 )(0.0941 )(0 )(NA )(NA )(NA )
Estimates ( 5 )-0.5570.167100.8843000
(p-val)(4e-04 )(0.1479 )(NA )(0 )(NA )(NA )(NA )
Estimates ( 6 )-0.4521000.7293000
(p-val)(0.1514 )(NA )(NA )(0.0052 )(NA )(NA )(NA )
Estimates ( 7 )0000.3034000
(p-val)(NA )(NA )(NA )(0.0028 )(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
3.03028833849435
-216.600133623590
12.1887671074146
89.0269219288254
-31.2417210535998
47.4931283037929
96.095156896652
112.511537960985
-133.013735140608
60.0581848410245
26.7565927410412
-87.5181319799948
-6.29431625088024
1.22340105839952
-159.440570126092
58.6564610902413
-89.773674299403
91.4309586838258
25.8875185603329
-9.73946292707545
-291.233115233575
119.336266541885
-52.0408251748705
24.8823074952532
53.9537502095724
23.2241365262458
-15.5309300348547
82.7246304027614
-38.2439985117063
-221.805717252218
-198.908827059517
-58.11749441816
-147.454151694735
-85.2028012754715
106.995820302892
-78.772783323145
-12.1911146374120
-193.971045175054
-70.9702909354827
190.866700715401
27.3967802739874
64.0727220701659
-14.5383818257861
106.901654755185
-4.38906928749265
45.0984036906546
33.1764901736463
22.231120387308
147.524627769017
51.7118281167394
-28.7237016615745
70.8284122614036
-87.8560285732837
81.613987958633
-44.8346498341839
79.5175191254357
112.316487458716
96.0226511714281
72.7141328829457
60.9600474629728
48.5773500271653
90.611749564699
4.1892631312362
21.6255656695243
-67.9039099295764
59.3298066543175
37.4079454353086
97.2921729955656
-7.94642254892415
33.0786063107253
52.8232238839814
122.699265916495
142.225319459058
120.448954956233
83.0715678271285
-35.6125485477892
-78.6267598724303
-216.295009630473
184.833942389594
85.3032105696525
118.246672684025
130.929068226327
41.8800809667182
88.2766997283561
129.841077347885
33.2118544439418
-143.331778876415
272.973947353217
12.5249715674954
-36.9163750206053
-65.7946767986168
-338.80898903447
178.17514120769
51.2782125364492
-304.728284015758
84.5341534242361
-328.641393358524
-6.88015309353886
-97.3960132960183
233.19325550683
-143.799888569450
-217.386319167671
-447.352971256093
127.413532218176
-171.088439707962
-678.031389339213
-34.4945139636275
-209.357265337176
126.721523208693
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/17wt01292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/17wt01292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/27wt01292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/27wt01292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/37wt01292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/37wt01292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/4z5sk1292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/4z5sk1292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/5z5sk1292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/5z5sk1292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/6z5sk1292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/6z5sk1292441874.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/7z5sk1292441874.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t12924418897j4aq5gi4dbznca/7z5sk1292441874.ps (open in new window)


 
Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
 
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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