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*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: Mon, 20 Dec 2010 16:22:00 +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/20/t12928620342pye83rtkhkksm4.htm/, Retrieved Mon, 20 Dec 2010 17:20:41 +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/20/t12928620342pye83rtkhkksm4.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338 417.2 388. etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time21 seconds
R Server'George Udny Yule' @ 72.249.76.132


ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3sar1sar2sma1
Estimates ( 1 )-0.7012-0.3586-0.2358-0.2121-0.1384-0.5116
(p-val)(0 )(0 )(0 )(0.0645 )(0.1184 )(0 )
Estimates ( 2 )-0.7115-0.353-0.2264-0.08530-0.6352
(p-val)(0 )(0 )(0 )(0.2775 )(NA )(0 )
Estimates ( 3 )-0.7147-0.353-0.223900-0.6811
(p-val)(0 )(0 )(0 )(NA )(NA )(0 )
Estimates ( 4 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )


Estimated ARIMA Residuals
Value
0.558114162488688
3.04918901256191
6.88456095781543
43.5424800511233
-15.3610535105023
11.719418350577
-41.4975093803626
-29.4147704807797
42.7791663055472
-52.7353645720034
0.082640277581364
30.3083625240939
-38.4841860191872
-19.5749543044829
-23.7492831825000
-4.07041377652383
23.1708216552513
-14.2120699507476
-7.20295776996004
46.3389132076608
-15.1968709927009
44.5947081668534
2.55150472256053
-62.6265247197598
-16.8667779948743
35.3221036016387
21.0128963006131
19.2045376015729
10.0715287313672
-12.3379324326363
23.7250837242701
27.9493661781467
-7.82696733072323
1.51787590408526
-43.3396612631901
-20.5556075265990
4.77620707655331
4.21881816185140
36.9651947976983
15.8459765378789
-19.2695911698982
2.5815249066099
21.0847746262387
-17.9736841938492
-10.6102360253935
-4.7431180327391
-7.32854220143668
9.44599277914735
-25.3509152340645
24.5508992419954
33.3864869070814
-17.0401945471652
-15.1551455983824
-3.03575534417757
14.4699412910511
23.5227800709759
7.54966892171966
15.4731067344016
17.1163454574935
35.9960008050701
-0.174916625962433
-14.8264593684129
-34.1036582688032
-33.4437513342800
-39.2729977846999
0.466994937132942
16.1027037325886
4.59589486048379
-31.3955335779141
3.5192102996049
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2.88912912224151
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1.18361736060884
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12.6829068261476
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21.5698780304533
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22.3697063046893
5.08051463474868
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29.0699731463832
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42.0120710289269
15.6150151639386
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-7.84602202731772
14.7171204846783
36.8037187708953
1.23991234543521
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15.5921432528049
27.459202351316
24.0877454340059
-28.8158241680150
-9.99110648339158
9.65767217892192
9.9061817986193
30.8957124271159
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30.4253861369169
36.4922247709454
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0.956206324095468
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1.09007299241495
-17.5160048291072
45.6023199855153
6.36547051620219
-9.4394134289446
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21.3792025388811
39.1452970706012
13.6252468554970
21.2754328281184
5.05575622458804
14.0652734835693
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64.582168001053
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53.4354495948275
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12.0996567842741
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26.4616710380440
6.20577222841575
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1.04698721681677
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13.8993797383673
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2.56438370403771
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15.8440524956104
37.6507328635405
-32.6162269977264
-14.1140526403644
46.6806968082893
-14.9195225067592
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26.4468426563873
-22.2655810664998
17.6739523964994
21.6116516249742
-45.0627484772458
6.04016128202197
11.8694567285954
7.89964095840496
-10.9322539577485
-14.8200938842108
10.5766707244454
4.27606418637428
14.8346838449268
-23.6965276782746
-1.25267721188302
-9.1071792067438
1.24210578097280
18.0466338809328
-21.2349319682852
49.6065946977256
-48.4528084049867
13.5017634471806
15.4645123205003
-6.38415469147308
-20.6765728661298
4.08123262633114
-14.1492447492420
24.8855490827511
-15.4108497786899
26.8003806325185
-9.39402397915145
15.9364422898571
-14.8410341215291
-9.04369826848382
6.14756153464624
-5.90887595724958
-8.17755892893074
-10.4526703441041
-12.5876586913155
-8.13774035668867
38.3430593650681
21.1192463164415
23.8741914918194
-0.0452888297571786
-17.4647487278131
-7.96680072020336
-7.2140114154745
4.17428455562539
-16.3654320871175
8.3177608589171
-8.76565530558554
-0.542717194122272
10.6384003869353
3.43598485775388
-7.27767334212603
42.9627763987345
6.21311351430089
-26.8232864978746
19.3980622443454
-2.64904564086123
-42.8613021491187
-20.6029678611273
-13.3479693578336
32.641184053248
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-8.67549814363142
4.79702296077498
47.2421372015374
3.61600639573065
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5.09222815618141
-12.1924297506154
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0.938687977196568
5.15901709537283
15.2654019945528
15.7326060103669
-14.9571444547003
3.9551229791794
22.4140499229367
-11.7844888989943
21.1311367652284
-20.1678187815258
-36.9437837613718
4.61911169997772
33.0581560449671
26.6914844690140
4.72490353041573
-7.00441575459646
-20.1299879476181
7.5239229126626
9.68121634565823
-14.2180790759740
6.88131988986847
-10.6590946757309
18.1628203668947
-2.34237505122537
2.51137560981232
-28.8783116945579
-19.9587744614791
-19.7327824015556
-6.13356640995335
11.8276038281327
24.1599215251754
7.68055771654381
-20.8118979847537
-18.2120292262575
22.1344902921426
-2.19080640241889
14.8128924197282
-15.9735997266248
-0.622002110452479
-13.4590836441381
-8.6188684456311
10.0557959842088
8.8162571310375
6.35366804494212
-7.04133844775424
-1.82204241920956
-30.7145259374633
6.39024835338528
6.81756020586934
21.3775227158597
-1.25443926666305
9.16816214818594
-6.6753145945592
-5.57962689071211
3.07693727401469
0.127569347236472
15.088766814011
-23.8822251879549
28.2274384029243
11.8720084445919
20.0747908070768
-5.75754566989742
-32.268748893925
-9.79600213264086
14.337598212806
13.6089450078025
8.90472642311055
-15.5333762239867
34.4836423645929
-8.48581739294748
33.5972420838766
27.4518774029079
90.7195033237117
-63.2101281114645
-33.0610523266803
-52.3422846552236
-31.8517050411529
-20.0429360247541
-16.7078609472891
-5.21865667169652
-8.0463135311409
12.0680920349959
-14.8529205874186
5.89408973754072
3.92350420382715
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3.33100851830804
-11.7806915842093
53.0308486454331
31.7373240453167
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34.9412716946989
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20.6177970718521
33.8648937757674
-18.6180054038891
32.824974729468
-15.8579800083214
1.04375412001764
2.98857204828555
-47.8353340209834
18.3592002779908
-5.41269362012121
27.4286253722381
3.39636325227269
18.7993666654111
-28.9255902550611
43.6397917120822
-18.4194603304921
-2.57962288772197
-3.11315029008015
-7.19205323462766
30.7845350977517
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/17oy91292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/17oy91292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/27oy91292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/27oy91292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/37oy91292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/37oy91292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/47oy91292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/47oy91292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/5igxc1292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/5igxc1292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/6igxc1292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/6igxc1292862098.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/7igxc1292862098.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t12928620342pye83rtkhkksm4/7igxc1292862098.ps (open in new window)


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