R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(274,291,280,258,252,251,224,225,234,233,229,208,224,226,223,205,201,202,183,188,200,206,211,201,299,244,251,241,244,252,234,246,265,277,287,275,320,338,342,322,323,343,315,334,359,362,378,345,422,430,443,431,425,432,387,396,411,421,424,410,464,486,490,459,454,446,406,412,428,429,425,396,429,439,424,379,370,353,322,322,338,348,350,312,358,378,352,312,310,292,276,269,286,292,288,255,304,299,293,275,272,264,234,231,263,264,264,245,297,317,318,315,312,310,306,313,350,354,371,357,419,425,424,399,393,378,371,364,384,377,383,352)
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = 'FALSE'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> library(lattice)
> if (par1 == 'TRUE') par1 <- TRUE
> if (par1 == 'FALSE') par1 <- FALSE
> par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
> par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
> par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
> par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
> armaGR <- function(arima.out, names, n){
+ try1 <- arima.out$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)))
[[1]]
            [,1]      [,2]       [,3]       [,4]
[1,]  0.60986651 0.2809597 -0.7406826 -0.4766436
[2,] -0.46168295 0.0000000  0.3759619 -0.4476267
[3,] -0.05767576 0.0000000  0.0000000 -0.4570152
[4,]  0.00000000 0.0000000  0.0000000 -0.4782520
[5,]          NA        NA         NA         NA
[6,]          NA        NA         NA         NA
[7,]          NA        NA         NA         NA
[8,]          NA        NA         NA         NA

[[2]]
        [,1]   [,2]    [,3]  [,4]
[1,] 0.00000 0.0046 0.00000 0e+00
[2,] 0.29502     NA 0.40911 1e-05
[3,] 0.57672     NA      NA 1e-05
[4,]      NA     NA      NA 0e+00
[5,]      NA     NA      NA    NA
[6,]      NA     NA      NA    NA
[7,]      NA     NA      NA    NA
[8,]      NA     NA      NA    NA

[[3]]
[[3]][[1]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    method = "ML")

Coefficients:
         ar1     ar2      ma1     sar1
      0.6099  0.2810  -0.7407  -0.4766
s.e.  0.1264  0.0974   0.0983   0.0887

sigma^2 estimated as 196.2:  log likelihood = -484.55,  aic = 979.11

[[3]][[2]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    method = "ML")

Coefficients:
         ar1     ar2      ma1     sar1
      0.6099  0.2810  -0.7407  -0.4766
s.e.  0.1264  0.0974   0.0983   0.0887

sigma^2 estimated as 196.2:  log likelihood = -484.55,  aic = 979.11

[[3]][[3]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    fixed = last.arma$next.vector, method = "ML")

Coefficients:
          ar1  ar2    ma1     sar1
      -0.4617    0  0.376  -0.4476
s.e.   0.4391    0  0.454   0.0940

sigma^2 estimated as 219.4:  log likelihood = -490.96,  aic = 989.93

[[3]][[4]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    fixed = last.arma$next.vector, method = "ML")

Coefficients:
          ar1  ar2  ma1     sar1
      -0.0577    0    0  -0.4570
s.e.   0.1031    0    0   0.0961

sigma^2 estimated as 220.3:  log likelihood = -491.26,  aic = 988.52


$aic
[1] 979.1070 989.9263 988.5187 986.8306

Warning messages:
1: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
2: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
3: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
> postscript(file="/var/wessaorg/rcomp/tmp/18osh1322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> resid <- arimaSelectplot(selection)
> dev.off()
null device 
          1 
> resid
Time Series:
Start = 1 
End = 132 
Frequency = 1 
  [1]   0.158193940   0.083914580   0.045638245   0.014614534   0.006231146
  [6]   0.004264751  -0.021483493  -0.017847381  -0.007344631  -0.007559389
 [11]  -0.010692774  -0.180833397  -1.043707425 -13.320226017   6.345698704
 [16]   3.967610833   1.983345032   1.880600001   7.217213198   3.967054854
 [21]   2.872272235   6.378608616   8.363840149  10.223887420  73.873802925
 [26] -60.072163266   9.973223039  10.615687991   8.480871267   8.370478113
 [31]   5.112569365   9.096606177   8.880210718   9.681912855   9.643702307
 [36]   3.552774363 -15.350158730  46.054731233   4.278036561  -6.253318621
 [41]   0.833218474  15.268265833  -8.666364818   9.648707587   9.787347647
 [46]  -5.727343318   7.924146418 -21.436182383   6.514285649  23.810723451
 [51]   8.976381770   3.869853634  -7.716211342  -7.972265193 -22.003632551
 [56]  -8.044968393  -7.650155433   2.468257740 -10.091406732   8.811047966
 [61]  -7.833206601   8.946783842  -4.342989505 -15.625731862  -3.084076260
 [66] -21.068032842  -3.977057979  -7.729871169  -4.006766339  -6.006804765
 [71] -13.275768639  -7.063104413 -31.875670889  -7.419228038 -23.436224188
 [76] -24.016356632  -4.851260657 -16.059572459  10.370613756  -6.720170321
 [81]   0.031884571   4.913221821   3.082747071 -15.693684473   2.488218333
 [86]   4.712069678 -19.422835770  -2.533461514   5.091296177  -4.814841370
 [91]  18.818232836  -8.639726611   0.438117511   0.170812634  -3.251383493
 [96]   0.698960769   8.992348214 -19.914157566  13.794525759  25.148645506
[101]   3.599766608   9.669819922  -6.594372998   0.388813413  15.503207350
[106]  -5.936565779   0.864095170  16.357626882   5.310299717  13.826723151
[111]  16.923230646  25.985238852   0.988012509  10.543793388  20.211428605
[116]  12.958608746  12.537420493   1.398683216  18.869294615  12.484135584
[121]  12.028446186  -1.918786119   1.050613315 -15.075612498  -3.873486184
[126] -10.430936020   8.290762769  -8.917549033 -15.258797575 -10.477648755
[131]  -3.786098688 -14.901259417
> postscript(file="/var/wessaorg/rcomp/tmp/2mfmc1322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3xhfj1322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/48pcg1322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> cpgram(resid, main='Residual Cumulative Periodogram')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/5kfk71322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(resid, main='Residual Histogram', xlab='values of Residuals')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/6mbpn1322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/7e4i71322814043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(resid, main='Residual Normal Q-Q Plot')
> qqline(resid)
> dev.off()
null device 
          1 
> ncols <- length(selection[[1]][1,])
> nrows <- length(selection[[2]][,1])-1
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/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="/var/wessaorg/rcomp/tmp/81a7a1322814043.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="/var/wessaorg/rcomp/tmp/9zzrl1322814043.tab") 
> 
> try(system("convert tmp/18osh1322814043.ps tmp/18osh1322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/2mfmc1322814043.ps tmp/2mfmc1322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/3xhfj1322814043.ps tmp/3xhfj1322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/48pcg1322814043.ps tmp/48pcg1322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/5kfk71322814043.ps tmp/5kfk71322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/6mbpn1322814043.ps tmp/6mbpn1322814043.png",intern=TRUE))
character(0)
> try(system("convert tmp/7e4i71322814043.ps tmp/7e4i71322814043.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.856   0.319   3.302