R version 2.12.1 (2010-12-16)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(9676,8642,9402,9610,9294,9448,10319,9548,9801,9596,8923,9746,9829,9125,9782,9441,9162,9915,10444,10209,9985,9842,9429,10132,9849,9172,10313,9819,9955,10048,10082,10541,10208,10233,9439,9963,10158,9225,10474,9757,10490,10281,10444,10640,10695,10786,9832,9747,10411,9511,10402,9701,10540,10112,10915,11183,10384,10834,9886,10216,10943,9867,10203,10837,10573,10647,11502,10656,10866,10835,9945,10331)
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = 'FALSE'
> 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]       [,5]
 [1,] 0.07807921 0.3042662 0.4610019 -0.3676464 -0.3767030
 [2,] 0.00000000 0.3296376 0.4992818 -0.3846219 -0.3903577
 [3,]         NA        NA        NA         NA         NA
 [4,]         NA        NA        NA         NA         NA
 [5,]         NA        NA        NA         NA         NA
 [6,]         NA        NA        NA         NA         NA
 [7,]         NA        NA        NA         NA         NA
 [8,]         NA        NA        NA         NA         NA
 [9,]         NA        NA        NA         NA         NA
[10,]         NA        NA        NA         NA         NA

[[2]]
         [,1]    [,2]    [,3]   [,4]    [,5]
 [1,] 0.49718 0.00703 0.00052 0.0221 0.02476
 [2,]      NA 0.00211 0.00004 0.0134 0.01834
 [3,]      NA      NA      NA     NA      NA
 [4,]      NA      NA      NA     NA      NA
 [5,]      NA      NA      NA     NA      NA
 [6,]      NA      NA      NA     NA      NA
 [7,]      NA      NA      NA     NA      NA
 [8,]      NA      NA      NA     NA      NA
 [9,]      NA      NA      NA     NA      NA
[10,]      NA      NA      NA     NA      NA

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

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

Coefficients:
         ar1     ar2     ar3     sar1     sar2
      0.0781  0.3043  0.4610  -0.3676  -0.3767
s.e.  0.1144  0.1093  0.1263   0.1568   0.1640

sigma^2 estimated as 96127:  log likelihood = -432.11,  aic = 876.22

[[3]][[2]]

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

Coefficients:
         ar1     ar2     ar3     sar1     sar2
      0.0781  0.3043  0.4610  -0.3676  -0.3767
s.e.  0.1144  0.1093  0.1263   0.1568   0.1640

sigma^2 estimated as 96127:  log likelihood = -432.11,  aic = 876.22

[[3]][[3]]
NULL

[[3]][[4]]
NULL

[[3]][[5]]
NULL


$aic
[1] 876.2231 874.6920

Warning message:
In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
> postscript(file="/var/www/rcomp/tmp/1a2a61322828740.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 = 72 
Frequency = 1 
 [1]    9.675990    8.641984    9.401975    9.609965    9.293960    9.447952
 [7]   10.318946    9.547942    9.800937    9.595934    8.922933    9.745930
[13]  107.212495  321.362214  175.011914 -351.349903 -388.720395  339.807778
[19]  206.289065  539.399567  -67.142940    2.465431  160.912524  223.371913
[25] -235.326470 -186.643074  382.409470  208.666875  448.016710 -147.274460
[31] -655.495721  123.936526  242.065913  420.153833 -148.379122 -251.121003
[37]   62.046950   74.804439  314.583724 -274.836209  507.562049  162.905524
[43]   -2.240652  -48.903847  306.564572  469.321210  114.740097 -713.030142
[49] -158.115611   63.620728  109.335152 -221.832032  334.494310 -181.482730
[55]  275.045316  426.617972 -229.944888  -27.621275 -139.038753  210.959285
[61]  470.674231  230.816245 -578.226293  616.745093   -3.992505  284.599032
[67]  272.359119 -647.254147   42.526039 -141.108192  175.214803 -134.780718
> postscript(file="/var/www/rcomp/tmp/2e40c1322828740.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/www/rcomp/tmp/35ui11322828740.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/www/rcomp/tmp/4h1e41322828740.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/www/rcomp/tmp/519bg1322828740.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/www/rcomp/tmp/6c81v1322828740.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/www/rcomp/tmp/7wdu71322828740.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/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/www/rcomp/tmp/8f0gq1322828740.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/www/rcomp/tmp/93qwi1322828740.tab") 
> 
> try(system("convert tmp/1a2a61322828740.ps tmp/1a2a61322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/2e40c1322828740.ps tmp/2e40c1322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/35ui11322828740.ps tmp/35ui11322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/4h1e41322828740.ps tmp/4h1e41322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/519bg1322828740.ps tmp/519bg1322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/6c81v1322828740.ps tmp/6c81v1322828740.png",intern=TRUE))
character(0)
> try(system("convert tmp/7wdu71322828740.ps tmp/7wdu71322828740.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  4.336   0.836   5.149