R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(2150.3,2425.7,2642.0,2291.5,2570.7,2526.6,2266.2,1981.9,2630.3,2942.6,2713.4,2437.5,2678.9,2582.0,2780.0,2512.4,2658.4,2708.7,2518.7,2018.3,2579.3,2693.5,2468.8,2122.8,2412.8,2370.6,2642.5,2634.2,2457.5,2579.1,2505.9,1903.2,2660.2,2844.1,2607.1,2356.0,2659.9,2531.4,2845.7,2654.3,2588.2,2789.6,2533.1,1846.5,2796.3,2895.6,2472.2,2584.4,2630.4,2663.1,3176.2,2856.7,2551.4,3088.7,2628.3,2226.2,3023.6,3077.9,3084.1,2990.3,2949.6,3014.7,3517.7,3121.2,3067.4,3174.6,2676.3,2424.0,3195.1,3146.6,3506.7,3528.5)
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.3'
> 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]       [,5]       [,6]
 [1,] -0.5910393 -0.4143984 0.2533948 -0.04853146 -0.4751535 0.01841932
 [2,] -0.5844471 -0.4084655 0.2590334 -0.05317992 -0.4835281 0.00000000
 [3,] -0.6346370 -0.4466812 0.2268690  0.00000000 -0.4819813 0.00000000
 [4,] -0.7679915 -0.6253070 0.0000000  0.00000000 -0.4885475 0.00000000
 [5,]         NA         NA        NA          NA         NA         NA
 [6,]         NA         NA        NA          NA         NA         NA
 [7,]         NA         NA        NA          NA         NA         NA
 [8,]         NA         NA        NA          NA         NA         NA
 [9,]         NA         NA        NA          NA         NA         NA
[10,]         NA         NA        NA          NA         NA         NA
[11,]         NA         NA        NA          NA         NA         NA
[12,]         NA         NA        NA          NA         NA         NA

[[2]]
         [,1]    [,2]    [,3]    [,4]    [,5]    [,6]
 [1,] 0.16244 0.22691 0.37959 0.90818 0.00391 0.92123
 [2,] 0.15994 0.22471 0.35852 0.89830 0.00066      NA
 [3,] 0.00002 0.00857 0.11095      NA 0.00066      NA
 [4,] 0.00000 0.00001      NA      NA 0.00128      NA
 [5,]      NA      NA      NA      NA      NA      NA
 [6,]      NA      NA      NA      NA      NA      NA
 [7,]      NA      NA      NA      NA      NA      NA
 [8,]      NA      NA      NA      NA      NA      NA
 [9,]      NA      NA      NA      NA      NA      NA
[10,]      NA      NA      NA      NA      NA      NA
[11,]      NA      NA      NA      NA      NA      NA
[12,]      NA      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      ma1     sar1    sar2
      -0.5910  -0.4144  0.2534  -0.0485  -0.4752  0.0184
s.e.   0.4183   0.3397  0.2864   0.4191   0.1588  0.1855

sigma^2 estimated as 2.403e-06:  log likelihood = 295.79,  aic = -577.57

[[3]][[2]]

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

Coefficients:
          ar1      ar2     ar3      ma1     sar1    sar2
      -0.5910  -0.4144  0.2534  -0.0485  -0.4752  0.0184
s.e.   0.4183   0.3397  0.2864   0.4191   0.1588  0.1855

sigma^2 estimated as 2.403e-06:  log likelihood = 295.79,  aic = -577.57

[[3]][[3]]

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

Coefficients:
          ar1      ar2     ar3      ma1     sar1  sar2
      -0.5844  -0.4085  0.2590  -0.0532  -0.4835     0
s.e.   0.4112   0.3333  0.2801   0.4145   0.1353     0

sigma^2 estimated as 2.404e-06:  log likelihood = 295.78,  aic = -579.56

[[3]][[4]]

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

Coefficients:
          ar1      ar2     ar3  ma1     sar1  sar2
      -0.6346  -0.4467  0.2269    0  -0.4820     0
s.e.   0.1391   0.1649  0.1405    0   0.1349     0

sigma^2 estimated as 2.406e-06:  log likelihood = 295.77,  aic = -581.55

[[3]][[5]]
NULL

[[3]][[6]]
NULL


$aic
[1] -577.5740 -579.5643 -581.5476 -581.0031

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/www/html/freestat/rcomp/tmp/1jznc1229455403.ps",horizontal=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]  5.776828e-05  2.308274e-05  1.304777e-05  1.334403e-05  7.634410e-06
 [6]  6.806259e-06  8.772257e-06  1.146756e-05  2.293549e-06 -9.017527e-07
[11]  1.323368e-06 -5.000783e-05 -3.624475e-04  2.852917e-03  1.826702e-03
[16]  1.401399e-03  1.245057e-04 -3.306963e-04 -9.347440e-04  1.046556e-03
[21]  2.357789e-03  2.970996e-03  1.559002e-03  2.118444e-03 -1.272406e-03
[26]  4.072018e-04 -1.099474e-03 -2.628904e-03  1.511736e-03  1.462579e-04
[31]  1.128280e-04  1.513527e-04 -8.072830e-04  5.954123e-04 -1.370499e-03
[36] -2.078608e-04 -7.988372e-04  9.628827e-05 -1.721486e-04  4.268905e-04
[41]  3.443806e-04 -4.572250e-04  6.667161e-04  2.271425e-03 -1.491784e-03
[46] -1.090297e-03  2.756128e-04 -2.569955e-03  7.580779e-04 -1.989224e-03
[51]  4.624601e-05 -5.057061e-04  2.577594e-03 -1.183880e-03  8.122897e-04
[56] -4.378658e-03  1.852677e-03  5.151744e-05 -9.355119e-04 -2.295647e-03
[61]  5.817518e-04  1.215522e-03  3.162960e-04 -2.856612e-04 -8.097442e-04
[66]  2.197993e-03  2.019121e-03 -1.950179e-03 -1.214700e-04  7.249847e-04
[71] -2.074202e-03 -3.254514e-03
> postscript(file="/var/www/html/freestat/rcomp/tmp/26hli1229455403.ps",horizontal=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/html/freestat/rcomp/tmp/3httv1229455403.ps",horizontal=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/html/freestat/rcomp/tmp/4vmdh1229455403.ps",horizontal=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/html/freestat/rcomp/tmp/5g9ci1229455403.ps",horizontal=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/html/freestat/rcomp/tmp/6t3gt1229455403.ps",horizontal=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/html/freestat/rcomp/tmp/7f1td1229455403.ps",horizontal=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/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/html/freestat/rcomp/tmp/8ht7x1229455403.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/html/freestat/rcomp/tmp/9puwm1229455403.tab") 
> 
> system("convert tmp/1jznc1229455403.ps tmp/1jznc1229455403.png")
> system("convert tmp/26hli1229455403.ps tmp/26hli1229455403.png")
> system("convert tmp/3httv1229455403.ps tmp/3httv1229455403.png")
> system("convert tmp/4vmdh1229455403.ps tmp/4vmdh1229455403.png")
> system("convert tmp/5g9ci1229455403.ps tmp/5g9ci1229455403.png")
> system("convert tmp/6t3gt1229455403.ps tmp/6t3gt1229455403.png")
> system("convert tmp/7f1td1229455403.ps tmp/7f1td1229455403.png")
> 
> 
> proc.time()
   user  system elapsed 
  6.134   1.836   6.727