R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(655362,873127,1107897,1555964,1671159,1493308,2957796,2638691,1305669,1280496,921900,867888,652586,913831,1108544,1555827,1699283,1509458,3268975,2425016,1312703,1365498,934453,775019,651142,843192,1146766,1652601,1465906,1652734,2922334,2702805,1458956,1410363,1019279,936574,708917,885295,1099663,1576220,1487870,1488635,2882530,2677026,1404398,1344370,936865,872705,628151,953712,1160384,1400618,1661511,1495347,2918786,2775677,1407026,1370199,964526,850851,683118,847224,1073256,1514326,1503734,1507712,2865698,2788128,1391596,1366378,946295,859626)
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.9'
> par1 = 'FALSE'
> par9 <- '1'
> par8 <- '0'
> par7 <- '1'
> par6 <- '2'
> par5 <- '12'
> par4 <- '1'
> par3 <- '0'
> par2 <- '0.9'
> par1 <- 'FALSE'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), ARIMA Backward Selection (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimabackwardselection.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #
> library(lattice)
> if (par1 == 'TRUE') par1 <- TRUE
> if (par1 == 'FALSE') par1 <- FALSE
> par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
> par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
> par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
> par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
> armaGR <- function(arima.out, names, n){
+ try1 <- arima.out$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,] 0.1527525 0.2174897 -0.3677055 -0.6062105
[2,] 0.0000000 0.1827391 -0.2230088 -0.6120851
[3,] 0.0000000 0.0000000 -0.1806417 -0.6312748
[4,] 0.0000000 0.0000000  0.0000000 -0.6702182
[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,] 0.68917 0.13233 0.32937 0.00022
[2,]      NA 0.16846 0.07920 0.00020
[3,]      NA      NA 0.09771 0.00017
[4,]      NA      NA      NA 0.00020
[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     sma1
      0.1528  0.2175  -0.3677  -0.6062
s.e.  0.3802  0.1428   0.3742   0.1550

sigma^2 estimated as 330691697:  log likelihood = -676.42,  aic = 1362.84

[[3]][[2]]

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

Coefficients:
         ar1     ar2      ma1     sma1
      0.1528  0.2175  -0.3677  -0.6062
s.e.  0.3802  0.1428   0.3742   0.1550

sigma^2 estimated as 330691697:  log likelihood = -676.42,  aic = 1362.84

[[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     sma1
        0  0.1827  -0.2230  -0.6121
s.e.    0  0.1313   0.1251   0.1556

sigma^2 estimated as 330685176:  log likelihood = -676.49,  aic = 1360.97

[[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     sma1
        0    0  -0.1806  -0.6313
s.e.    0    0   0.1076   0.1591

sigma^2 estimated as 339372962:  log likelihood = -677.46,  aic = 1360.91


$aic
[1] 1362.843 1360.974 1360.914 1361.543

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/1m4lh1386001446.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]    171.7247    222.3153    275.4541    373.9378    398.7639    360.3581
 [7]    666.6090    601.5192    319.3373    313.7908    233.4615    221.1144
[13]   -544.7615   7768.6591   1525.1091    250.5774   5148.3726   3894.4855
[19]  53806.5313 -27505.0156  -3659.5456  15140.3087   5152.7061 -17305.5089
[25]  -3390.7924 -11959.3814   5992.4906  20845.3286 -41411.5442  23340.0741
[31] -35252.0786  28968.5090  36223.0093  23838.3055  23744.9776  30333.5484
[37]  18237.7066   6102.6487  -4434.7911  -5347.1278 -22777.5566 -20803.0605
[43] -34832.5468   9255.3072   8180.6728  -2544.1909  -7365.2346   -468.6017
[49] -10988.9813  15219.9021  12805.4159 -38337.7835  16906.7895  -5747.1111
[55] -12808.3388  27252.1549   9489.5010   4864.3728   2874.8801  -3907.1252
[61]   5406.6553 -12534.0525 -15405.8814  -3489.0556 -19712.8429  -6381.5883
[67] -19262.9835  17517.9697   2653.6486   1612.0886  -2589.8934  -1226.4199
> postscript(file="/var/wessaorg/rcomp/tmp/235881386001446.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/3mlqb1386001446.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/4upc81386001446.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/5zja51386001446.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/69avv1386001446.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/7i2hu1386001446.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/8j4t51386001446.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/9qzl81386001446.tab") 
> 
> try(system("convert tmp/1m4lh1386001446.ps tmp/1m4lh1386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/235881386001446.ps tmp/235881386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/3mlqb1386001446.ps tmp/3mlqb1386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/4upc81386001446.ps tmp/4upc81386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/5zja51386001446.ps tmp/5zja51386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/69avv1386001446.ps tmp/69avv1386001446.png",intern=TRUE))
character(0)
> try(system("convert tmp/7i2hu1386001446.ps tmp/7i2hu1386001446.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  6.454   1.122   7.543