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) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > x <- c(4581945 + ,3874038 + ,4086290 + ,4364364 + ,3793586 + ,4533914 + ,4823043 + ,3981535 + ,4746356 + ,5284534 + ,4264830 + ,3924674 + ,3734753 + ,3762290 + ,3609739 + ,3877594 + ,3636415 + ,3578195 + ,3604342 + ,3459513 + ,3366571 + ,3371277 + ,3724848 + ,3350830 + ,3305159 + ,3390736 + ,3349758 + ,3253655 + ,3734250 + ,3455433 + ,2966726 + ,2993716 + ,3009320 + ,3169713 + ,3170061 + ,3368934 + ,3292638 + ,3337344 + ,3208306 + ,3359130 + ,3223078 + ,3437159 + ,3400156 + ,3657576 + ,3765613 + ,3481921 + ,3604800 + ,3981340 + ,3734078 + ,4018173 + ,3887417 + ,3919880 + ,4014466 + ,4197758 + ,3896531 + ,3964742 + ,4201847 + ,4050512 + ,3997402 + ,4314479 + ,4925744 + ,5130631 + ,4444855 + ,3967319 + ,3931250 + ,4235952 + ,4169219 + ,3779064 + ,3558810 + ,3699466 + ,3650693 + ,3525633 + ,3470276 + ,3859094 + ,3661155 + ,3356365 + ,3344440 + ,3338684 + ,3404294 + ,3289319 + ,3469252 + ,3571850 + ,3639914 + ,3091730 + ,3078149 + ,3188115 + ,3246082 + ,3486992 + ,3378187 + ,3282306 + ,3288345 + ,3325749 + ,3352262 + ,3531954 + ,3722622 + ,3809365 + ,3750617 + ,3615286 + ,3696556 + ,4123959 + ,4136163 + ,3933392 + ,4035576 + ,4551202 + ,4032195 + ,3970893 + ,4489016 + ,5426127 + ,4578224 + ,4126390 + ,4892100 + ,4128697 + ,4408721 + ,4199465 + ,4074767 + ,4161758 + ,3891319 + ,4470302 + ,4283111 + ,3845962 + ,3911471 + ,3798478 + ,3644313 + ,3784029 + ,3647134 + ,3994662 + ,3607836 + ,3566008 + ,3511412 + ,3258665 + ,3486573 + ,3369443 + ,3465544 + ,3905224 + ,3733881 + ,3220642 + ,3225812 + ,3354461 + ,3352261 + ,3450652) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '4' > par4 = '0' > par3 = '1' > par2 = '0.0' > 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,] 0.02826675 -0.3371604 0.10882336 -0.3235397 -0.1656463 0.07408965 [2,] 0.00000000 -0.3454487 0.09675144 -0.2951851 -0.1805257 0.07217063 [3,] 0.00000000 -0.3451831 0.09722797 -0.2957440 -0.1146795 0.07980863 [4,] 0.00000000 -0.3522466 0.09087344 -0.2797624 -0.1222955 0.00000000 [5,] 0.00000000 -0.3534165 0.00000000 -0.2748591 -0.1137944 0.00000000 [6,] 0.00000000 -0.3171647 0.00000000 -0.2985234 0.0000000 0.00000000 [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 [13,] NA NA NA NA NA NA [14,] NA NA NA NA NA NA [,7] [1,] 0.05234371 [2,] 0.06605395 [3,] 0.00000000 [4,] 0.00000000 [5,] 0.00000000 [6,] 0.00000000 [7,] NA [8,] NA [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.98051 0.33417 0.82711 0.77964 0.81826 0.55602 0.94202 [2,] NA 0.00011 0.23250 0.00103 0.79876 0.57014 0.92553 [3,] NA 0.00011 0.22932 0.00097 0.19991 0.38108 NA [4,] NA 0.00007 0.25626 0.00132 0.17542 NA NA [5,] NA 0.00010 NA 0.00131 0.21377 NA NA [6,] NA 0.00029 NA 0.00076 NA NA NA [7,] NA NA NA NA NA NA NA [8,] NA NA NA NA NA NA NA [9,] NA NA NA NA NA NA NA [10,] NA NA NA NA NA NA NA [11,] NA NA NA NA NA NA NA [12,] NA NA NA NA NA NA NA [13,] NA NA NA NA NA NA NA [14,] NA 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 sma1 0.0283 -0.3372 0.1088 -0.3235 -0.1656 0.0741 0.0523 s.e. 1.1547 0.3478 0.4973 1.1540 0.7195 0.1255 0.7184 sigma^2 estimated as 0.004827: log likelihood = 173.21, aic = -330.41 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.0283 -0.3372 0.1088 -0.3235 -0.1656 0.0741 0.0523 s.e. 1.1547 0.3478 0.4973 1.1540 0.7195 0.1255 0.7184 sigma^2 estimated as 0.004827: log likelihood = 173.21, aic = -330.41 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 -0.3454 0.0968 -0.2952 -0.1805 0.0722 0.0661 s.e. 0 0.0866 0.0807 0.0879 0.7067 0.1268 0.7053 sigma^2 estimated as 0.004827: log likelihood = 173.21, aic = -332.41 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 -0.3452 0.0972 -0.2957 -0.1147 0.0798 0 s.e. 0 0.0865 0.0805 0.0877 0.0890 0.0908 0 sigma^2 estimated as 0.004827: log likelihood = 173.2, aic = -334.4 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 -0.3522 0.0909 -0.2798 -0.1223 0 0 s.e. 0 0.0861 0.0797 0.0853 0.0898 0 0 sigma^2 estimated as 0.004856: log likelihood = 172.82, aic = -335.64 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 -0.3534 0 -0.2749 -0.1138 0 0 s.e. 0 0.0881 0 0.0838 0.0911 0 0 sigma^2 estimated as 0.004903: log likelihood = 172.17, aic = -336.34 [[3]][[7]] NULL $aic [1] -330.4125 -332.4118 -334.4039 -335.6358 -336.3428 -336.7955 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 4: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean, : some AR parameters were fixed: setting transform.pars = FALSE 5: 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/1wsfy1324592891.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 = 140 Frequency = 1 [1] 0.015337625 -0.152548373 0.022232910 0.018021512 -0.113716163 [6] 0.153283172 0.061549130 -0.111082989 0.153222896 0.104692666 [11] -0.122109788 -0.093371586 -0.128550840 -0.052851607 -0.090778114 [16] 0.044085534 -0.080994126 -0.015611300 -0.026410384 -0.045533845 [21] -0.046147519 -0.024739213 0.081555937 -0.088223852 -0.005531002 [26] -0.014846022 -0.010835584 -0.035038516 0.126289547 -0.054521828 [31] -0.120720657 -0.053833996 -0.048301861 0.031850361 -0.001110323 [36] 0.076801963 -0.007299814 0.039256822 -0.036516363 0.049680551 [41] -0.044228354 0.072369134 -0.010953128 0.098466385 0.046058365 [46] -0.030709395 0.033634866 0.091806048 -0.023749288 0.095933242 [51] -0.024257104 0.035719256 0.016067789 0.064341426 -0.054695654 [56] 0.021994508 0.039194795 -0.014359681 -0.004132575 0.066002747 [61] 0.149590460 0.105370435 -0.066858141 -0.110419415 -0.075644776 [66] 0.021398177 -0.024224378 -0.089822417 -0.097160345 -0.018743230 [71] -0.041820216 -0.040830822 -0.039210934 0.083561316 -0.039204544 [76] -0.062571264 -0.041700901 -0.033220490 0.002443826 -0.039914159 [81] 0.046642880 0.026130878 0.046952505 -0.144002635 -0.030468410 [86] -0.029026264 0.012774809 0.070104955 -0.005804952 -0.007657367 [91] -0.009596529 0.008055209 0.007921465 0.057993200 0.070257529 [96] 0.060928250 0.020763617 -0.016504888 0.018503545 0.106231204 [101] 0.040356072 -0.003761646 0.027561943 0.121025550 -0.077521174 [106] 0.004548499 0.084138190 0.218965297 -0.079132818 -0.055561184 [111] 0.103983219 -0.156843531 0.068267960 -0.094023363 -0.020258066 [116] -0.025115048 -0.070432582 0.114457615 -0.035853504 -0.068040743 [121] -0.025787793 -0.057814705 -0.058924228 0.004393618 -0.050081364 [126] 0.082882796 -0.096127844 -0.002813751 -0.058057013 -0.082909183 [131] 0.026288711 -0.051013170 0.032140492 0.107233239 0.001618114 [136] -0.112101477 -0.039145987 -0.011694075 -0.007278034 0.028725796 > postscript(file="/var/wessaorg/rcomp/tmp/2rvx11324592891.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/3g9cu1324592891.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/422bh1324592891.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/51ynt1324592891.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/6zt7q1324592891.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/7nz3a1324592891.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/87km31324592891.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/9c1241324592891.tab") > > try(system("convert tmp/1wsfy1324592891.ps tmp/1wsfy1324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/2rvx11324592891.ps tmp/2rvx11324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/3g9cu1324592891.ps tmp/3g9cu1324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/422bh1324592891.ps tmp/422bh1324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/51ynt1324592891.ps tmp/51ynt1324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/6zt7q1324592891.ps tmp/6zt7q1324592891.png",intern=TRUE)) character(0) > try(system("convert tmp/7nz3a1324592891.ps tmp/7nz3a1324592891.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 2.829 0.411 3.247