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Type 'q()' to quit R. > x <- c(2921.44,2981.85,3080.58,3106.22,3119.31,3061.26,3097.31,3161.69,3257.16,3277.01,3295.32,3363.99,3494.17,3667.03,3813.06,3917.96,3895.51,3801.06,3570.12,3701.61,3862.27,3970.1,4138.52,4199.75,4290.89,4443.91,4502.64,4356.98,4591.27,4696.96,4621.4,4562.84,4202.52,4296.49,4435.23,4105.18,4116.68,3844.49,3720.98,3674.4,3857.62,3801.06,3504.37,3032.6,3047.03,2962.34,2197.82,2014.45,1862.83,1905.41,1810.99,1670.07,1864.44,2052.02,2029.6,2070.83,2293.41,2443.27,2513.17) > par9 = '0' > par8 = '0' > par7 = '0' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > 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 > par6 <- 11 > 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,] 0.3154536 -0.03268620 0.1626164 0.06748630 0.2901602 -0.2270238 [2,] 0.3152247 -0.03253029 0.1632960 0.06639370 0.2902141 -0.2279354 [3,] 0.3143660 -0.03879477 0.1716975 0.06825880 0.2978289 -0.2309293 [4,] 0.3038949 0.00000000 0.1624282 0.07456125 0.2918746 -0.2323357 [5,] 0.3100826 0.00000000 0.1578654 0.06025212 0.2960571 -0.2427647 [6,] 0.3214170 0.00000000 0.1736222 0.00000000 0.3110169 -0.2498125 [7,] 0.3318906 0.00000000 0.0000000 0.00000000 0.3196471 -0.2231789 [8,] 0.2738363 0.00000000 0.0000000 0.00000000 0.2635575 0.0000000 [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 [15,] NA NA NA NA NA NA [16,] NA NA NA NA NA NA [17,] NA NA NA NA NA NA [18,] NA NA NA NA NA NA [19,] NA NA NA NA NA NA [20,] NA NA NA NA NA NA [21,] NA NA NA NA NA NA [22,] NA NA NA NA NA NA [,7] [,8] [,9] [,10] [,11] [1,] -0.04888615 0.03048928 -0.004281092 -0.2438145 0.2825404 [2,] -0.04847934 0.02942999 0.000000000 -0.2448370 0.2826185 [3,] -0.04177098 0.00000000 0.000000000 -0.2450436 0.2874202 [4,] -0.04982629 0.00000000 0.000000000 -0.2477840 0.2891178 [5,] 0.00000000 0.00000000 0.000000000 -0.2572552 0.2843855 [6,] 0.00000000 0.00000000 0.000000000 -0.2609188 0.2848766 [7,] 0.00000000 0.00000000 0.000000000 -0.2820014 0.3113980 [8,] 0.00000000 0.00000000 0.000000000 -0.2877056 0.2376631 [9,] NA NA NA NA NA [10,] NA NA NA NA NA [11,] NA NA NA NA NA [12,] NA NA NA NA NA [13,] NA NA NA NA NA [14,] NA NA NA NA NA [15,] NA NA NA NA NA [16,] NA NA NA NA NA [17,] NA NA NA NA NA [18,] NA NA NA NA NA [19,] NA NA NA NA NA [20,] NA NA NA NA NA [21,] NA NA NA NA NA [22,] NA NA NA NA NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [1,] 0.01358 0.79277 0.20365 0.59247 0.02654 0.08280 0.69606 0.80801 0.97208 [2,] 0.01346 0.79358 0.19611 0.58616 0.02645 0.07552 0.69729 0.80884 NA [3,] 0.01359 0.74954 0.15772 0.57586 0.01909 0.07071 0.73121 NA NA [4,] 0.01326 NA 0.16793 0.53658 0.02019 0.06929 0.67575 NA NA [5,] 0.01118 NA 0.17869 0.60335 0.01844 0.05354 NA NA NA [6,] 0.00763 NA 0.12712 NA 0.01113 0.04621 NA NA NA [7,] 0.00691 NA NA NA 0.01043 0.07612 NA NA NA [8,] 0.02432 NA NA NA 0.03304 NA NA NA NA [9,] NA NA NA NA NA NA NA NA NA [10,] NA NA NA NA NA NA NA NA NA [11,] NA NA NA NA NA NA NA NA NA [12,] NA NA NA NA NA NA NA NA NA [13,] NA NA NA NA NA NA NA NA NA [14,] NA NA NA NA NA NA NA NA NA [15,] NA NA NA NA NA NA NA NA NA [16,] NA NA NA NA NA NA NA NA NA [17,] NA NA NA NA NA NA NA NA NA [18,] NA NA NA NA NA NA NA NA NA [19,] NA NA NA NA NA NA NA NA NA [20,] NA NA NA NA NA NA NA NA NA [21,] NA NA NA NA NA NA NA NA NA [22,] NA NA NA NA NA NA NA NA NA [,10] [,11] [1,] 0.04911 0.02271 [2,] 0.04168 0.02259 [3,] 0.04155 0.01883 [4,] 0.03894 0.01805 [5,] 0.02930 0.01950 [6,] 0.02705 0.01961 [7,] 0.01816 0.01155 [8,] 0.01822 0.04432 [9,] NA NA [10,] NA NA [11,] NA NA [12,] NA NA [13,] NA NA [14,] NA NA [15,] NA NA [16,] NA NA [17,] NA NA [18,] NA NA [19,] NA NA [20,] NA NA [21,] NA NA [22,] NA NA [[3]] [[3]][[1]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 0.3155 -0.0327 0.1626 0.0675 0.2902 -0.2270 -0.0489 0.0305 s.e. 0.1230 0.1237 0.1261 0.1252 0.1267 0.1281 0.1244 0.1248 ar9 ar10 ar11 -0.0043 -0.2438 0.2825 s.e. 0.1217 0.1207 0.1199 sigma^2 estimated as 22528: log likelihood = -373.96, aic = 771.91 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 0.3155 -0.0327 0.1626 0.0675 0.2902 -0.2270 -0.0489 0.0305 s.e. 0.1230 0.1237 0.1261 0.1252 0.1267 0.1281 0.1244 0.1248 ar9 ar10 ar11 -0.0043 -0.2438 0.2825 s.e. 0.1217 0.1207 0.1199 sigma^2 estimated as 22528: log likelihood = -373.96, aic = 771.91 [[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 ar4 ar5 ar6 ar7 ar8 ar9 0.3152 -0.0325 0.1633 0.0664 0.2902 -0.2279 -0.0485 0.0294 0 s.e. 0.1228 0.1236 0.1246 0.1211 0.1267 0.1255 0.1239 0.1210 0 ar10 ar11 -0.2448 0.2826 s.e. 0.1170 0.1199 sigma^2 estimated as 22529: log likelihood = -373.96, aic = 769.91 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 0.3144 -0.0388 0.1717 0.0683 0.2978 -0.2309 -0.0418 0 0 s.e. 0.1228 0.1208 0.1197 0.1212 0.1229 0.1250 0.1209 0 0 ar10 ar11 -0.2450 0.2874 s.e. 0.1171 0.1183 sigma^2 estimated as 22554: log likelihood = -373.99, aic = 767.97 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 0.3039 0 0.1624 0.0746 0.2919 -0.2323 -0.0498 0 0 -0.2478 s.e. 0.1183 0 0.1161 0.1198 0.1216 0.1252 0.1184 0 0 0.1168 ar11 0.2891 s.e. 0.1182 sigma^2 estimated as 22592: log likelihood = -374.04, aic = 766.08 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 0.3101 0 0.1579 0.0603 0.2961 -0.2428 0 0 0 -0.2573 s.e. 0.1178 0 0.1158 0.1152 0.1216 0.1228 0 0 0 0.1147 ar11 0.2844 s.e. 0.1179 sigma^2 estimated as 22665: log likelihood = -374.13, aic = 764.25 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 ar11 0.3214 0 0.1736 0 0.3110 -0.2498 0 0 0 -0.2609 0.2849 s.e. 0.1158 0 0.1120 0 0.1181 0.1223 0 0 0 0.1147 0.1183 sigma^2 estimated as 22783: log likelihood = -374.26, aic = 762.53 [[3]][[8]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 ar11 0.3319 0 0 0 0.3196 -0.2232 0 0 0 -0.2820 0.3114 s.e. 0.1181 0 0 0 0.1204 0.1234 0 0 0 0.1157 0.1190 sigma^2 estimated as 23737: log likelihood = -375.45, aic = 762.9 [[3]][[9]] NULL [[3]][[10]] NULL [[3]][[11]] NULL $aic [1] 771.9128 769.9140 767.9731 766.0762 764.2528 762.5256 762.8982 764.0482 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 6: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean, : some AR parameters were fixed: setting transform.pars = FALSE 7: 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/rcomp/tmp/1daxl1260550408.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 = 59 Frequency = 1 [1] 2.921438 52.364354 74.165025 -1.178408 4.409368 -59.557568 [7] 34.571524 36.994637 79.742325 -4.543796 28.282504 54.866233 [13] 103.886233 89.992223 99.328442 34.565001 -46.886276 -106.355664 [19] -218.918825 175.906024 115.061743 98.759338 173.139766 66.281982 [25] -35.400606 84.871279 -29.664098 -214.565649 264.935146 121.458586 [31] -134.848773 -37.725379 -267.300780 70.979754 132.692038 -313.585159 [37] 91.807436 -233.265597 -32.197431 -72.116623 280.923141 -187.689911 [43] -271.722235 -255.866236 168.193153 -294.718501 -571.422163 72.241063 [49] 43.753158 8.324766 -12.087312 42.888309 63.074632 89.959894 [55] 18.852531 59.978854 43.644884 168.767056 17.926784 > postscript(file="/var/www/html/rcomp/tmp/2ouyy1260550408.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/rcomp/tmp/38tut1260550408.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/rcomp/tmp/4wbpx1260550408.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/rcomp/tmp/5xcvp1260550408.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/rcomp/tmp/6jv8h1260550408.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/rcomp/tmp/7c7cl1260550408.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/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/rcomp/tmp/8spju1260550408.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/rcomp/tmp/96shd1260550408.tab") > system("convert tmp/1daxl1260550408.ps tmp/1daxl1260550408.png") > system("convert tmp/2ouyy1260550408.ps tmp/2ouyy1260550408.png") > system("convert tmp/38tut1260550408.ps tmp/38tut1260550408.png") > system("convert tmp/4wbpx1260550408.ps tmp/4wbpx1260550408.png") > system("convert tmp/5xcvp1260550408.ps tmp/5xcvp1260550408.png") > system("convert tmp/6jv8h1260550408.ps tmp/6jv8h1260550408.png") > system("convert tmp/7c7cl1260550408.ps tmp/7c7cl1260550408.png") > > > proc.time() user system elapsed 3.241 1.042 4.701