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Type 'q()' to quit R. > x <- c(1901,1395,1639,1643,1751,1797,1373,1558,1555,2061,2010,2119,1985,1963,2017,1975,1589,1679,1392,1511,1449,1767,1899,2179,2217,2049,2343,2175,1607,1702,1764,1766,1615,1953,2091,2411,2550,2351,2786,2525,2474,2332,1978,1789,1904,1997,2207,2453,1948,1384,1989,2140,2100,2045,2083,2022,1950,1422,1859,2147) > 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,] -0.3627116 -0.3459528 -0.3918348 -0.3335048 -0.3115216 -0.3431274 [2,] -0.3137211 -0.2563651 -0.3290698 -0.2594135 -0.2632802 -0.2939537 [3,] -0.2532453 -0.2094892 -0.2476862 -0.2189322 -0.2052906 -0.2329718 [4,] -0.2246597 -0.1823762 -0.2102896 -0.1842634 0.0000000 -0.1914915 [5,] -0.1965019 -0.1558356 -0.1765830 0.0000000 0.0000000 -0.1541146 [6,] -0.1759828 -0.1655445 -0.1692538 0.0000000 0.0000000 0.0000000 [7,] -0.1554522 -0.1786381 -0.1527251 0.0000000 0.0000000 0.0000000 [8,] -0.1602606 -0.1977004 0.0000000 0.0000000 0.0000000 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,] -0.3748508 -0.3103093 -0.2306448 -0.3800849 -0.3864357 [2,] -0.3052056 -0.2516861 0.0000000 -0.3249815 -0.3144995 [3,] -0.2612004 0.0000000 0.0000000 -0.2597732 -0.2664273 [4,] -0.2245982 0.0000000 0.0000000 -0.2255490 -0.2313642 [5,] -0.1914203 0.0000000 0.0000000 -0.2047037 -0.1821247 [6,] -0.1877420 0.0000000 0.0000000 -0.2077479 -0.1693466 [7,] -0.1845633 0.0000000 0.0000000 -0.2074852 0.0000000 [8,] -0.2088013 0.0000000 0.0000000 -0.2179074 0.0000000 [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,] 0.00470 0.00864 0.00457 0.01421 0.01917 0.00893 0.00445 0.02017 0.09291 [2,] 0.01390 0.03435 0.01501 0.04852 0.04628 0.02297 0.01530 0.05324 NA [3,] 0.04858 0.08773 0.05827 0.09687 0.12040 0.07058 0.04061 NA NA [4,] 0.08174 0.14047 0.11362 0.16868 NA 0.13444 0.07788 NA NA [5,] 0.13055 0.20538 0.18330 NA NA 0.22392 0.13213 NA NA [6,] 0.17465 0.19528 0.20889 NA NA NA 0.15049 NA NA [7,] 0.23187 0.17485 0.26321 NA NA NA 0.16838 NA NA [8,] 0.00000 0.00000 NA NA NA NA 0.00000 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,] 0.00544 0.00812 [2,] 0.01658 0.02621 [3,] 0.05276 0.06104 [4,] 0.09667 0.10580 [5,] 0.13301 0.19663 [6,] 0.14009 0.24606 [7,] 0.14718 NA [8,] 0.00000 NA [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 -0.3627 -0.3460 -0.3918 -0.3335 -0.3115 -0.3431 -0.3749 -0.3103 s.e. 0.1223 0.1263 0.1317 0.1311 0.1285 0.1259 0.1256 0.1291 ar9 ar10 ar11 -0.2306 -0.3801 -0.3864 s.e. 0.1345 0.1305 0.1399 sigma^2 estimated as 47890: log likelihood = -403.26, aic = 830.52 [[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 -0.3627 -0.3460 -0.3918 -0.3335 -0.3115 -0.3431 -0.3749 -0.3103 s.e. 0.1223 0.1263 0.1317 0.1311 0.1285 0.1259 0.1256 0.1291 ar9 ar10 ar11 -0.2306 -0.3801 -0.3864 s.e. 0.1345 0.1305 0.1399 sigma^2 estimated as 47890: log likelihood = -403.26, aic = 830.52 [[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 -0.3137 -0.2564 -0.3291 -0.2594 -0.2633 -0.2940 -0.3052 -0.2517 s.e. 0.1230 0.1178 0.1305 0.1282 0.1288 0.1252 0.1214 0.1271 ar9 ar10 ar11 0 -0.325 -0.3145 s.e. 0 0.131 0.1372 sigma^2 estimated as 50595: log likelihood = -404.67, aic = 831.34 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 -0.2532 -0.2095 -0.2477 -0.2189 -0.2053 -0.2330 -0.2612 0 0 s.e. 0.1253 0.1203 0.1278 0.1294 0.1299 0.1261 0.1243 0 0 ar10 ar11 -0.2598 -0.2664 s.e. 0.1309 0.1390 sigma^2 estimated as 54429: log likelihood = -406.52, aic = 833.03 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 -0.2247 -0.1824 -0.2103 -0.1843 0 -0.1915 -0.2246 0 0 s.e. 0.1265 0.1218 0.1306 0.1320 0 0.1259 0.1248 0 0 ar10 ar11 -0.2255 -0.2314 s.e. 0.1333 0.1405 sigma^2 estimated as 57121: log likelihood = -407.73, aic = 833.45 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 -0.1965 -0.1558 -0.1766 0 0 -0.1541 -0.1914 0 0 -0.2047 s.e. 0.1279 0.1215 0.1309 0 0 0.1252 0.1251 0 0 0.1341 ar11 -0.1821 s.e. 0.1392 sigma^2 estimated as 59249: log likelihood = -408.67, aic = 833.35 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 -0.1760 -0.1655 -0.1693 0 0 0 -0.1877 0 0 -0.2077 s.e. 0.1279 0.1262 0.1331 0 0 0 0.1287 0 0 0.1387 ar11 -0.1693 s.e. 0.1444 sigma^2 estimated as 61113: log likelihood = -409.4, aic = 832.81 [[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 -0.1555 -0.1786 -0.1527 0 0 0 -0.1846 0 0 -0.2075 s.e. 0.1286 0.1299 0.1351 0 0 0 0.1322 0 0 0.1411 ar11 0 s.e. 0 sigma^2 estimated as 62875: log likelihood = -410.07, aic = 832.13 [[3]][[9]] NULL [[3]][[10]] NULL [[3]][[11]] NULL $aic [1] 830.5230 831.3446 833.0336 833.4513 833.3485 832.8066 832.1335 831.4020 Warning messages: 1: In log(s2) : NaNs produced 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 8: 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/19gp31260292370.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 = 60 Frequency = 1 [1] 1.900999 -470.536737 169.952254 -50.869781 87.381756 99.754258 [7] -370.613121 132.217130 -129.588316 535.527804 59.675457 105.949953 [13] 10.228952 -108.572912 99.842194 -49.010156 -380.827192 59.711844 [19] -328.883110 111.766778 -95.667190 318.370088 152.977853 272.051540 [25] 181.488320 -153.598480 259.309058 -139.273952 -568.111324 70.646233 [31] -11.542648 14.854480 -128.723235 436.710406 140.751751 239.081127 [37] 343.551999 -122.566487 360.285283 -215.856442 30.988706 -104.232470 [43] -397.316024 -181.401375 -7.400441 169.729999 196.804811 262.119410 [49] -350.993260 -685.975150 419.218916 58.932403 -50.873026 57.698542 [55] 114.629460 -144.935245 -143.616015 -381.583790 255.832105 126.211325 > postscript(file="/var/www/html/rcomp/tmp/265pv1260292370.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/37xt81260292370.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/4iowg1260292370.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/5tdbz1260292370.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/6gmx61260292370.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/70cww1260292370.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/82ro11260292370.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/90pe91260292370.tab") > > system("convert tmp/19gp31260292370.ps tmp/19gp31260292370.png") > system("convert tmp/265pv1260292370.ps tmp/265pv1260292370.png") > system("convert tmp/37xt81260292370.ps tmp/37xt81260292370.png") > system("convert tmp/4iowg1260292370.ps tmp/4iowg1260292370.png") > system("convert tmp/5tdbz1260292370.ps tmp/5tdbz1260292370.png") > system("convert tmp/6gmx61260292370.ps tmp/6gmx61260292370.png") > system("convert tmp/70cww1260292370.ps tmp/70cww1260292370.png") > > > proc.time() user system elapsed 2.552 1.072 7.065