R version 2.8.0 (2008-10-20) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 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(205597 + ,205471 + ,211064 + ,212856 + ,217036 + ,219302 + ,219759 + ,221388 + ,220834 + ,221788 + ,222358 + ,222972 + ,224164 + ,224915 + ,226294 + ,224690 + ,227021 + ,229284 + ,229189 + ,230032 + ,229389 + ,231053 + ,232560 + ,232681 + ,231555 + ,231428 + ,232141 + ,234939 + ,235424 + ,235471 + ,236355 + ,238693 + ,236958 + ,237060 + ,239282 + ,238252 + ,241552 + ,236230 + ,238909 + ,240723 + ,242120 + ,242100 + ,243276 + ,244677 + ,243494 + ,244902 + ,245247 + ,245578 + ,243052 + ,238121 + ,241863 + ,241203 + ,243634 + ,242351 + ,245180 + ,246126 + ,244424 + ,245166 + ,247258 + ,245094 + ,246020 + ,243082 + ,245555 + ,243685 + ,247277 + ,245029 + ,246169 + ,246778 + ,244577 + ,246048 + ,245775 + ,245328 + ,245477 + ,241903 + ,243219 + ,248088 + ,248521 + ,247389 + ,249057 + ,248916 + ,249193 + ,250768 + ,253106 + ,249829 + ,249447 + ,246755 + ,250785 + ,250140 + ,255755 + ,254671 + ,253919 + ,253741 + ,252729 + ,253810 + ,256653 + ,255231 + ,258405 + ,251061 + ,254811 + ,254895 + ,258325 + ,257608 + ,258759 + ,258621 + ,257852 + ,260560 + ,262358 + ,260812 + ,261165 + ,257164 + ,260720 + ,259581 + ,264743 + ,261845 + ,262262 + ,261631 + ,258953 + ,259966 + ,262850 + ,262204 + ,263418 + ,262752 + ,266433 + ,267722 + ,266003 + ,262971 + ,265521 + ,264676 + ,270223 + ,269508 + ,268457 + ,265814 + ,266680 + ,263018 + ,269285 + ,269829 + ,270911 + ,266844 + ,271244 + ,269907 + ,271296 + ,270157 + ,271322 + ,267179 + ,264101 + ,265518 + ,269419 + ,268714 + ,272482 + ,268351 + ,268175 + ,270674 + ,272764 + ,272599 + ,270333 + ,270846 + ,270491 + ,269160 + ,274027 + ,273784 + ,276663 + ,274525 + ,271344 + ,271115 + ,270798 + ,273911 + ,273985 + ,271917 + ,273338 + ,270601 + ,273547 + ,275363 + ,281229 + ,277793 + ,279913 + ,282500 + ,280041 + ,282166 + ,290304 + ,283519 + ,287816 + ,285226 + ,287595 + ,289741 + ,289148 + ,288301 + ,290155 + ,289648 + ,288225 + ,289351 + ,294735 + ,305333) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '1' > 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,] 0.18954215 0.02934537 -0.07409761 -0.4380209 1.0870738 -0.08823338 [2,] 0.08992975 0.00000000 -0.07867043 -0.3403995 1.0782845 -0.08238130 [3,] 0.00000000 0.00000000 -0.08095644 -0.2518934 1.0728953 -0.07547137 [4,] 0.00000000 0.00000000 -0.09627345 -0.2424442 0.9923736 0.00000000 [5,] 0.00000000 0.00000000 0.00000000 -0.2354317 0.9849051 0.00000000 [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 [13,] NA NA NA NA NA NA [14,] NA NA NA NA NA NA [,7] [1,] -0.9677868 [2,] -0.9396878 [3,] -0.9522534 [4,] -0.9137293 [5,] -0.8738939 [6,] NA [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,] 0.55842 0.79939 0.43271 0.16750 0 0.38172 0 [2,] 0.74274 NA 0.37517 0.19774 0 0.41122 0 [3,] NA NA 0.35546 0.00320 0 0.44666 0 [4,] NA NA 0.25497 0.00360 0 NA 0 [5,] NA NA NA 0.00703 0 NA 0 [6,] NA NA NA NA 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 0.1895 0.0293 -0.0741 -0.4380 1.0871 -0.0882 -0.9678 s.e. 0.3233 0.1153 0.0942 0.3161 0.1017 0.1006 0.0917 sigma^2 estimated as 4392048: log likelihood = -1741.35, aic = 3498.7 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1895 0.0293 -0.0741 -0.4380 1.0871 -0.0882 -0.9678 s.e. 0.3233 0.1153 0.0942 0.3161 0.1017 0.1006 0.0917 sigma^2 estimated as 4392048: log likelihood = -1741.35, aic = 3498.7 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.0899 0 -0.0787 -0.3404 1.0783 -0.0824 -0.9397 s.e. 0.2736 0 0.0885 0.2633 0.1005 0.1000 0.0364 sigma^2 estimated as 4479850: log likelihood = -1741.42, aic = 3496.84 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 -0.0810 -0.2519 1.0729 -0.0755 -0.9523 s.e. 0 0 0.0874 0.0843 0.0990 0.0990 0.0180 sigma^2 estimated as 4447790: log likelihood = -1741.49, aic = 3494.99 [[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 -0.0963 -0.2424 0.9924 0 -0.9137 s.e. 0 0 0.0843 0.0822 0.0140 0 0.0818 sigma^2 estimated as 4527494: log likelihood = -1741.88, aic = 3493.75 [[3]][[6]] NULL [[3]][[7]] NULL $aic [1] 3498.700 3496.844 3494.988 3493.751 3493.036 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 log(s2) : NaNs produced 3: In log(s2) : NaNs produced 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 > postscript(file="/var/www/html/rcomp/tmp/1xc9y1229272217.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 = 192 Frequency = 1 [1] 205.596845 -102.691479 4661.252142 2606.409476 4140.476125 [6] 3369.112213 1349.168721 2039.997534 196.601009 871.864037 [11] 820.701541 826.292952 1468.930403 1088.162361 -159.897558 [16] -1923.045961 407.953044 1386.801801 -80.222675 314.021730 [21] -212.689419 1114.172304 1463.674157 345.984586 -1051.294484 [26] -404.455714 -1070.746742 2180.861638 -580.329329 -1258.951885 [31] 677.309256 1647.064810 -1034.529392 -713.211149 1544.160721 [36] -792.546103 2902.769038 -4287.166646 -53.734154 1427.278294 [41] -150.058708 -816.710361 785.302430 591.717362 -502.392150 [46] 767.961199 -265.202749 326.298636 -2782.378514 -4628.124357 [51] 857.645540 -1483.049812 263.463631 -1694.660001 1771.529000 [56] 431.841121 -1053.522060 5.391337 1272.392948 -1811.072537 [61] 444.022178 -1202.198840 -42.258441 -2301.737309 1294.693784 [66] -2237.292613 -418.372360 -308.982807 -1643.934600 377.685825 [71] -1132.934742 -474.808020 -35.152774 -1997.376189 -1219.019171 [76] 4211.867638 -495.806219 -1355.685889 932.534466 -973.528948 [81] 913.232084 1053.381539 1674.949382 -2296.789652 -992.881092 [86] -893.490726 1546.557898 -1107.284599 3569.119586 82.592809 [91] -1754.656375 -1020.576595 -501.501989 -94.975902 1725.265079 [96] -270.528257 2992.320066 -4400.622848 414.692388 -157.535733 [101] 791.900218 -168.102331 331.268901 -609.089742 -105.910275 [106] 1785.290019 973.107756 -482.144678 -12.552850 -1401.944386 [111] 798.469980 -1507.001459 2418.179117 -1906.463169 -963.979052 [116] -1165.794321 -2342.849806 -683.033212 1352.694170 384.980755 [121] 881.639282 2337.826612 1816.937473 1398.527122 -3631.388139 [126] -3243.761264 1109.571905 -1430.320007 5917.002253 -166.136516 [131] -2578.624532 -1773.859902 -228.693150 -1498.589558 3157.341089 [136] 862.690145 -871.103594 -3127.900132 2723.108564 -1090.299608 [141] 1167.223364 -1398.392797 -471.781061 -3044.226418 -4501.166665 [146] 2837.718153 1407.507628 -1182.674769 1899.468424 -2477.769546 [151] -2099.055170 1972.880429 2462.795370 -390.211562 -3246.702842 [156] 1237.294516 -313.507859 417.971522 2182.011716 -132.754088 [161] 821.987778 -405.036704 -4393.872227 -1602.556024 -788.183873 [166] 1888.181956 -334.953421 -1046.762514 1268.968018 -432.718943 [171] -345.710364 1534.715907 4002.477471 -1064.074711 1307.430703 [176] 2919.976059 -1912.993809 961.419665 7811.124331 -3893.698596 [181] 3212.650371 1005.712578 -979.351022 1846.680795 -2640.909551 [186] 16.688154 1205.672690 -1027.392225 -1363.520686 -42.790988 [191] 3875.851761 13057.273830 > postscript(file="/var/www/html/rcomp/tmp/26fa11229272217.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/397io1229272217.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/4pegj1229272217.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/544h81229272217.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/6f32e1229272217.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/7l75p1229272217.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/8gutb1229272217.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/9jjrz1229272218.tab") > > system("convert tmp/1xc9y1229272217.ps tmp/1xc9y1229272217.png") > system("convert tmp/26fa11229272217.ps tmp/26fa11229272217.png") > system("convert tmp/397io1229272217.ps tmp/397io1229272217.png") > system("convert tmp/4pegj1229272217.ps tmp/4pegj1229272217.png") > system("convert tmp/544h81229272217.ps tmp/544h81229272217.png") > system("convert tmp/6f32e1229272217.ps tmp/6f32e1229272217.png") > system("convert tmp/7l75p1229272217.ps tmp/7l75p1229272217.png") > > > proc.time() user system elapsed 12.371 2.376 14.055