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(6827,6178,7084,8162,8462,9644,10466,10748,9963,8194,6848,7027,7269,6775,7819,8371,9069,10248,11030,10882,10333,9109,7685,7602,8350,7829,8829,9948,10638,11253,11424,11391,10665,9396,7775,7933,8186,7444,8484,9864,10252,12282,11637,11577,12417,9637,8094,9280,8334,7899,9994,10078,10801,12950,12222,12246,13281,10366,8730,9614,8639,8772,10894,10455,11179,10588,10794,12770,13812,10857,9290,10925,9491,8919,11607,8852,12537,14759,13667,13731,15110,12185,10645,12161,10840,10436,13589,13402,13103,14933,14147,14057,16234,12389,11595,12772) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '0.3' > 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,] 0.2981467 0.0004849588 0.2375307 -0.9659329 -0.4127908 -0.1314554 [2,] 0.2982452 0.0000000000 0.2375663 -0.9658138 -0.4120300 -0.1311219 [3,] 0.2975663 0.0000000000 0.2371004 -0.9662178 -0.2203461 0.0000000 [4,] 0.3181727 0.0000000000 0.2257648 -0.9805149 0.0000000 0.0000000 [5,] 0.2550481 0.0000000000 0.0000000 -0.8942188 0.0000000 0.0000000 [6,] 0.0000000 0.0000000000 0.0000000 -0.7645620 0.0000000 0.0000000 [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,] -0.2222458 [2,] -0.2229836 [3,] -0.4121813 [4,] -0.5688864 [5,] -0.5319267 [6,] -0.5654026 [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,] 0.05453 0.99714 0.09306 0 0.49813 0.71921 0.71464 [2,] 0.05222 NA 0.09001 0 0.48460 0.71467 0.70566 [3,] 0.04992 NA 0.08834 0 0.28179 NA 0.03495 [4,] 0.01851 NA 0.07934 0 NA NA 0.00000 [5,] 0.07589 NA NA 0 NA NA 0.00000 [6,] NA NA NA 0 NA NA 0.00000 [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 0.2981 0.0005 0.2375 -0.9659 -0.4128 -0.1315 -0.2222 s.e. 0.1530 0.1348 0.1399 0.1348 0.6068 0.3645 0.6059 sigma^2 estimated as 0.1001: log likelihood = -25.99, aic = 67.99 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2981 0.0005 0.2375 -0.9659 -0.4128 -0.1315 -0.2222 s.e. 0.1530 0.1348 0.1399 0.1348 0.6068 0.3645 0.6059 sigma^2 estimated as 0.1001: log likelihood = -25.99, aic = 67.99 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2982 0 0.2376 -0.9658 -0.4120 -0.1311 -0.2230 s.e. 0.1516 0 0.1386 0.1171 0.5871 0.3575 0.5885 sigma^2 estimated as 0.1001: log likelihood = -25.99, aic = 65.99 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2976 0 0.2371 -0.9662 -0.2203 0 -0.4122 s.e. 0.1497 0 0.1376 0.1163 0.2035 0 0.1925 sigma^2 estimated as 0.1003: log likelihood = -26.06, aic = 64.12 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.3182 0 0.2258 -0.9805 0 0 -0.5689 s.e. 0.1327 0 0.1272 0.1379 0 0 0.1063 sigma^2 estimated as 0.1011: log likelihood = -26.58, aic = 63.17 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2550 0 0 -0.8942 0 0 -0.5319 s.e. 0.1421 0 0 0.0839 0 0 0.1003 sigma^2 estimated as 0.108: log likelihood = -28.15, aic = 64.3 [[3]][[7]] NULL $aic [1] 67.98905 65.98907 64.12238 63.16526 64.30013 65.22773 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/1jvdo1323187407.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 = 96 Frequency = 1 [1] 0.0081603392 0.0033261930 0.0026633326 0.0025322865 0.0021669249 [6] 0.0023577133 0.0023815977 0.0022035091 0.0016132475 0.0005938126 [11] -0.0002079595 -0.0087064700 -0.0508624942 0.0855762493 0.0691405797 [16] -0.2172615721 0.0662557288 -0.0138414192 -0.0340199312 -0.1898379650 [21] -0.0214604537 0.2240861250 0.1408039025 -0.0199420047 0.2554654715 [26] 0.2073943880 0.1030834768 0.2180363343 0.1975391868 -0.1370304990 [31] -0.3276450434 -0.2436455921 -0.2318104747 -0.0841064098 -0.1870697106 [36] -0.0753787190 -0.2433421049 -0.2710995677 -0.2036681483 0.0169546355 [41] -0.1519443333 0.3480367788 -0.2940309195 -0.1627793079 0.5166755632 [46] -0.2771686991 -0.0850359985 0.4846744714 -0.4179465569 -0.0652463031 [51] 0.4117193775 -0.3114314034 -0.0492399985 0.1907877819 -0.1765096353 [56] -0.0638763965 0.3456922943 -0.0940677993 -0.0044505141 0.1166813982 [61] -0.3022848821 0.2017914542 0.2945606534 -0.3215969183 -0.1128548878 [66] -1.1454238446 -0.5211195974 0.3132133020 0.2735467933 0.0528680693 [71] 0.1468922432 0.5050403602 -0.0251406223 -0.0842508679 0.3127539456 [76] -1.1856394852 0.6672182338 0.8109912728 0.2082989619 -0.0865027083 [81] 0.2284668636 0.1717917911 0.2563379332 0.2944490432 0.1418361391 [86] 0.1720235621 0.3973630486 0.7814974541 -0.4924749569 -0.0310743993 [91] -0.1425044603 -0.3607326514 0.1220396329 -0.2826083484 0.2155518607 [96] -0.0286197005 > postscript(file="/var/wessaorg/rcomp/tmp/27sey1323187407.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/3uwye1323187407.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/4ce0n1323187407.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/581on1323187407.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/6m4ym1323187407.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/75rz01323187407.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/8cvww1323187407.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/9q9ly1323187407.tab") > > try(system("convert tmp/1jvdo1323187407.ps tmp/1jvdo1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/27sey1323187407.ps tmp/27sey1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/3uwye1323187407.ps tmp/3uwye1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/4ce0n1323187407.ps tmp/4ce0n1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/581on1323187407.ps tmp/581on1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/6m4ym1323187407.ps tmp/6m4ym1323187407.png",intern=TRUE)) character(0) > try(system("convert tmp/75rz01323187407.ps tmp/75rz01323187407.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 9.650 1.156 10.886