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Type 'q()' to quit R. > x <- c(10.81,9.12,11.03,12.74,9.98,11.62,9.40,9.27,7.76,8.78,10.65,10.95,12.36,10.85,11.84,12.14,11.65,8.86,7.63,7.38,7.25,8.03,7.75,7.16,7.18,7.51,7.07,7.11,8.98,9.53,10.54,11.31,10.36,11.44,10.45,10.69,11.28,11.96,13.52,12.89,14.03,16.27,16.17,17.25,19.38,26.20,33.53,32.20,38.45,44.86,41.67,36.06,39.76,36.81,42.65,46.89,53.61,57.59,67.82,71.89,75.51,68.49,62.72,70.39,59.77,57.27,67.96,67.85,76.98,81.08,91.66,84.84,85.73,84.61,92.91,99.80,121.19,122.04,131.76,138.48,153.47,189.95,182.22,198.08,135.36,125.02,143.50,173.95,188.75,167.44,158.95,169.53,113.66,107.59,92.67,85.35,90.13,89.31,105.12,125.83,135.81,142.43,163.39,168.21,185.35,188.50,199.91,210.73,192.06,204.62,235.00,261.09,256.88,251.53,257.25,243.10,283.75) > 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,] 0.26344642 0.09110153 -0.11773129 -0.1762629 0.74895686 0.02582116 [2,] 0.25859542 0.08973175 -0.11469325 -0.1691786 0.85310231 0.00000000 [3,] 0.09123486 0.10264442 -0.09464944 0.0000000 0.84639822 0.00000000 [4,] 0.00000000 0.11493291 -0.08582472 0.0000000 0.82618611 0.00000000 [5,] 0.00000000 0.10493052 0.00000000 0.0000000 0.79143589 0.00000000 [6,] 0.00000000 0.00000000 0.00000000 0.0000000 0.82709425 0.00000000 [7,] 0.00000000 0.00000000 0.00000000 0.0000000 0.03969347 0.00000000 [8,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 [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,] -0.7208132 [2,] -0.8136565 [3,] -0.8094338 [4,] -0.7779164 [5,] -0.7335542 [6,] -0.7805199 [7,] 0.0000000 [8,] 0.0000000 [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.55519 0.40213 0.25509 0.69132 0.32857 0.83602 0.34891 [2,] 0.56512 0.40750 0.26127 0.70429 0.13161 NA 0.18639 [3,] 0.35334 0.29790 0.33280 NA 0.17951 NA 0.23300 [4,] NA 0.24061 0.38046 NA 0.11279 NA 0.17054 [5,] NA 0.28322 NA NA 0.12676 NA 0.19325 [6,] NA NA NA NA 0.12552 NA 0.18356 [7,] NA NA NA NA 0.68906 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 0.2634 0.0911 -0.1177 -0.1763 0.7490 0.0258 -0.7208 s.e. 0.4451 0.1083 0.1029 0.4427 0.7632 0.1245 0.7662 sigma^2 estimated as 161.0: log likelihood = -459.43, aic = 934.87 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2634 0.0911 -0.1177 -0.1763 0.7490 0.0258 -0.7208 s.e. 0.4451 0.1083 0.1029 0.4427 0.7632 0.1245 0.7662 sigma^2 estimated as 161.0: log likelihood = -459.43, aic = 934.87 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2586 0.0897 -0.1147 -0.1692 0.8531 0 -0.8137 s.e. 0.4482 0.1079 0.1016 0.4446 0.5616 0 0.6119 sigma^2 estimated as 161.0: log likelihood = -459.45, aic = 932.9 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.0912 0.1026 -0.0946 0 0.8464 0 -0.8094 s.e. 0.0979 0.0981 0.0973 0 0.6266 0 0.6750 sigma^2 estimated as 161.3: log likelihood = -459.52, aic = 931.04 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1149 -0.0858 0 0.8262 0 -0.7779 s.e. 0 0.0974 0.0975 0 0.5169 0 0.5640 sigma^2 estimated as 162.4: log likelihood = -459.95, aic = 929.91 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1049 0 0 0.7914 0 -0.7336 s.e. 0 0.0973 0 0 0.5145 0 0.5605 sigma^2 estimated as 163.5: log likelihood = -460.34, aic = 928.68 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 0 0.8271 0 -0.7805 s.e. 0 0 0 0 0.5359 0 0.5834 sigma^2 estimated as 165.2: log likelihood = -460.92, aic = 927.84 [[3]][[8]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 0 0.0397 0 0 s.e. 0 0 0 0 0.0990 0 0 sigma^2 estimated as 166: log likelihood = -461.1, aic = 926.19 $aic [1] 934.8656 932.9045 931.0401 929.9065 928.6788 927.8371 926.1932 924.3540 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 max(i) : no non-missing arguments to max; returning -Inf 8: In max(i) : no non-missing arguments to max; returning -Inf 9: In max(try.data.frame[, 4], na.rm = TRUE) : no non-missing arguments to max; returning -Inf > postscript(file="/var/www/html/rcomp/tmp/1h6vh1292946811.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 = 117 Frequency = 1 [1] 0.01080999 -1.68866812 1.90849474 1.70865235 -2.75782485 [6] 1.63870752 -2.21825043 -0.12989755 -1.50880997 1.01919614 [11] 1.86852626 0.29976357 1.40888836 -1.44291803 0.91418546 [16] 0.23212416 -0.38044601 -2.85509730 -1.14188049 -0.24483985 [21] -0.07006285 0.73951266 -0.35422680 -0.60190804 -0.03596780 [26] 0.38993715 -0.47929654 0.02809196 1.88944980 0.66074479 [31] 1.05882297 0.77992337 -0.94483985 1.04903909 -0.97888583 [36] 0.26341915 0.58920613 0.66690115 1.57746513 -0.63158774 [41] 1.06577320 2.21816859 -0.14009041 1.04943602 2.16770880 [46] 6.77713105 7.36929654 -1.33952643 6.22658085 6.38300844 [51] -3.25192182 -5.58499311 3.65474944 -3.03891338 5.84396935 [56] 4.19713105 6.63545290 3.70929050 9.93904683 4.12279232 [61] 3.37191578 -7.27443517 -5.64337782 7.89268039 -10.76686586 [66] -2.38290425 10.45819011 -0.27830033 8.86325985 3.94201997 [71] 10.17393575 -6.98155244 0.74630962 -0.84135181 8.52903135 [76] 6.58555105 21.81154470 0.94923369 9.29567676 6.72436628 [81] 14.62759858 36.31725675 -8.14995696 16.13070950 -62.75532719 [86] -10.29554331 18.15054416 30.17651196 13.95095658 -21.34373945 [91] -8.87582057 10.31325985 -56.46500519 -7.51801796 -14.61316944 [96] -7.94953851 7.26957473 -0.40956947 15.07646459 19.50133369 [101] 9.39253657 7.46586795 21.29699760 4.40004304 19.35767443 [106] 3.39093939 12.00222664 11.11055623 -18.85973481 12.59254865 [111] 29.75244616 25.26794814 -4.60614088 -5.61277080 4.88802477 [116] -14.34132255 39.96965384 > postscript(file="/var/www/html/rcomp/tmp/2h6vh1292946811.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/www/html/rcomp/tmp/3h6vh1292946811.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/www/html/rcomp/tmp/4h6vh1292946811.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/www/html/rcomp/tmp/5axc21292946811.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/www/html/rcomp/tmp/6axc21292946811.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/www/html/rcomp/tmp/7axc21292946811.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/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/8tazz1292946811.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/9mjy21292946811.tab") > try(system("convert tmp/1h6vh1292946811.ps tmp/1h6vh1292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/2h6vh1292946811.ps tmp/2h6vh1292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/3h6vh1292946811.ps tmp/3h6vh1292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/4h6vh1292946811.ps tmp/4h6vh1292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/5axc21292946811.ps tmp/5axc21292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/6axc21292946811.ps tmp/6axc21292946811.png",intern=TRUE)) character(0) > try(system("convert tmp/7axc21292946811.ps tmp/7axc21292946811.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 8.517 2.207 20.965