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Type 'q()' to quit R. > x <- c(128.7,136.9,156.9,109.1,122.3,123.9,90.9,77.9,120.3,118.9,125.5,98.9,102.9,105.9,117.6,113.6,115.9,118.9,77.6,81.2,123.1,136.6,112.1,95.1,96.3,105.7,115.8,105.7,105.7,111.1,82.4,60,107.3,99.3,113.5,108.9,100.2,103.9,138.7,120.2,100.2,143.2,70.9,85.2,133,136.6,117.9,106.3,122.3,125.5,148.4,126.3,99.6,140.4,80.3,92.6,138.5,110.9,119.6,105,109,129.4,148.6,101.4,134.8,143.7,81.6,90.3,141.5,140.7,140.2,100.2,125.7,119.6,134.7,109,116.3,146.9,97.4,89.4,132.1,139.8,129,112.5,121.9,121.7,123.1,131.6,119.3,132.5,98.3,85.1,131.7,129.3,90.7,78.6,68.9,79.1,83.5,74.1,59.7,93.3,61.3,56.6,98.5) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '0.5' > 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] [,7] [1,] 0.1977983 0.2885035 0.1853687 -0.8515980 0.06433729 0.10049079 -0.9999994 [2,] 0.0000000 0.1598879 0.1341520 -0.6545457 0.06517707 0.10252395 -1.0000080 [3,] 0.0000000 0.1648610 0.1410693 -0.6541622 0.00000000 0.08485375 -1.0002397 [4,] 0.0000000 0.1535191 0.1250545 -0.6383070 0.00000000 0.00000000 -1.0000916 [5,] 0.0000000 0.1244437 0.0000000 -0.6023852 0.00000000 0.00000000 -1.0001292 [6,] 0.0000000 0.0000000 0.0000000 -0.5588058 0.00000000 0.00000000 -0.9981497 [7,] 0.0000000 0.0000000 0.0000000 -0.6339159 0.00000000 0.00000000 0.0000000 [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 [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.68527 0.39279 0.30306 0.07498 0.64037 0.47252 0.00005 [2,] NA 0.20222 0.25086 0.00000 0.63864 0.46382 0.00007 [3,] NA 0.18485 0.22021 0.00000 NA 0.52056 0.00671 [4,] NA 0.21026 0.26501 0.00000 NA NA 0.08256 [5,] NA 0.30243 NA 0.00000 NA NA 0.03594 [6,] NA NA NA 0.00000 NA NA 0.15899 [7,] NA NA NA 0.00000 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 0.1978 0.2885 0.1854 -0.8516 0.0643 0.1005 -1.0000 s.e. 0.4866 0.3361 0.1790 0.4731 0.1373 0.1393 0.2368 sigma^2 estimated as 0.307: log likelihood = -87.86, aic = 191.71 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1978 0.2885 0.1854 -0.8516 0.0643 0.1005 -1.0000 s.e. 0.4866 0.3361 0.1790 0.4731 0.1373 0.1393 0.2368 sigma^2 estimated as 0.307: log likelihood = -87.86, aic = 191.71 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1599 0.1342 -0.6545 0.0652 0.1025 -1.0000 s.e. 0 0.1245 0.1161 0.1067 0.1384 0.1394 0.2418 sigma^2 estimated as 0.3077: log likelihood = -87.88, aic = 189.76 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1649 0.1411 -0.6542 0 0.0849 -1.0002 s.e. 0 0.1235 0.1143 0.1069 0 0.1316 0.3612 sigma^2 estimated as 0.3025: log likelihood = -88, aic = 187.99 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1535 0.1251 -0.6383 0 0 -1.0001 s.e. 0 0.1217 0.1116 0.1040 0 0 0.5703 sigma^2 estimated as 0.2992: log likelihood = -88.21, aic = 186.41 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1244 0 -0.6024 0 0 -1.0001 s.e. 0 0.1201 0 0.0928 0 0 0.4704 sigma^2 estimated as 0.3034: log likelihood = -88.83, aic = 185.67 [[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 -0.5588 0 0 -0.9981 s.e. 0 0 0 0.0790 0 0 0.7035 sigma^2 estimated as 0.3078: log likelihood = -89.39, aic = 184.79 $aic [1] 191.7147 189.7627 187.9905 186.4108 185.6674 184.7852 210.5055 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 > postscript(file="/var/www/html/rcomp/tmp/1z4qe1259843264.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 = 105 Frequency = 1 [1] 0.0065498063 0.0032047833 0.0027957355 0.0002486565 0.0007535965 [6] 0.0006933563 -0.0008928665 -0.0014458862 0.0007414606 0.0006062339 [11] 0.0008362757 -0.0067867285 -0.0421705074 -0.1292583279 -0.2465492510 [16] 1.1953350532 0.3013918646 0.2145873226 -0.2327215449 0.5140427558 [21] 0.2460805806 0.6021761893 -0.6532684744 -0.0663719774 -0.1707784977 [26] 0.0883268107 -0.1222512513 0.4650743632 -0.0354725052 0.1060790869 [31] 0.3722424486 -0.6733712868 0.0320294303 -0.5197861809 0.5998126098 [36] 1.0124230601 0.0766761574 -0.0795570399 0.7889513317 0.5271059438 [41] -0.7404990668 1.1465025072 -0.9440273468 0.7056903331 0.4139659514 [46] 0.3267277177 -0.5038557676 -0.0886109619 0.6138682949 0.2045170770 [51] 0.2191359711 0.0742266617 -1.0328646743 0.5531087240 -0.3289804097 [56] 0.6386241705 0.2319920025 -1.0433123727 -0.0093496928 0.0177845696 [61] 0.0271751997 0.6295779102 0.2861920718 -0.9542528939 1.1469103306 [66] 0.2004188368 -0.4694498779 0.2333107086 0.2541349629 0.2844374161 [71] 0.2377560941 -0.8912531834 0.4302638547 -0.3608306817 -0.3887789171 [76] -0.2740975448 0.1578812865 0.6045288139 0.4979682532 -0.1214195581 [81] -0.2916919408 0.2945910867 -0.1809524921 0.0336060260 0.0992505172 [86] -0.2146966203 -0.8499649687 0.9197903674 -0.0530495350 -0.2824211307 [91] 0.5940182125 -0.2723110189 -0.1468022095 -0.0932901217 -1.6448434635 [96] -0.7151913081 -1.2654202793 -0.3726295748 -0.6814884113 -0.0059948501 [101] -0.8168773340 0.5891012090 0.7718570796 0.2603553727 0.2920773114 > postscript(file="/var/www/html/rcomp/tmp/2huv31259843264.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/34xuw1259843264.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/4xbh51259843264.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/5bs121259843264.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/6c10d1259843264.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/7jy4b1259843264.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/8b5lt1259843264.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/9t9w01259843264.tab") > system("convert tmp/1z4qe1259843264.ps tmp/1z4qe1259843264.png") > system("convert tmp/2huv31259843264.ps tmp/2huv31259843264.png") > system("convert tmp/34xuw1259843264.ps tmp/34xuw1259843264.png") > system("convert tmp/4xbh51259843264.ps tmp/4xbh51259843264.png") > system("convert tmp/5bs121259843264.ps tmp/5bs121259843264.png") > system("convert tmp/6c10d1259843264.ps tmp/6c10d1259843264.png") > system("convert tmp/7jy4b1259843264.ps tmp/7jy4b1259843264.png") > > > proc.time() user system elapsed 11.270 1.915 12.601