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Type 'q()' to quit R. > x <- c(100 + ,108.1560276 + ,114.0150276 + ,102.1880309 + ,110.3672031 + ,96.8602511 + ,94.1944583 + ,99.51621961 + ,94.06333487 + ,97.5541476 + ,78.15062422 + ,81.2434643 + ,92.36262465 + ,96.06324371 + ,114.0523777 + ,110.6616666 + ,104.9171949 + ,90.00187193 + ,95.7008067 + ,86.02741157 + ,84.85287668 + ,100.04328 + ,80.91713823 + ,74.06539709 + ,77.30281369 + ,97.23043249 + ,90.75515676 + ,100.5614455 + ,92.01293267 + ,99.24012138 + ,105.8672755 + ,90.9920463 + ,93.30624423 + ,91.17419413 + ,77.33295039 + ,91.1277721 + ,85.01249943 + ,83.90390242 + ,104.8626302 + ,110.9039108 + ,95.43714373 + ,111.6238727 + ,108.8925403 + ,96.17511682 + ,101.9740205 + ,99.11953031 + ,86.78158147 + ,118.4195003 + ,118.7441447 + ,106.5296192 + ,134.7772694 + ,104.6778714 + ,105.2954304 + ,139.4139849 + ,103.6060491 + ,99.78182974 + ,103.4610301 + ,120.0594945 + ,96.71377168 + ,107.1308929 + ,105.3608372 + ,111.6942359 + ,132.0519998 + ,126.8037879 + ,154.4824253 + ,141.5570984 + ,109.9506882 + ,127.904198 + ,133.0888617 + ,120.0796299 + ,117.5557142 + ,143.0362309 + ,159.982927 + ,128.5991124 + ,149.7373327 + ,126.8169313 + ,140.9639674 + ,137.6691981 + ,117.9402337 + ,122.3095247 + ,127.7804207 + ,136.1677176 + ,116.2405856 + ,123.1576893 + ,116.3400234 + ,108.6119282 + ,125.8982264 + ,112.8003105 + ,107.5182447 + ,135.0955413 + ,115.5096488 + ,115.8640759 + ,104.5883906 + ,163.7213386 + ,113.4482275 + ,98.0428844 + ,116.7868521 + ,126.5330444 + ,113.0336597 + ,124.3392163 + ,109.8298759 + ,124.4434777 + ,111.5039454 + ,102.0350019 + ,116.8726598 + ,112.2073122 + ,101.1513902 + ,124.4255108) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '0.0' > 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,] 0.1565496 -0.08953042 0.2033049 -0.8037358 0.1526378 -0.03697698 [2,] 0.1445591 -0.09385071 0.2031284 -0.7980812 0.1569475 0.00000000 [3,] 0.1995485 0.00000000 0.2374348 -0.8568060 0.1508865 0.00000000 [4,] 0.1757303 0.00000000 0.2380270 -0.8382487 0.0000000 0.00000000 [5,] 0.0000000 0.00000000 0.1737802 -1.3304828 0.0000000 0.00000000 [6,] 0.0000000 0.00000000 0.0000000 -1.3971385 0.0000000 0.00000000 [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,] -0.9999693 [2,] -1.0000412 [3,] -1.0000147 [4,] -0.8360010 [5,] -1.2106789 [6,] -1.1770825 [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,] 0.40504 0.52428 0.14441 0 0.19633 0.78568 0.00046 [2,] 0.43354 0.50570 0.14776 0 0.18258 NA 0.00008 [3,] 0.18494 NA 0.06672 0 0.19953 NA 0.00003 [4,] 0.24172 NA 0.06397 0 NA NA 0.00002 [5,] NA NA 0.11552 0 NA NA 0.00001 [6,] NA NA NA 0 NA NA 0.00005 [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 0.1565 -0.0895 0.2033 -0.8037 0.1526 -0.0370 -1.0000 s.e. 0.1872 0.1401 0.1382 0.1458 0.1173 0.1356 0.2762 sigma^2 estimated as 0.01006: log likelihood = 71.31, aic = -126.61 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1565 -0.0895 0.2033 -0.8037 0.1526 -0.0370 -1.0000 s.e. 0.1872 0.1401 0.1382 0.1458 0.1173 0.1356 0.2762 sigma^2 estimated as 0.01006: log likelihood = 71.31, aic = -126.61 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1446 -0.0939 0.2031 -0.7981 0.1569 0 -1.0000 s.e. 0.1838 0.1405 0.1393 0.1464 0.1169 0 0.2442 sigma^2 estimated as 0.01016: log likelihood = 71.27, aic = -128.54 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1995 0 0.2374 -0.8568 0.1509 0 -1.0000 s.e. 0.1495 0 0.1281 0.0907 0.1169 0 0.2293 sigma^2 estimated as 0.01018: log likelihood = 71.04, aic = -130.08 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1757 0 0.2380 -0.8382 0 0 -0.8360 s.e. 0.1492 0 0.1271 0.0910 0 0 0.1848 sigma^2 estimated as 0.01141: log likelihood = 70.28, aic = -130.57 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0.1738 -1.3305 0 0 -1.2107 s.e. 0 0 0.1095 0.1385 0 0 0.2557 sigma^2 estimated as 0.004492: log likelihood = 69.58, aic = -131.17 [[3]][[7]] NULL $aic [1] -126.6102 -128.5368 -130.0812 -130.5667 -131.1651 -130.5918 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/www/html/rcomp/tmp/1dz9d1259858682.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 = 108 Frequency = 1 [1] 2.658793e-03 1.249781e-03 8.627610e-04 5.464790e-04 5.055868e-04 [6] 3.005909e-04 2.314297e-04 2.540043e-04 1.723842e-04 1.897612e-04 [11] -3.943515e-05 -2.634135e-03 -1.625461e-02 -1.482983e-02 4.297891e-02 [16] 6.760993e-02 -9.130624e-03 -2.731490e-02 1.543143e-02 -5.508365e-02 [21] -1.818575e-02 3.912028e-02 4.560970e-02 -2.571149e-02 -8.222487e-02 [26] 3.446710e-02 -6.494806e-02 5.478809e-02 -2.987146e-02 1.144860e-01 [31] 9.501827e-02 1.288978e-02 2.173387e-02 -5.857867e-02 -1.784647e-03 [36] 9.755094e-02 -1.135501e-02 -8.830444e-02 1.792049e-02 6.616468e-02 [41] -9.920741e-03 1.036072e-01 3.692643e-02 9.653544e-03 2.690290e-02 [46] -2.506036e-02 2.465422e-02 1.688768e-01 1.123385e-01 -3.611619e-02 [51] 2.801710e-02 -1.314123e-01 -3.994108e-02 1.246556e-01 -6.649141e-02 [56] -2.806852e-02 -3.259325e-02 7.604146e-02 2.994552e-02 1.229998e-02 [61] -2.968407e-02 -4.796040e-03 1.968736e-02 2.730475e-02 1.639721e-01 [66] 2.713939e-02 -9.868373e-02 3.674758e-02 5.955034e-02 -3.463541e-02 [71] 5.111978e-02 8.702477e-02 1.391236e-01 -7.118700e-02 -5.395509e-02 [76] -1.208294e-01 -3.990434e-03 -3.840572e-02 -4.981240e-02 -1.022393e-02 [81] 1.325169e-02 3.868595e-02 1.822814e-02 -3.272878e-02 -8.572387e-02 [86] -9.836927e-02 -6.237888e-02 -5.896304e-02 -8.495152e-02 6.284601e-02 [91] 2.322888e-02 3.522846e-02 -7.327604e-02 2.042142e-01 2.025100e-02 [96] -1.314772e-01 -4.606603e-02 5.147610e-02 -9.094391e-02 2.351609e-02 [101] -7.808586e-02 8.138696e-03 -6.437489e-03 -3.883453e-02 4.774378e-02 [106] -6.020138e-02 1.880288e-02 8.711641e-02 > postscript(file="/var/www/html/rcomp/tmp/29qxy1259858682.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/37m091259858682.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/4eeol1259858682.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/5yyg61259858682.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/6t8jg1259858682.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/7sfy11259858682.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/85oc51259858682.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/9w3q91259858682.tab") > > system("convert tmp/1dz9d1259858682.ps tmp/1dz9d1259858682.png") > system("convert tmp/29qxy1259858682.ps tmp/29qxy1259858682.png") > system("convert tmp/37m091259858682.ps tmp/37m091259858682.png") > system("convert tmp/4eeol1259858682.ps tmp/4eeol1259858682.png") > system("convert tmp/5yyg61259858682.ps tmp/5yyg61259858682.png") > system("convert tmp/6t8jg1259858682.ps tmp/6t8jg1259858682.png") > system("convert tmp/7sfy11259858682.ps tmp/7sfy11259858682.png") > > > proc.time() user system elapsed 8.705 1.739 10.693