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Type 'q()' to quit R. > x <- c(921365,987921,1132614,1332224,1418133,1411549,1695920,1636173,1539653,1395314,1127575,1036076,989236,1008380,1207763,1368839,1469798,1498721,1761769,1653214,1599104,1421179,1163995,1037735,1015407,1039210,1258049,1469445,1552346,1549144,1785895,1662335,1629440,1467430,1202209,1076982,1039367,1063449,1335135,1491602,1591972,1641248,1898849,1798580,1762444,1622044,1368955,1262973,1195650,1269530,1479279,1607819,1712466,1721766,1949843,1821326,1757802,1590367,1260647,1149235,1016367,1027885,1262159,1520854,1544144,1564709,1821776,1741365,1623386,1498658,1241822,1136029) > 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] [1,] 0.4852665 0.1181742 0.1100183 -0.70222470 0.0005897642 0.07875202 [2,] 0.4856584 0.1182871 0.1099432 -0.70262215 0.0000000000 0.07861834 [3,] 0.4729357 0.1071155 0.1172631 -0.68477811 0.0000000000 0.00000000 [4,] 0.2671459 0.0000000 0.1248822 -0.46048057 0.0000000000 0.00000000 [5,] 0.0000000 0.0000000 0.0713206 -0.21420784 0.0000000000 0.00000000 [6,] 0.0000000 0.0000000 0.0000000 -0.20269059 0.0000000000 0.00000000 [7,] 0.0000000 0.0000000 0.0000000 -0.08756788 0.0000000000 0.00000000 [8,] 0.0000000 0.0000000 0.0000000 0.00000000 0.0000000000 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,] -0.9993266 [2,] -0.9994420 [3,] -0.9969488 [4,] -1.0004125 [5,] -0.9993339 [6,] -1.0001529 [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,] 0.17265 0.49143 0.43070 0.03985 0.99815 0.73903 0.15083 [2,] 0.17074 0.47602 0.42886 0.03598 NA 0.69932 0.15309 [3,] 0.18473 0.50990 0.39526 0.04172 NA NA 0.25479 [4,] 0.78585 NA 0.59726 0.60769 NA NA 0.42867 [5,] NA NA 0.60483 0.09280 NA NA 0.22925 [6,] NA NA NA 0.09970 NA NA 0.12233 [7,] NA NA NA 0.50350 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 0.4853 0.1182 0.1100 -0.7022 0.0006 0.0788 -0.9993 s.e. 0.3519 0.1708 0.1387 0.3347 0.2534 0.2354 0.6873 sigma^2 estimated as 172.9: log likelihood = -245.79, aic = 507.57 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.4853 0.1182 0.1100 -0.7022 0.0006 0.0788 -0.9993 s.e. 0.3519 0.1708 0.1387 0.3347 0.2534 0.2354 0.6873 sigma^2 estimated as 172.9: log likelihood = -245.79, aic = 507.57 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.4857 0.1183 0.1099 -0.7026 0 0.0786 -0.9994 s.e. 0.3506 0.1650 0.1381 0.3281 0 0.2027 0.6914 sigma^2 estimated as 172.9: log likelihood = -245.79, aic = 505.57 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.4729 0.1071 0.1173 -0.6848 0 0 -0.9969 s.e. 0.3528 0.1617 0.1370 0.3297 0 0 0.8678 sigma^2 estimated as 170.4: log likelihood = -245.86, aic = 503.73 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.2671 0 0.1249 -0.4605 0 0 -1.0004 s.e. 0.9793 0 0.2352 0.8927 0 0 1.2563 sigma^2 estimated as 170.8: log likelihood = -246.07, aic = 502.14 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0.0713 -0.2142 0 0 -0.9993 s.e. 0 0 0.1372 0.1257 0 0 0.8237 sigma^2 estimated as 171.3: log likelihood = -246.12, aic = 500.24 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 -0.2027 0 0 -1.0002 s.e. 0 0 0 0.1215 0 0 0.6394 sigma^2 estimated as 172: log likelihood = -246.25, aic = 498.51 [[3]][[8]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 -0.0876 0 0 0 s.e. 0 0 0 0.1302 0 0 0 sigma^2 estimated as 318.6: log likelihood = -253.76, aic = 511.52 $aic [1] 507.5747 505.5747 503.7260 502.1370 500.2373 498.5070 511.5194 509.9505 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/1zo371292417045.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 = 72 Frequency = 1 [1] 0.55418550 0.27422547 0.23893795 0.25744560 0.23850679 [6] 0.19590351 0.27406518 0.21792149 0.15739763 0.08493126 [11] -0.03685975 -0.75265685 -3.77853555 -24.39470755 22.37150877 [16] -17.02649764 4.25354142 15.01044403 -9.78036831 -19.25406447 [21] 15.39934062 -11.48278220 5.10910891 -15.75065653 10.87675974 [26] 3.11708013 7.68283834 20.26038060 -6.87905486 -13.75838106 [31] -12.57095693 -6.61615839 7.81698645 7.98928255 -0.97660562 [36] 1.43220587 -7.13978050 -0.62452618 21.97775973 -22.82311436 [41] 4.69845179 21.07536795 6.99311819 10.79466645 0.22500873 [46] 11.16385203 12.32852099 13.55227822 -10.89222177 20.57945743 [51] -32.91976194 -16.97199662 -1.29412590 -15.94304169 -14.06440685 [56] -11.15844232 -11.18021576 -11.72694314 -35.76765764 -7.69089782 [61] -34.18407912 -30.57347914 17.41268748 59.55349975 -25.99242661 [66] 2.42270691 14.85371369 17.97945239 -20.16795534 13.03287333 [71] 29.62721801 4.83191878 > postscript(file="/var/www/html/rcomp/tmp/2rg3a1292417045.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/3rg3a1292417045.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/4rg3a1292417045.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/5rg3a1292417045.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/6k7kd1292417045.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/7k7kd1292417045.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/8gyil1292417045.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/9r8z61292417045.tab") > > try(system("convert tmp/1zo371292417045.ps tmp/1zo371292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/2rg3a1292417045.ps tmp/2rg3a1292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/3rg3a1292417045.ps tmp/3rg3a1292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/4rg3a1292417045.ps tmp/4rg3a1292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/5rg3a1292417045.ps tmp/5rg3a1292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/6k7kd1292417045.ps tmp/6k7kd1292417045.png",intern=TRUE)) character(0) > try(system("convert tmp/7k7kd1292417045.ps tmp/7k7kd1292417045.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 9.738 1.978 35.677