R version 2.9.0 (2009-04-17) Copyright (C) 2009 The R Foundation for Statistical Computing ISBN 3-900051-07-0 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(149,139,135,130,127,122,117,112,113,149,157,157,147,137,132,125,123,117,114,111,112,144,150,149,134,123,116,117,111,105,102,95,93,124,130,124,115,106,105,105,101,95,93,84,87,116,120,117,109,105,107,109,109,108,107,99,103,131,137,135) > par9 = '0' > par8 = '0' > par7 = '0' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '1' > par1 = 'FALSE' > 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 > par6 <- 11 > 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,] -0.08360930 -0.4013939 -0.3662080 -0.4193066 -0.3142875 -0.3507039 [2,] -0.06349464 -0.3875330 -0.3464318 -0.4047543 -0.2992791 -0.3364275 [3,] 0.00000000 -0.3916938 -0.3264583 -0.3865829 -0.2761012 -0.3196996 [4,] NA NA NA NA NA NA [5,] NA NA NA NA NA NA [6,] NA NA NA NA NA NA [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 [15,] NA NA NA NA NA NA [16,] NA NA NA NA NA NA [17,] NA NA NA NA NA NA [18,] NA NA NA NA NA NA [19,] NA NA NA NA NA NA [20,] NA NA NA NA NA NA [21,] NA NA NA NA NA NA [22,] NA NA NA NA NA NA [,7] [,8] [,9] [,10] [,11] [1,] -0.3061428 -0.4268445 -0.3185735 -0.4350710 -0.04711439 [2,] -0.2869060 -0.4104049 -0.3007029 -0.4321061 0.00000000 [3,] -0.2700916 -0.3971470 -0.2748818 -0.4073188 0.00000000 [4,] NA NA NA NA NA [5,] NA NA NA NA NA [6,] NA NA NA NA NA [7,] NA NA NA NA NA [8,] NA NA NA NA NA [9,] NA NA NA NA NA [10,] NA NA NA NA NA [11,] NA NA NA NA NA [12,] NA NA NA NA NA [13,] NA NA NA NA NA [14,] NA NA NA NA NA [15,] NA NA NA NA NA [16,] NA NA NA NA NA [17,] NA NA NA NA NA [18,] NA NA NA NA NA [19,] NA NA NA NA NA [20,] NA NA NA NA NA [21,] NA NA NA NA NA [22,] NA NA NA NA NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [1,] 0.53376 0.00127 0.00706 0.00156 0.02045 0.00818 0.02129 0.00088 0.02073 [2,] 0.59353 0.00087 0.00410 0.00111 0.01849 0.00696 0.01522 0.00045 0.01670 [3,] NA 0.00080 0.00447 0.00121 0.02062 0.00820 0.01813 0.00054 0.01820 [4,] NA NA NA NA NA NA NA NA NA [5,] NA NA NA NA NA NA NA NA NA [6,] NA NA NA NA NA NA NA NA NA [7,] NA NA NA NA NA NA NA NA NA [8,] NA NA NA NA NA NA NA NA NA [9,] NA NA NA NA NA NA NA NA NA [10,] NA NA NA NA NA NA NA NA NA [11,] NA NA NA NA NA NA NA NA NA [12,] NA NA NA NA NA NA NA NA NA [13,] NA NA NA NA NA NA NA NA NA [14,] NA NA NA NA NA NA NA NA NA [15,] NA NA NA NA NA NA NA NA NA [16,] NA NA NA NA NA NA NA NA NA [17,] NA NA NA NA NA NA NA NA NA [18,] NA NA NA NA NA NA NA NA NA [19,] NA NA NA NA NA NA NA NA NA [20,] NA NA NA NA NA NA NA NA NA [21,] NA NA NA NA NA NA NA NA NA [22,] NA NA NA NA NA NA NA NA NA [,10] [,11] [1,] 0.00134 0.74715 [2,] 0.00138 NA [3,] 0.00135 NA [4,] NA NA [5,] NA NA [6,] NA NA [7,] NA NA [8,] NA NA [9,] NA NA [10,] NA NA [11,] NA NA [12,] NA NA [13,] NA NA [14,] NA NA [15,] NA NA [16,] NA NA [17,] NA NA [18,] NA NA [19,] NA NA [20,] NA NA [21,] NA NA [22,] NA NA [[3]] [[3]][[1]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 -0.0836 -0.4014 -0.3662 -0.4193 -0.3143 -0.3507 -0.3061 -0.4268 s.e. 0.1334 0.1172 0.1301 0.1250 0.1311 0.1271 0.1286 0.1203 ar9 ar10 ar11 -0.3186 -0.4351 -0.0471 s.e. 0.1332 0.1277 0.1453 sigma^2 estimated as 54.22: log likelihood = -204.09, aic = 432.17 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 -0.0836 -0.4014 -0.3662 -0.4193 -0.3143 -0.3507 -0.3061 -0.4268 s.e. 0.1334 0.1172 0.1301 0.1250 0.1311 0.1271 0.1286 0.1203 ar9 ar10 ar11 -0.3186 -0.4351 -0.0471 s.e. 0.1332 0.1277 0.1453 sigma^2 estimated as 54.22: log likelihood = -204.09, aic = 432.17 [[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 ar4 ar5 ar6 ar7 ar8 -0.0635 -0.3875 -0.3464 -0.4048 -0.2993 -0.3364 -0.2869 -0.4104 s.e. 0.1182 0.1093 0.1150 0.1168 0.1228 0.1194 0.1141 0.1091 ar9 ar10 ar11 -0.3007 -0.4321 0 s.e. 0.1213 0.1274 0 sigma^2 estimated as 54.34: log likelihood = -204.14, aic = 430.28 [[3]][[4]] NULL [[3]][[5]] NULL [[3]][[6]] NULL [[3]][[7]] NULL [[3]][[8]] NULL [[3]][[9]] NULL [[3]][[10]] NULL [[3]][[11]] NULL $aic [1] 432.1733 430.2782 428.5647 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 > postscript(file="/var/www/html/rcomp/tmp/1vprx1260383637.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 = 60 Frequency = 1 [1] 0.1489998 -6.8276979 -0.6333056 -4.4417472 -3.1871003 -5.6192685 [7] -4.4522265 -5.3937987 -2.1110010 23.0171679 -4.2241550 1.1666588 [13] -3.0996540 -1.2243908 -1.4481557 -5.5806608 -2.1275915 -2.4022179 [19] -0.4212441 1.1898875 -10.5345333 15.9339157 -7.6911832 -1.2734301 [25] -9.9625418 -4.9685248 -6.2763473 -1.1862552 -9.4190437 -3.8375920 [31] -4.3013748 -6.0675565 -17.1899968 11.7677661 -12.6355094 -8.2171728 [37] -7.1380343 -4.9194865 -3.7409290 -3.8141670 -6.2532785 -4.1374379 [43] -0.8586429 -6.0101173 -7.8679317 12.1046682 -7.0705219 -2.0654618 [49] -2.5410957 1.0839812 1.9782487 1.5176869 2.7071178 5.5079157 [55] 7.3479451 1.8187557 0.4249442 20.3056341 2.5874555 6.4376706 > postscript(file="/var/www/html/rcomp/tmp/2tbs71260383637.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/39vy31260383637.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/4p0gg1260383637.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/5fjl81260383637.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/6dolm1260383637.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/76pu11260383637.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/8pc2y1260383637.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/903q91260383637.tab") > system("convert tmp/1vprx1260383637.ps tmp/1vprx1260383637.png") > system("convert tmp/2tbs71260383637.ps tmp/2tbs71260383637.png") > system("convert tmp/39vy31260383637.ps tmp/39vy31260383637.png") > system("convert tmp/4p0gg1260383637.ps tmp/4p0gg1260383637.png") > system("convert tmp/5fjl81260383637.ps tmp/5fjl81260383637.png") > system("convert tmp/6dolm1260383637.ps tmp/6dolm1260383637.png") > system("convert tmp/76pu11260383637.ps tmp/76pu11260383637.png") > > > proc.time() user system elapsed 2.416 1.080 2.828