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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 = '2' > par7 = '1' > 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 <- 3 > par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial > par7 <- 3 > 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,] 0.78235553 0.1469648 -0.5697168 -0.7026567 -0.03976262 0.49544396 [2,] 0.80502094 0.1073632 -0.5471199 -0.7268202 0.00000000 0.47408119 [3,] 1.20279712 0.0000000 -0.2363991 -1.0571000 0.00000000 0.05710134 [4,] 1.15468298 0.0000000 -0.1909939 -0.9999990 0.00000000 0.00000000 [5,] 1.12501923 0.0000000 -0.1649791 -1.0000004 0.00000000 0.00000000 [6,] 0.62615715 0.0000000 0.0000000 -0.5110069 0.00000000 0.00000000 [7,] 0.09931423 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 [8,] 0.00000000 0.0000000 0.0000000 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 [15,] NA NA NA NA NA NA [16,] NA NA NA NA NA NA [,7] [,8] [1,] 0.7539241 0.2197569 [2,] 0.7544783 0.2193538 [3,] 0.7604422 0.2134901 [4,] 0.7577848 0.2155531 [5,] 0.9648905 0.0000000 [6,] 0.9614141 0.0000000 [7,] 0.9584112 0.0000000 [8,] 0.9606916 0.0000000 [9,] NA NA [10,] NA NA [11,] NA NA [12,] NA NA [13,] NA NA [14,] NA NA [15,] NA NA [16,] NA NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0.16648 0.82268 0.16265 0.22412 0.95102 0.23407 2e-05 0.18700 [2,] 0.08687 0.57330 0.00373 0.10824 NA 0.04761 2e-05 0.18792 [3,] 0.00000 NA 0.29312 0.00027 NA 0.83373 0e+00 0.14301 [4,] 0.00000 NA 0.02825 0.00000 NA NA 0e+00 0.13655 [5,] 0.00000 NA 0.06769 0.00000 NA NA 0e+00 NA [6,] 0.18993 NA NA 0.32909 NA NA 0e+00 NA [7,] 0.45002 NA NA NA NA NA 0e+00 NA [8,] NA NA NA NA NA NA 0e+00 NA [9,] NA NA NA NA NA NA NA NA [10,] NA NA NA NA NA NA NA NA [11,] NA NA NA NA NA NA NA NA [12,] NA NA NA NA NA NA NA NA [13,] NA NA NA NA NA NA NA NA [14,] NA NA NA NA NA NA NA NA [15,] NA NA NA NA NA NA NA NA [16,] NA 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 ma2 ma3 sar1 sar2 0.7824 0.1470 -0.5697 -0.7027 -0.0398 0.4954 0.7539 0.2198 s.e. 0.5574 0.6524 0.4021 0.5710 0.6441 0.4114 0.1623 0.1643 sigma^2 estimated as 7.488: log likelihood = -160.32, aic = 338.64 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2 0.7824 0.1470 -0.5697 -0.7027 -0.0398 0.4954 0.7539 0.2198 s.e. 0.5574 0.6524 0.4021 0.5710 0.6441 0.4114 0.1623 0.1643 sigma^2 estimated as 7.488: log likelihood = -160.32, aic = 338.64 [[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 ma2 ma3 sar1 sar2 0.8050 0.1074 -0.5471 -0.7268 0 0.4741 0.7545 0.2194 s.e. 0.4613 0.1894 0.1802 0.4447 0 0.2337 0.1624 0.1644 sigma^2 estimated as 7.48: log likelihood = -160.32, aic = 336.65 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2 1.2028 0 -0.2364 -1.0571 0 0.0571 0.7604 0.2135 s.e. 0.2347 0 0.2226 0.2708 0 0.2707 0.1404 0.1436 sigma^2 estimated as 7.536: log likelihood = -158.91, aic = 331.83 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2 1.1547 0 -0.1910 -1.0000 0 0 0.7578 0.2156 s.e. 0.0845 0 0.0847 0.0072 0 0 0.1391 0.1426 sigma^2 estimated as 7.568: log likelihood = -158.94, aic = 329.88 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2 1.1250 0 -0.1650 -1.0000 0 0 0.9649 0 s.e. 0.0869 0 0.0885 0.0088 0 0 0.0156 0 sigma^2 estimated as 8.017: log likelihood = -160.01, aic = 330.01 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 sar1 sar2 0.6262 0 0 -0.511 0 0 0.9614 0 s.e. 0.4719 0 0 0.519 0 0 0.0170 0 sigma^2 estimated as 8.407: log likelihood = -162.03, aic = 332.06 [[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 ma2 ma3 sar1 sar2 0.0993 0 0 0 0 0 0.9584 0 s.e. 0.1306 0 0 0 0 0 0.0178 0 sigma^2 estimated as 8.644: log likelihood = -162.4, aic = 330.79 $aic [1] 338.6425 336.6460 331.8274 329.8761 330.0118 332.0588 330.7905 329.3661 There were 19 warnings (use warnings() to see them) > postscript(file="/var/www/html/rcomp/tmp/1tva81260488738.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] 0.14899908 -2.83985249 -0.85813001 -1.31358127 -0.71445596 -1.34192462 [7] -1.28523763 -1.28523529 0.42713399 10.24599419 1.26541533 -0.20007311 [13] -2.59710802 -0.34046082 -1.12505165 -2.09210840 1.09451382 -1.29486722 [19] 1.91202196 1.61407928 -0.13638784 -2.50693303 -1.41872557 -0.83441443 [25] -5.31657392 -0.87801340 -2.06732624 7.92815856 -4.84877893 0.15598475 [31] -0.09998428 -4.11237536 -2.54876319 0.62465439 0.21667556 -5.06637098 [37] 5.87686928 1.00859309 5.55568381 -1.52538403 1.84565098 -0.42337918 [43] 0.90001572 -2.37804485 5.14436335 -1.19905716 -1.67987985 2.92431340 [49] 0.35254015 4.56355969 2.49901329 1.70618768 3.63501629 4.36973164 [55] 0.44503340 0.53464716 1.06262547 0.09437031 2.14588902 0.66008366 > postscript(file="/var/www/html/rcomp/tmp/2vdwr1260488738.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/316qb1260488738.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/42xto1260488738.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/5fxbv1260488738.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/6jdc81260488738.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/7ti171260488738.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/8g5e81260488738.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/9e7xa1260488738.tab") > system("convert tmp/1tva81260488738.ps tmp/1tva81260488738.png") > system("convert tmp/2vdwr1260488738.ps tmp/2vdwr1260488738.png") > system("convert tmp/316qb1260488738.ps tmp/316qb1260488738.png") > system("convert tmp/42xto1260488738.ps tmp/42xto1260488738.png") > system("convert tmp/5fxbv1260488738.ps tmp/5fxbv1260488738.png") > system("convert tmp/6jdc81260488738.ps tmp/6jdc81260488738.png") > system("convert tmp/7ti171260488738.ps tmp/7ti171260488738.png") > > > proc.time() user system elapsed 12.250 3.036 20.257