R version 2.8.0 (2008-10-20) Copyright (C) 2008 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(0.42,0.74,1.02,1.51,1.86,1.59,1.03,0.44,0.82,0.86,0.57,0.59,0.95,0.98,1.23,1.17,0.84,0.74,0.65,0.91,1.19,1.3,1.53,1.94,1.79,1.95,2.26,2.04,2.16,2.75,2.79,2.88,3.36,2.97,3.1,2.49,2.2,2.25,2.09,2.79,3.14,2.93,2.65,2.67,2.26,2.35,2.13,2.18,2.9,2.63,2.67,1.81,1.33,0.88,1.28,1.26,1.26,1.29,1.1,1.37,1.21,1.74,1.76,1.48,1.04,1.62,1.49,1.79,1.8,1.58,1.86,1.74,1.59,1.26,1.13,1.92,2.61,2.26,2.41,2.26,2.03,2.86,2.55,2.27,2.26,2.57,3.07,2.76,2.51,2.87,3.14,3.11,3.16,2.47,2.57,2.89,2.63,2.38,1.69,1.96,2.19,1.87,1.6,1.63,1.22,1.21,1.49,1.64,1.66,1.77,1.82,1.78,1.28,1.29,1.37,1.12,1.51,2.24,2.94,3.09) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '1.6' > 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,] 0.5826512 -0.1196168 -0.074762 -0.4940056 0.09360844 0.02374791 [2,] 0.5756807 -0.1199621 -0.073694 -0.4912949 0.08861612 0.00000000 [3,] 0.7206904 -0.1638318 0.000000 -0.6293203 0.08928661 0.00000000 [4,] 0.7164007 -0.1571830 0.000000 -0.6225323 0.00000000 0.00000000 [5,] 0.7063074 -0.1698538 0.000000 -0.6696386 0.00000000 0.00000000 [6,] -0.8205787 0.0000000 0.000000 0.9586037 0.00000000 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,] -0.9999921 [2,] -0.9999944 [3,] -0.9999964 [4,] -0.9649807 [5,] 0.0000000 [6,] 0.0000000 [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,] 0.15865 0.30843 0.50494 0.22277 0.39952 0.83492 0.00000 [2,] 0.17146 0.30497 0.51394 0.23532 0.41292 NA 0.00000 [3,] 0.01551 0.09828 NA 0.02934 0.40866 NA 0.00000 [4,] 0.02314 0.11396 NA 0.04246 NA NA 0.14581 [5,] 0.00307 0.08098 NA 0.00333 NA NA NA [6,] 0.00000 NA NA 0.00000 NA NA NA [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 0.5827 -0.1196 -0.0748 -0.4940 0.0936 0.0237 -1.0000 s.e. 0.4106 0.1169 0.1118 0.4029 0.1107 0.1137 0.1871 sigma^2 estimated as 0.3807: log likelihood = -124.51, aic = 265.03 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.5827 -0.1196 -0.0748 -0.4940 0.0936 0.0237 -1.0000 s.e. 0.4106 0.1169 0.1118 0.4029 0.1107 0.1137 0.1871 sigma^2 estimated as 0.3807: log likelihood = -124.51, aic = 265.03 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.5757 -0.1200 -0.0737 -0.4913 0.0886 0 -1.0000 s.e. 0.4183 0.1164 0.1125 0.4118 0.1078 0 0.2074 sigma^2 estimated as 0.3789: log likelihood = -124.53, aic = 263.07 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7207 -0.1638 0 -0.6293 0.0893 0 -1.0000 s.e. 0.2933 0.0983 0 0.2852 0.1077 0 0.2022 sigma^2 estimated as 0.3803: log likelihood = -124.73, aic = 261.46 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7164 -0.1572 0 -0.6225 0 0 -0.965 s.e. 0.3112 0.0987 0 0.3034 0 0 0.659 sigma^2 estimated as 0.3891: log likelihood = -125.08, aic = 260.16 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7063 -0.1699 0 -0.6696 0 0 0 s.e. 0.2336 0.0965 0 0.2234 0 0 0 sigma^2 estimated as 0.6846: log likelihood = -146.36, aic = 300.72 [[3]][[7]] NULL $aic [1] 265.0257 263.0695 261.4602 260.1604 300.7155 295.9644 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/13cg01228933433.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 = 120 Frequency = 1 [1] 0.0002495736 0.3615349517 0.3889430220 0.9205325373 0.8085745672 [6] -0.4462795873 -0.7964157364 -0.6713032467 0.3816332231 -0.1435001781 [11] -0.4375856939 0.0073839250 0.4156179257 -0.0178008753 0.4628226092 [16] -0.0890024132 -0.4408670562 -0.0786449688 -0.1601680629 0.3088892889 [21] 0.3953174878 0.2006469135 0.5239858256 0.9774665865 -0.2618190185 [26] 0.5986984355 0.8535178609 -0.4697232871 0.5102644911 1.6525681700 [31] 0.1332543502 0.5496943502 1.7177486808 -1.1228800288 0.7908057323 [36] -1.7754561977 -0.6171458119 -0.0445787258 -0.6600254660 1.7789172471 [41] 0.8470038652 -0.5214175536 -0.5337135988 0.1746514113 -1.1913899881 [46] 0.2455528135 -0.7658511183 0.0576489791 1.8657825234 -0.9465459554 [51] 0.3846795261 -2.1876490986 -0.8767795608 -1.0185412018 0.3554708436 [56] -0.4012721114 -0.1289334724 -0.0370800749 -0.4022614765 0.4690317024 [61] -0.3877317520 1.1035518022 -0.0221705926 -0.4630535375 -0.6876736681 [66] 1.1074691344 -0.4429359644 0.7271857463 0.0076058380 -0.3834632768 [71] 0.7077653880 -0.3191288841 -0.2412778382 -0.6304789031 -0.2479965764 [76] 1.5103248617 1.6265495276 -0.8623085114 0.8022277101 -0.3061241965 [81] -0.4368891596 2.3185569433 -1.0491747274 -0.4402674541 0.0623294757 [86] 0.7729259619 1.4083528528 -0.9084986845 -0.4050398652 1.1167174919 [91] 0.7256735095 -0.0224367597 0.3529149147 -1.9450091953 0.4531681325 [96] 0.6931869995 -0.9139329421 -0.6068143422 -1.7350612950 0.5328104682 [101] 0.2024310905 -0.9447263259 -0.5839866764 -0.0354571367 -0.9816922431 [106] -0.0919263665 0.3496085332 0.1663300364 0.0239095158 0.2820655328 [111] 0.1380512871 -0.0375650906 -0.9729621708 0.0801022679 0.0171935176 [116] -0.5486251488 0.7152876111 1.5830628217 1.9647758568 0.6706923336 > postscript(file="/var/www/html/rcomp/tmp/2iftj1228933433.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/3makz1228933433.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/4q2w51228933433.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/5a04b1228933434.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/68um51228933434.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/746cw1228933434.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/8yzm11228933434.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/95axu1228933434.tab") > > system("convert tmp/13cg01228933433.ps tmp/13cg01228933433.png") > system("convert tmp/2iftj1228933433.ps tmp/2iftj1228933433.png") > system("convert tmp/3makz1228933433.ps tmp/3makz1228933433.png") > system("convert tmp/4q2w51228933433.ps tmp/4q2w51228933433.png") > system("convert tmp/5a04b1228933434.ps tmp/5a04b1228933434.png") > system("convert tmp/68um51228933434.ps tmp/68um51228933434.png") > system("convert tmp/746cw1228933434.ps tmp/746cw1228933434.png") > > > proc.time() user system elapsed 7.359 1.908 9.123