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(2350.44,2440.25,2408.64,2472.81,2407.6,2454.62,2448.05,2497.84,2645.64,2756.76,2849.27,2921.44,2981.85,3080.58,3106.22,3119.31,3061.26,3097.31,3161.69,3257.16,3277.01,3295.32,3363.99,3494.17,3667.03,3813.06,3917.96,3895.51,3801.06,3570.12,3701.61,3862.27,3970.1,4138.52,4199.75,4290.89,4443.91,4502.64,4356.98,4591.27,4696.96,4621.4,4562.84,4202.52,4296.49,4435.23,4105.18,4116.68,3844.49,3720.98,3674.4,3857.62,3801.06,3504.37,3032.6,3047.03,2962.34,2197.82,2014.45) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '1.9' > 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,] 0.89835166 -0.2115469 0.2373349 -0.7346392 0.09650143 -0.1766312 [2,] 0.89887401 -0.2125535 0.2374155 -0.7337475 0.01273167 -0.1754421 [3,] 0.90059788 -0.2114201 0.2351228 -0.7335781 0.00000000 -0.1748271 [4,] 0.90082562 -0.1956080 0.2247985 -0.7370833 0.00000000 0.0000000 [5,] -0.09644651 0.0000000 0.2075470 0.3452025 0.00000000 0.0000000 [6,] 0.00000000 0.0000000 0.2157245 0.2473323 0.00000000 0.0000000 [7,] 0.00000000 0.0000000 0.0000000 0.2580369 0.00000000 0.0000000 [8,] 0.00000000 0.0000000 0.0000000 0.0000000 0.00000000 0.0000000 [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,] -0.0862317 [2,] 0.0000000 [3,] 0.0000000 [4,] 0.0000000 [5,] 0.0000000 [6,] 0.0000000 [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,] 0.00004 0.25393 0.11808 0.00007 0.95286 0.31231 0.95892 [2,] 0.00004 0.24812 0.11732 0.00007 0.93799 0.31331 NA [3,] 0.00003 0.24979 0.11121 0.00007 NA 0.31454 NA [4,] 0.00002 0.28754 0.13025 0.00003 NA NA NA [5,] 0.90990 NA 0.22135 0.68638 NA NA NA [6,] NA NA 0.12696 0.06947 NA NA NA [7,] NA NA NA 0.07318 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 0.8984 -0.2115 0.2373 -0.7346 0.0965 -0.1766 -0.0862 s.e. 0.2001 0.1833 0.1493 0.1691 1.6243 0.1731 1.6661 sigma^2 estimated as 2.144e+11: log likelihood = -839.57, aic = 1695.13 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.8984 -0.2115 0.2373 -0.7346 0.0965 -0.1766 -0.0862 s.e. 0.2001 0.1833 0.1493 0.1691 1.6243 0.1731 1.6661 sigma^2 estimated as 2.144e+11: log likelihood = -839.57, aic = 1695.13 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.8989 -0.2126 0.2374 -0.7337 0.0127 -0.1754 0 s.e. 0.2003 0.1820 0.1491 0.1695 0.1629 0.1723 0 sigma^2 estimated as 2.144e+11: log likelihood = -839.57, aic = 1693.14 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.9006 -0.2114 0.2351 -0.7336 0 -0.1748 0 s.e. 0.1983 0.1817 0.1452 0.1696 0 0.1722 0 sigma^2 estimated as 2.145e+11: log likelihood = -839.57, aic = 1691.15 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.9008 -0.1956 0.2248 -0.7371 0 0 0 s.e. 0.1913 0.1821 0.1463 0.1606 0 0 0 sigma^2 estimated as 2.206e+11: log likelihood = -840.07, aic = 1690.14 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.0964 0 0.2075 0.3452 0 0 0 s.e. 0.8483 0 0.1678 0.8504 0 0 0 sigma^2 estimated as 2.325e+11: log likelihood = -841.4, aic = 1690.81 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0.2157 0.2473 0 0 0 s.e. 0 0 0.1392 0.1336 0 0 0 sigma^2 estimated as 2.326e+11: log likelihood = -841.41, aic = 1688.82 [[3]][[8]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 0.2580 0 0 0 s.e. 0 0 0 0.1414 0 0 0 sigma^2 estimated as 2.428e+11: log likelihood = -842.58, aic = 1689.16 $aic [1] 1695.133 1693.139 1691.145 1690.137 1690.808 1688.819 1689.156 1690.588 Warning messages: 1: In log(s2) : NaNs produced 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/1imf61229251242.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 = 59 Frequency = 1 [1] 2542.045 181764.234 -111974.552 165222.596 -181221.875 [6] 146361.516 -51787.727 120462.802 298242.899 181830.324 [11] 175823.714 132987.355 118061.367 224603.866 9506.649 [16] 32182.709 -160904.116 135982.598 136082.924 224544.706 [21] -3080.493 51664.950 179722.741 329423.685 433801.987 [26] 343871.492 248566.646 -137018.382 -267123.099 -642454.071 [31] 565897.714 360503.320 257784.315 498770.055 82044.679 [36] 297675.656 472350.680 93481.693 -553588.531 1002137.138 [41] 142277.704 -324137.321 -136230.770 -1262016.980 654685.353 [46] 328822.965 -1245568.445 360486.521 -991627.004 -133598.368 [51] -109436.456 603699.714 -336109.394 -819838.501 -1092704.307 [56] 319333.161 -299471.591 -1630650.765 79412.444 > postscript(file="/var/www/html/rcomp/tmp/2ymi41229251242.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/3h8jg1229251242.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/4rprt1229251242.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/57gi21229251242.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/6xov01229251242.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/7225m1229251242.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/86pe21229251242.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/9t5wp1229251242.tab") > > system("convert tmp/1imf61229251242.ps tmp/1imf61229251242.png") > system("convert tmp/2ymi41229251242.ps tmp/2ymi41229251242.png") > system("convert tmp/3h8jg1229251242.ps tmp/3h8jg1229251242.png") > system("convert tmp/4rprt1229251242.ps tmp/4rprt1229251242.png") > system("convert tmp/57gi21229251242.ps tmp/57gi21229251242.png") > system("convert tmp/6xov01229251242.ps tmp/6xov01229251242.png") > system("convert tmp/7225m1229251242.ps tmp/7225m1229251242.png") > > > proc.time() user system elapsed 5.940 1.905 8.653