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Type 'q()' to quit R. > x <- c(14929387.5,14717825.3,15826281.2,16301309.6,15033016.9,16998460.6,14066462.7,13328937.3,17319718.2,17586426.8,15887037.4,17935679.1,15869489,15892510.9,17556558.1,16791643,15953688.5,18144913.6,14390881,13885708.7,17332571.5,17152595.8,16003877.1,16841467.1,14783398.1,14667847.5,17714362.2,16282088,15014866.2,17722582.4,13876509.4,15495489.6,17799521.1,17920079.1,17248022.4,18813782.4,16249688.3,17823358.5,20424438.3,17814218.7,19699959.6,19776328.1,15679833.1,17119266.5,20092613,20863688.3,20925203.1,21032593,20664684.3,19711511.4,22553293.4,19498332.9,20722827.8,21321275,17960847.7,17789654.9,20003708.5,21169851.7,20422839.4,19810562.3) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '1.0' > 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] [,7] [1,] -0.1133595 0.2283020 0.3465972 -0.6568888 -0.8919332 -0.5307998 0.5269657 [2,] -0.1135157 0.2519700 0.3446038 -0.6663256 -0.4606487 -0.3976614 0.0000000 [3,] 0.0000000 0.3118652 0.3509299 -0.7561259 -0.4447237 -0.3780463 0.0000000 [4,] 0.0000000 0.2277259 0.2829636 -0.6308541 -0.2998836 0.0000000 0.0000000 [5,] 0.0000000 0.0000000 0.2325059 -0.5376432 -0.2878712 0.0000000 0.0000000 [6,] 0.0000000 0.0000000 0.0000000 -0.4850324 -0.2613914 0.0000000 0.0000000 [7,] 0.0000000 0.0000000 0.0000000 -0.4689470 0.0000000 0.0000000 0.0000000 [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 [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.84828 0.61964 0.10122 0.27032 0.70206 0.43879 0.8699 [2,] 0.83505 0.52674 0.08469 0.20726 0.01544 0.07579 NA [3,] NA 0.06717 0.02927 0.00001 0.01335 0.07583 NA [4,] NA 0.17759 0.07217 0.00006 0.04943 NA NA [5,] NA NA 0.14598 0.00003 0.06245 NA NA [6,] NA NA NA 0.00003 0.09165 NA NA [7,] NA NA NA 0.00005 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 -0.1134 0.2283 0.3466 -0.6569 -0.8919 -0.5308 0.5270 s.e. 0.5896 0.4572 0.2077 0.5896 2.3187 0.6803 3.2016 sigma^2 estimated as 6.353e+11: log likelihood = -709.44, aic = 1434.88 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.1134 0.2283 0.3466 -0.6569 -0.8919 -0.5308 0.5270 s.e. 0.5896 0.4572 0.2077 0.5896 2.3187 0.6803 3.2016 sigma^2 estimated as 6.353e+11: log likelihood = -709.44, aic = 1434.88 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.1135 0.2520 0.3446 -0.6663 -0.4606 -0.3977 0 s.e. 0.5425 0.3954 0.1961 0.5219 0.1840 0.2196 0 sigma^2 estimated as 6.621e+11: log likelihood = -709.46, aic = 1432.93 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.3119 0.3509 -0.7561 -0.4447 -0.3780 0 s.e. 0 0.1669 0.1567 0.1505 0.1738 0.2088 0 sigma^2 estimated as 6.716e+11: log likelihood = -709.5, aic = 1431 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.2277 0.2830 -0.6309 -0.2999 0 0 s.e. 0 0.1667 0.1543 0.1450 0.1493 0 0 sigma^2 estimated as 7.748e+11: log likelihood = -710.85, aic = 1431.69 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0.2325 -0.5376 -0.2879 0 0 s.e. 0 0 0.1577 0.1176 0.1514 0 0 sigma^2 estimated as 8.101e+11: log likelihood = -711.81, aic = 1431.61 [[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 -0.4850 -0.2614 0 0 s.e. 0 0 0 0.1057 0.1524 0 0 sigma^2 estimated as 8.552e+11: log likelihood = -712.9, aic = 1431.8 $aic [1] 1434.878 1432.930 1430.999 1431.692 1431.611 1431.803 1432.551 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/freestat/rcomp/tmp/18aol1229705090.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] 8619.4840 3690.8750 3353.0602 2918.1582 1180.6706 [6] 2790.3211 -340.0531 -990.1517 2895.1261 2858.5354 [11] 974.2795 -5393.4265 -52689.3318 203631.7586 611587.8968 [16] -902089.5733 -19957.6206 208199.4858 -692462.2232 -111576.8089 [21] -579131.9227 -712061.0778 186141.0495 -1078673.5415 -550433.2899 [26] -334949.3611 1364258.5651 -330606.8670 -477042.7764 344139.2630 [31] -139997.0357 2116982.5965 -258202.6513 58537.6351 648995.2289 [36] 726395.2066 -151577.0965 1579479.3344 682028.8952 -1021581.2143 [41] 2545255.9166 -1261809.7496 -886499.1954 -54292.4320 344255.1294 [46] 896049.1222 1292779.7174 -640992.6554 1753012.5738 -1235027.3824 [51] -474758.9648 -982919.1909 -313836.3094 -317953.7594 516391.6625 [56] -1407091.4973 -1266824.6926 -49343.5033 -640711.0120 -1411638.0195 > postscript(file="/var/www/html/freestat/rcomp/tmp/2xvqa1229705090.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/freestat/rcomp/tmp/3mb6i1229705090.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/freestat/rcomp/tmp/4zz1j1229705090.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/freestat/rcomp/tmp/5uu8u1229705090.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/freestat/rcomp/tmp/60kj41229705090.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/freestat/rcomp/tmp/7lbon1229705090.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/8j69l1229705090.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/freestat/rcomp/tmp/9wsow1229705090.tab") > > system("convert tmp/18aol1229705090.ps tmp/18aol1229705090.png") > system("convert tmp/2xvqa1229705090.ps tmp/2xvqa1229705090.png") > system("convert tmp/3mb6i1229705090.ps tmp/3mb6i1229705090.png") > system("convert tmp/4zz1j1229705090.ps tmp/4zz1j1229705090.png") > system("convert tmp/5uu8u1229705090.ps tmp/5uu8u1229705090.png") > system("convert tmp/60kj41229705090.ps tmp/60kj41229705090.png") > system("convert tmp/7lbon1229705090.ps tmp/7lbon1229705090.png") > > > proc.time() user system elapsed 9.031 1.871 9.745