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Type 'q()' to quit R. > x <- c(43880,43110,44496,44164,40399,36763,37903,35532,35533,32110,33374,35462,33508,36080,34560,38737,38144,37594,36424,36843,37246,38661,40454,44928,48441,48140,45998,47369,49554,47510,44873,45344,42413,36912,43452,42142,44382,43636,44167,44423,42868,43908,42013,38846,35087,33026,34646,37135,37985,43121,43722,43630,42234,39351,39327,35704,30466,28155,29257,29998,32529,34787,33855,34556,31348,30805,28353,24514,21106,21346,23335,24379,26290,30084,29429,30632,27349,27264,27474,24482,21453,18788,19282,19713,21917,23812,23785,24696,24562,23580,24939,23899,21454,19761,19815,20780,23462,25005,24725,26198,27543,26471,26558,25317,22896,22248,23406,25073,27691,30599,31948,32946,34012,32936,32974,30951,29812,29010,31068,32447,34844,35676,35387,36488,35652,33488,32914,29781,27951) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '1' > 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,] 0.4656550 0.1733705 0.02664216 -0.58014190 0.1315967 -0.01129618 [2,] 0.4679914 0.1727239 0.02564531 -0.58221105 0.1320496 0.00000000 [3,] 0.5371387 0.1853204 0.00000000 -0.64872155 0.1297026 0.00000000 [4,] 0.6140175 0.1511825 0.00000000 -0.69950364 0.0000000 0.00000000 [5,] 0.0000000 0.1046336 0.00000000 -0.08324885 0.0000000 0.00000000 [6,] 0.0000000 0.0984113 0.00000000 0.00000000 0.0000000 0.00000000 [7,] 0.0000000 0.0000000 0.00000000 0.00000000 0.0000000 0.00000000 [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,] -0.9999600 [2,] -1.0000305 [3,] -1.0001463 [4,] -0.9996226 [5,] -1.0005545 [6,] -1.0001797 [7,] -1.0000802 [8,] NA [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.37052 0.13784 0.84002 0.25532 0.24299 0.92193 0.00000 [2,] 0.37609 0.13969 0.84633 0.26166 0.24126 NA 0.00000 [3,] 0.11080 0.05755 NA 0.04935 0.24723 NA 0.00000 [4,] 0.15333 0.11162 NA 0.10077 NA NA 0.00080 [5,] NA 0.27000 NA 0.37782 NA NA 0.00086 [6,] NA 0.29414 NA NA NA NA 0.00022 [7,] NA NA NA NA NA NA 0.00003 [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 0.4657 0.1734 0.0266 -0.5801 0.1316 -0.0113 -1.0000 s.e. 0.5181 0.1161 0.1317 0.5076 0.1122 0.1150 0.1511 sigma^2 estimated as 2472690: log likelihood = -1031.32, aic = 2078.64 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.4657 0.1734 0.0266 -0.5801 0.1316 -0.0113 -1.0000 s.e. 0.5181 0.1161 0.1317 0.5076 0.1122 0.1150 0.1511 sigma^2 estimated as 2472690: log likelihood = -1031.32, aic = 2078.64 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.4680 0.1727 0.0256 -0.5822 0.1320 0 -1.0000 s.e. 0.5268 0.1162 0.1320 0.5163 0.1121 0 0.1476 sigma^2 estimated as 2478238: log likelihood = -1031.32, aic = 2076.65 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.5371 0.1853 0 -0.6487 0.1297 0 -1.0001 s.e. 0.3344 0.0967 0 0.3268 0.1116 0 0.1484 sigma^2 estimated as 2478177: log likelihood = -1031.34, aic = 2074.68 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.6140 0.1512 0 -0.6995 0 0 -0.9996 s.e. 0.4274 0.0944 0 0.4231 0 0 0.2909 sigma^2 estimated as 2450348: log likelihood = -1032.03, aic = 2074.06 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0.1046 0 -0.0832 0 0 -1.0006 s.e. 0 0.0944 0 0.0941 0 0 0.2929 sigma^2 estimated as 2463561: log likelihood = -1032.43, aic = 2072.86 [[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 0.0984 0 0 0 0 -1.0002 s.e. 0 0.0934 0 0 0 0 0.2630 sigma^2 estimated as 2481287: log likelihood = -1032.82, aic = 2071.64 $aic [1] 2078.638 2076.648 2074.684 2074.055 2072.865 2071.645 2070.750 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 6: 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/1c3g11292161819.ps",horizontal=F,onefile=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 = 129 Frequency = 1 [1] 25.334121 10.733313 8.197970 5.817593 1.235252 [6] -2.316840 -0.922734 -3.034062 -2.694871 -5.680562 [11] -3.955190 -24.300326 -174.886022 2351.465555 -2044.730457 [16] 2955.351343 2444.721938 1868.059869 -1854.358054 1758.720466 [21] 443.644907 3237.548814 335.811261 1467.710888 3732.616375 [26] -1134.034391 -2013.260664 -353.759047 3729.479873 84.246963 [31] -2491.505793 1177.762233 -2348.188870 -3782.954690 4334.636497 [36] -3338.717154 704.973534 -735.468922 1013.466003 -1177.756502 [41] -829.296325 2825.160133 -800.503303 -2580.418926 -2440.576155 [46] 613.080947 -1123.980520 628.722606 -277.564725 4359.673245 [51] 966.658987 -1741.215400 -506.331025 -1289.516291 1039.262250 [56] -2061.122157 -3377.834358 293.555707 -1203.289385 -1033.110740 [61] 1338.829956 1084.303436 -756.396613 -439.328945 -1929.685677 [66] 1011.807218 -1204.932081 -2090.232652 -869.504823 2587.931414 [71] -337.428318 -792.791370 445.342169 2308.712325 -325.086558 [76] -46.514832 -1725.548235 1233.391479 1452.790082 -1024.144001 [81] -626.533412 -578.716924 -1703.750810 -967.693321 783.160383 [86] 277.262824 280.121750 -138.602359 1393.180847 256.034928 [91] 2042.991632 1021.399136 -102.117200 228.313005 -1940.733678 [96] -427.676635 1166.438714 -137.477911 -34.334097 440.232268 [101] 2646.431610 88.817282 465.390508 719.649417 50.576988 [106] 1205.125117 -673.015509 187.479887 866.019546 1106.661162 [111] 1521.412848 -184.254339 1950.310305 119.990408 395.824167 [116] -97.743886 1265.931697 1004.935901 132.268332 -89.918702 [121] 482.653495 -951.182486 -164.302950 126.310341 104.481441 [126] -938.403022 -46.978722 -1044.589520 543.713582 > postscript(file="/var/www/html/rcomp/tmp/2c3g11292161819.ps",horizontal=F,onefile=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/3c3g11292161819.ps",horizontal=F,onefile=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/4c3g11292161819.ps",horizontal=F,onefile=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/55cxm1292161819.ps",horizontal=F,onefile=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/65cxm1292161819.ps",horizontal=F,onefile=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/75cxm1292161819.ps",horizontal=F,onefile=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/8bexp1292161820.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/945ea1292161820.tab") > > try(system("convert tmp/1c3g11292161819.ps tmp/1c3g11292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/2c3g11292161819.ps tmp/2c3g11292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/3c3g11292161819.ps tmp/3c3g11292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/4c3g11292161819.ps tmp/4c3g11292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/55cxm1292161819.ps tmp/55cxm1292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/65cxm1292161819.ps tmp/65cxm1292161819.png",intern=TRUE)) character(0) > try(system("convert tmp/75cxm1292161819.ps tmp/75cxm1292161819.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 12.251 1.911 28.434