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Type 'q()' to quit R. > x <- c(112,118,132,129,121,135,148,148,136,119,104,118,115,126,141,135,125,149,170,170,158,133,114,140,145,150,178,163,172,178,199,199,184,162,146,166,171,180,193,181,183,218,230,242,209,191,172,194,196,196,236,235,229,243,264,272,237,211,180,201,204,188,235,227,234,264,302,293,259,229,203,229,242,233,267,269,270,315,364,347,312,274,237,278,284,277,317,313,318,374,413,405,355,306,271,306,315,301,356,348,355,422,465,467,404,347,305,336,340,318,362,348,363,435,491,505,404,359,310,337,360,342,406,396,420,472,548,559,463,407,362,405,417,391,419,461,472,535,622,606,508,461,390,432) > par9 = '1' > par8 = '0' > par7 = '1' > par6 = '2' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '0.5' > par1 = 'FALSE' > par9 <- '1' > par8 <- '0' > par7 <- '1' > par6 <- '2' > par5 <- '12' > par4 <- '1' > par3 <- '1' > par2 <- '0.5' > par1 <- 'FALSE' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 () > #Author: root > #To cite this work: Wessa P., (2013), ARIMA Backward Selection (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimabackwardselection.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > # > library(lattice) > if (par1 == 'TRUE') par1 <- TRUE > if (par1 == 'FALSE') par1 <- FALSE > par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter > par3 <- as.numeric(par3) #degree of non-seasonal differencing > par4 <- as.numeric(par4) #degree of seasonal differencing > par5 <- as.numeric(par5) #seasonal period > par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial > par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial > par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial > par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial > armaGR <- function(arima.out, names, n){ + try1 <- arima.out$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] [1,] 0.5751820 0.2156603 -0.9999961 -0.3416271 [2,] 0.2940262 0.0000000 -0.6248582 -0.3422920 [3,] 0.0000000 0.0000000 -0.3474233 -0.3292868 [4,] NA NA NA NA [5,] NA NA NA NA [6,] NA NA NA NA [7,] NA NA NA NA [8,] NA NA NA NA [[2]] [,1] [,2] [,3] [,4] [1,] 0.00000 0.01584 0.00000 0.00007 [2,] 0.50834 NA 0.10747 0.00025 [3,] NA NA 0.00016 0.00006 [4,] NA NA NA NA [5,] NA NA NA NA [6,] NA NA NA NA [7,] NA NA NA NA [8,] NA NA NA NA [[3]] [[3]][[1]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ma1 sma1 0.5752 0.2157 -1.0000 -0.3416 s.e. 0.0864 0.0883 0.0253 0.0832 sigma^2 estimated as 0.09101: log likelihood = -31.31, aic = 72.63 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ma1 sma1 0.5752 0.2157 -1.0000 -0.3416 s.e. 0.0864 0.0883 0.0253 0.0832 sigma^2 estimated as 0.09101: log likelihood = -31.31, aic = 72.63 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ma1 sma1 0.2940 0 -0.6249 -0.3423 s.e. 0.4434 0 0.3857 0.0909 sigma^2 estimated as 0.09834: log likelihood = -34.8, aic = 77.61 [[3]][[4]] NULL $aic [1] 72.62946 77.60868 75.80400 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 > postscript(file="/var/fisher/rcomp/tmp/1th4b1385303816.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 = 144 Frequency = 1 [1] 6.110100e-03 2.949232e-03 2.460083e-03 1.717833e-03 1.046699e-03 [6] 1.440257e-03 1.742195e-03 1.523504e-03 8.772897e-04 7.290024e-05 [11] -6.128126e-04 -6.369593e-03 -3.858609e-02 1.978761e-01 7.547800e-02 [16] -7.699690e-02 -8.939770e-02 3.516813e-01 3.759110e-01 1.553428e-01 [21] 1.299992e-01 -1.978252e-01 -1.835057e-01 3.831630e-01 4.143544e-01 [26] -6.489425e-02 4.743793e-01 -1.910309e-01 7.418281e-01 -4.296513e-01 [31] -5.078606e-02 -3.777833e-02 -8.602498e-02 7.718002e-02 1.796649e-01 [36] -1.409972e-01 5.359247e-02 6.636162e-02 -4.402357e-01 -1.233566e-01 [41] -9.753351e-02 7.253821e-01 -1.334746e-01 4.118544e-01 -4.356786e-01 [46] 1.361038e-01 1.044842e-02 -4.929325e-02 -1.070475e-01 -3.597087e-01 [51] 5.965133e-01 5.702355e-01 -4.118683e-02 -4.583897e-01 1.290189e-03 [56] -5.210192e-02 -2.246895e-01 -2.336854e-01 -5.072069e-01 -2.697119e-01 [61] -1.454059e-01 -7.725610e-01 2.225085e-01 -9.927129e-02 2.972244e-01 [66] 4.072487e-01 6.777616e-01 -2.381722e-01 7.823614e-03 -1.405186e-01 [71] 4.004747e-02 9.907998e-02 3.515924e-01 1.723289e-01 -2.757148e-01 [76] 2.299620e-01 -2.876483e-02 4.822250e-01 5.392037e-01 -1.384465e-01 [81] 8.230898e-02 -1.656359e-01 -2.888800e-01 3.187560e-01 -6.202890e-02 [86] 9.998660e-02 -7.788778e-03 -6.605840e-02 6.107670e-02 3.669121e-01 [91] -9.238389e-02 1.347082e-01 -2.512010e-01 -3.755549e-01 -1.007783e-01 [96] -1.772756e-01 -5.091983e-02 -1.966996e-01 2.663100e-01 -6.015064e-02 [101] 7.294081e-02 3.392685e-01 8.255604e-02 3.504255e-01 -1.948690e-01 [106] -2.529929e-01 -2.089319e-01 -2.953237e-01 -2.622127e-01 -3.848267e-01 [111] -3.710494e-01 -3.722176e-01 6.291907e-02 1.806699e-01 3.189782e-01 [116] 4.864503e-01 -7.783235e-01 4.155656e-02 -2.621293e-01 -2.835227e-01 [121] 3.374746e-01 1.121789e-01 4.507737e-01 2.194962e-01 3.988280e-01 [126] -3.325725e-01 4.130143e-01 1.641449e-01 2.311142e-03 -8.113689e-02 [131] 9.930489e-02 3.120301e-01 -5.120480e-02 -1.380826e-01 -8.674732e-01 [136] 9.701764e-01 -1.157107e-02 6.629907e-02 3.291315e-01 -4.201865e-01 [141] -8.567250e-02 1.794727e-01 -4.919897e-01 -1.150477e-01 > postscript(file="/var/fisher/rcomp/tmp/25ale1385303816.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/fisher/rcomp/tmp/3rohd1385303816.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/fisher/rcomp/tmp/4iebs1385303816.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/fisher/rcomp/tmp/5x9ue1385303816.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/fisher/rcomp/tmp/6anxv1385303816.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/fisher/rcomp/tmp/72ahl1385303816.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/fisher/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/fisher/rcomp/tmp/873er1385303816.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/fisher/rcomp/tmp/96azs1385303816.tab") > > try(system("convert tmp/1th4b1385303816.ps tmp/1th4b1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/25ale1385303816.ps tmp/25ale1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/3rohd1385303816.ps tmp/3rohd1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/4iebs1385303816.ps tmp/4iebs1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/5x9ue1385303816.ps tmp/5x9ue1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/6anxv1385303816.ps tmp/6anxv1385303816.png",intern=TRUE)) character(0) > try(system("convert tmp/72ahl1385303816.ps tmp/72ahl1385303816.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 5.156 0.894 6.048