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Type 'q()' to quit R. > x <- c(4,5,7,5,6,5,3,7,7,11,13,13,9,7,6,3,5,1,5,2,9,4,4,10,8,6,7,0,7,4,5,11,2,4,5,12,10,6,6,8,3,10,2,5,4,3,8,5,7,1,7,4,8,7,10,2,6,6,11,8,8,6,11,15,9,5,10,4,9,3,7,7,9,15,11,10,6,5,6,6,14,11,1,9,13,10,11,7,6,4,6,8,6,7,12,20,10,14,11,13,7,9,8,7,9,10,12,13,11,11,14,10,9,12,8,13,14,15,14,14,15,14,21,10,8,12,13,6,12,12) > par9 = '1' > par8 = '2' > par7 = '0' > par6 = '3' > par5 = '12' > par4 = '0' > par3 = '1' > par2 = '1' > par1 = 'FALSE' > par9 <- '1' > par8 <- '2' > par7 <- '0' > par6 <- '3' > par5 <- '12' > par4 <- '0' > par3 <- '1' > par2 <- '1' > 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] [,5] [,6] [1,] -0.6266700 -0.3381553 -0.2119657 0.09281622 -0.007858048 0.0763074 [2,] -0.6266305 -0.3380500 -0.2112610 0.03571310 0.000000000 0.1335406 [3,] -0.6264511 -0.3375104 -0.2091953 0.00000000 0.000000000 0.1683881 [4,] -0.5829995 -0.2994265 -0.1884320 0.00000000 0.000000000 0.0000000 [5,] NA NA NA NA NA NA [6,] NA NA NA NA NA NA [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 [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [1,] 0 0.00113 0.02928 0.98657 0.99288 0.98899 [2,] 0 0.00107 0.02774 0.95625 NA 0.83597 [3,] 0 0.00103 0.01748 NA NA 0.08077 [4,] 0 0.00252 0.03185 NA NA NA [5,] NA NA NA NA NA NA [6,] NA NA NA NA NA NA [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 [[3]] [[3]][[1]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 sar1 sar2 sma1 -0.6267 -0.3382 -0.2120 0.0928 -0.0079 0.0763 s.e. 0.0906 0.1014 0.0961 5.5023 0.8792 5.5163 sigma^2 estimated as 12.11: log likelihood = -344.34, aic = 702.68 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 sar1 sar2 sma1 -0.6267 -0.3382 -0.2120 0.0928 -0.0079 0.0763 s.e. 0.0906 0.1014 0.0961 5.5023 0.8792 5.5163 sigma^2 estimated as 12.11: log likelihood = -344.34, aic = 702.68 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 sar1 sar2 sma1 -0.6266 -0.3380 -0.2113 0.0357 0 0.1335 s.e. 0.0899 0.1009 0.0949 0.6496 0 0.6436 sigma^2 estimated as 12.11: log likelihood = -344.34, aic = 700.68 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 sar1 sar2 sma1 -0.6265 -0.3375 -0.2092 0 0 0.1684 s.e. 0.0898 0.1004 0.0869 0 0 0.0956 sigma^2 estimated as 12.11: log likelihood = -344.34, aic = 698.68 [[3]][[5]] NULL [[3]][[6]] NULL $aic [1] 702.6820 700.6801 698.6831 699.6859 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 > postscript(file="/var/wessaorg/rcomp/tmp/11iw91386165378.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 = 130 Frequency = 1 [1] 0.003999997 0.826650685 2.332814184 -0.599213633 0.624553031 [6] -0.622443295 -2.674126140 2.582951221 1.616246461 4.855621877 [11] 5.228097109 2.575464425 -2.326727056 -4.107264602 -3.932584967 [16] -5.007001488 -0.738818459 -3.863860631 1.984924109 -1.853665126 [21] 5.362330290 -1.595570312 -2.263806344 5.349625406 1.086601378 [26] -0.543832137 0.987009633 -6.624167752 2.658288732 -0.117841762 [31] -0.315255286 7.390232868 -6.433920005 -1.135209909 0.851499042 [36] 5.518297917 2.957993581 -2.589636780 -1.882688152 1.346983870 [41] -5.031496945 4.562606945 -4.830917458 -1.939425581 0.727019833 [46] -2.096326884 4.520242980 -1.343655429 1.100911430 -4.277590216 [51] 2.605750645 -1.074781123 3.737781105 0.980156726 3.909473318 [56] -5.294799546 -0.330694439 0.786303531 3.915323921 1.195292494 [61] -0.377181685 -1.246259254 2.680734332 6.638215058 -2.854432000 [66] -5.527734965 0.647605561 -4.581376948 2.147749090 -3.979234434 [71] 0.014379397 1.325445572 2.158382542 8.299538850 -0.017676263 [76] -2.180147678 -4.240668332 -3.749291417 -1.294737242 0.223608703 [81] 7.766659671 2.890860004 -9.181691238 2.173331100 4.645472628 [86] -1.283609261 2.147227617 -3.182187837 -3.081801934 -3.135961378 [91] -0.209175679 2.331032976 -1.798280757 0.353722872 6.915908583 [96] 10.685412176 -3.873885980 1.697693569 -2.557304652 -0.085422497 [101] -4.403908869 -1.183213246 -1.318546949 -2.599120573 1.757238252 [106] 1.646633724 1.927719845 1.209506984 0.162983650 -0.782872515 [111] 2.964794189 -2.524653225 -1.751707275 1.850332262 -3.072910850 [116] 3.735192488 3.113901862 2.199948320 0.685333170 -0.283411933 [121] 0.844240411 -0.450917812 6.211823226 -6.318035714 -6.442617909 [126] 0.187276553 1.047076431 -6.070859876 2.264789983 1.234883888 > postscript(file="/var/wessaorg/rcomp/tmp/2qul81386165378.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/wessaorg/rcomp/tmp/32mg41386165378.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/wessaorg/rcomp/tmp/4hzbk1386165378.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/wessaorg/rcomp/tmp/57tj81386165378.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/wessaorg/rcomp/tmp/6aeap1386165378.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/wessaorg/rcomp/tmp/7owpi1386165378.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/8ll291386165378.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/wessaorg/rcomp/tmp/9rsop1386165378.tab") > > try(system("convert tmp/11iw91386165378.ps tmp/11iw91386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/2qul81386165378.ps tmp/2qul81386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/32mg41386165378.ps tmp/32mg41386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/4hzbk1386165378.ps tmp/4hzbk1386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/57tj81386165378.ps tmp/57tj81386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/6aeap1386165378.ps tmp/6aeap1386165378.png",intern=TRUE)) character(0) > try(system("convert tmp/7owpi1386165378.ps tmp/7owpi1386165378.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 12.133 3.338 15.507