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Type 'q()' to quit R. > x <- c(46,62,66,59,58,61,41,27,58,70,49,59,44,36,72,45,56,54,53,35,61,52,47,51,52,63,74,45,51,64,36,30,55,64,39,40,63,45,59,55,40,64,27,28,45,57,45,69,60,56,58,50,51,53,37,22,55,70,62,58,39,49,58,47,42,62,39,40,72,70,54,65) > par9 = '0' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '0' > par2 = '1.4' > par1 = 'FALSE' > par9 <- '0' > par8 <- '2' > par7 <- '1' > par6 <- '3' > par5 <- '12' > par4 <- '1' > par3 <- '0' > par2 <- '1.4' > 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,] 0.7752800 0.01683318 -0.2051241 -0.6839401 -0.6385386 -0.3213367 [2,] 0.7904692 0.00000000 -0.1968865 -0.6917066 -0.6380289 -0.3226673 [3,] 0.2739495 0.00000000 0.0000000 -0.1586949 -0.6111974 -0.3027255 [4,] 0.1125448 0.00000000 0.0000000 0.0000000 -0.6078439 -0.2999462 [5,] 0.0000000 0.00000000 0.0000000 0.0000000 -0.5829105 -0.2598183 [6,] 0.0000000 0.00000000 0.0000000 0.0000000 -0.4619620 0.0000000 [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,] 0.01689 0.92197 0.14096 0.02559 0.00004 0.04227 [2,] 0.00459 NA 0.07635 0.01598 0.00004 0.04064 [3,] 0.60964 NA NA 0.76778 0.00005 0.05147 [4,] 0.41046 NA NA NA 0.00005 0.05367 [5,] NA NA NA NA 0.00008 0.08278 [6,] NA NA NA NA 0.00025 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 ma1 sar1 sar2 0.7753 0.0168 -0.2051 -0.6839 -0.6385 -0.3213 s.e. 0.3162 0.1712 0.1376 0.2993 0.1442 0.1551 sigma^2 estimated as 3978: log likelihood = -336.79, aic = 687.58 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 0.7753 0.0168 -0.2051 -0.6839 -0.6385 -0.3213 s.e. 0.3162 0.1712 0.1376 0.2993 0.1442 0.1551 sigma^2 estimated as 3978: log likelihood = -336.79, aic = 687.58 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 0.7905 0 -0.1969 -0.6917 -0.6380 -0.3227 s.e. 0.2694 0 0.1094 0.2797 0.1438 0.1545 sigma^2 estimated as 3978: log likelihood = -336.79, aic = 685.59 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 0.2739 0 0 -0.1587 -0.6112 -0.3027 s.e. 0.5340 0 0 0.5353 0.1408 0.1527 sigma^2 estimated as 4189: log likelihood = -337.99, aic = 685.99 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 0.1125 0 0 0 -0.6078 -0.2999 s.e. 0.1359 0 0 0 0.1401 0.1528 sigma^2 estimated as 4199: log likelihood = -338.03, aic = 684.06 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 0 0 0 0 -0.5829 -0.2598 s.e. 0 0 0 0 0.1393 0.1476 sigma^2 estimated as 4295: log likelihood = -338.37, aic = 682.75 $aic [1] 687.5771 685.5867 685.9857 684.0646 682.7466 683.5833 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/fisher/rcomp/tmp/19hht1384809308.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 = 72 Frequency = 1 [1] 0.2127456 0.3231083 0.3526641 0.3014342 0.2943058 [6] 0.3158359 0.1810911 0.1009041 0.2943058 0.3829455 [11] 0.2324204 0.3014342 -10.9885569 -147.3829021 39.1110015 [16] -81.4425159 -12.0783513 -42.4167899 67.0464277 37.8428419 [21] 18.4314513 -111.5995316 -11.2759437 -47.6190107 45.1295568 [26] 96.3949213 35.4549809 -42.5067325 -39.5106000 46.9122254 [31] -69.7450856 -7.4491178 -31.5356325 24.0379786 -54.5570371 [36] -93.2909029 105.2135965 -64.2380160 -91.5430828 42.1999755 [41] -94.5820429 28.8081776 -92.9181286 -15.7008914 -86.1670452 [46] -34.7676599 4.6506970 144.6067800 37.2453324 48.1742145 [51] -68.6546404 4.8782078 20.6251675 -59.8056977 -1.4059183 [56] -44.0178167 16.8375159 88.3821248 125.5456579 17.3818754 [61] -132.2571038 -36.9514982 -33.3829833 -22.3470579 -35.6064434 [66] 18.0077389 31.6056389 78.6548876 146.7542236 42.6573284 [71] 20.9997316 55.7429010 > postscript(file="/var/fisher/rcomp/tmp/2higf1384809308.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/3kt561384809308.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/4fp9z1384809308.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/5gwsj1384809308.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/6us721384809308.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/7xdj31384809308.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/86fyz1384809308.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/9lnk71384809308.tab") > > try(system("convert tmp/19hht1384809308.ps tmp/19hht1384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/2higf1384809308.ps tmp/2higf1384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/3kt561384809308.ps tmp/3kt561384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/4fp9z1384809308.ps tmp/4fp9z1384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/5gwsj1384809308.ps tmp/5gwsj1384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/6us721384809308.ps tmp/6us721384809308.png",intern=TRUE)) character(0) > try(system("convert tmp/7xdj31384809308.ps tmp/7xdj31384809308.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 8.178 1.493 9.651