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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 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '0' > par2 = '1.4' > par1 = 'FALSE' > par9 <- '1' > 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,] 0.7866985 0.05425570 -0.2307952 -0.6909556 -0.02209875 -0.04133627 [2,] 0.7833475 0.05275323 -0.2263444 -0.6914309 0.00000000 -0.03136478 [3,] 0.7728712 0.05373962 -0.2265600 -0.6828141 0.00000000 0.00000000 [4,] 0.8171547 0.00000000 -0.2012257 -0.7033161 0.00000000 0.00000000 [5,] 0.3548999 0.00000000 0.0000000 -0.2352164 0.00000000 0.00000000 [6,] 0.1135031 0.00000000 0.0000000 0.0000000 0.00000000 0.00000000 [7,] 0.0000000 0.00000000 0.0000000 0.0000000 0.00000000 0.00000000 [8,] 0.0000000 0.00000000 0.0000000 0.0000000 0.00000000 0.00000000 [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,] -0.9998907 [2,] -1.0000394 [3,] -1.0000108 [4,] -0.9999389 [5,] -1.0009368 [6,] -1.0000988 [7,] -0.9997896 [8,] 0.0000000 [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.00959 0.74888 0.10822 0.01518 0.9023 0.82059 0.01824 [2,] 0.01032 0.75441 0.10232 0.01642 NA 0.84853 0.00825 [3,] 0.00987 0.74778 0.10046 0.01599 NA NA 0.00610 [4,] 0.00116 NA 0.07238 0.00569 NA NA 0.00763 [5,] 0.46319 NA NA 0.63064 NA NA 0.02103 [6,] 0.38208 NA NA NA NA NA 0.03556 [7,] NA NA NA NA NA NA 0.18594 [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 0.7867 0.0543 -0.2308 -0.6910 -0.0221 -0.0413 -0.9999 s.e. 0.2946 0.1688 0.1417 0.2769 0.1793 0.1815 0.4127 sigma^2 estimated as 2769: log likelihood = -334.32, aic = 684.65 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7867 0.0543 -0.2308 -0.6910 -0.0221 -0.0413 -0.9999 s.e. 0.2946 0.1688 0.1417 0.2769 0.1793 0.1815 0.4127 sigma^2 estimated as 2769: log likelihood = -334.32, aic = 684.65 [[3]][[3]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7833 0.0528 -0.2263 -0.6914 0 -0.0314 -1.0000 s.e. 0.2965 0.1679 0.1366 0.2807 0 0.1636 0.3669 sigma^2 estimated as 2798: log likelihood = -334.33, aic = 682.66 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7729 0.0537 -0.2266 -0.6828 0 0 -1.0000 s.e. 0.2909 0.1664 0.1360 0.2761 0 0 0.3529 sigma^2 estimated as 2824: log likelihood = -334.35, aic = 680.7 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.8172 0 -0.2012 -0.7033 0 0 -0.9999 s.e. 0.2408 0 0.1102 0.2462 0 0 0.3634 sigma^2 estimated as 2829: log likelihood = -334.4, aic = 678.8 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.3549 0 0 -0.2352 0 0 -1.0009 s.e. 0.4810 0 0 0.4870 0 0 0.4237 sigma^2 estimated as 2953: log likelihood = -335.64, aic = 679.27 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1135 0 0 0 0 0 -1.0001 s.e. 0.1290 0 0 0 0 0 0.4665 sigma^2 estimated as 2965: log likelihood = -335.74, aic = 677.47 [[3]][[8]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0 0 0 0 0 0 -0.9998 s.e. 0 0 0 0 0 0 0.7485 sigma^2 estimated as 3005: log likelihood = -336.12, aic = 676.24 $aic [1] 684.6480 682.6630 680.6995 678.8019 679.2741 677.4715 676.2403 693.4610 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 7: In max(i) : no non-missing arguments to max; returning -Inf 8: In max(i) : no non-missing arguments to max; returning -Inf 9: In max(try.data.frame[, 4], na.rm = TRUE) : no non-missing arguments to max; returning -Inf > postscript(file="/var/wessaorg/rcomp/tmp/1kgay1386152126.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 0.3231082 0.3526640 0.3014341 0.2943058 [6] 0.3158358 0.1810910 0.1009041 0.2943058 0.3829454 [11] 0.2324203 0.3014341 -9.0773286 -121.7494055 32.3087546 [16] -67.2776355 -9.9775604 -35.0394131 55.3854972 31.2610927 [21] 15.2258577 -92.1896035 -9.3147268 -39.3368470 37.7716104 [26] 76.2692117 31.3733828 -38.8427728 -33.8408455 38.1607171 [31] -56.5921879 -4.9524909 -26.0113335 16.3558588 -46.5359194 [36] -80.5834385 94.1310737 -53.5794871 -75.2479032 30.4926584 [41] -85.3119258 26.9837040 -83.3593177 -12.8274567 -76.3514404 [46] -32.2318628 -0.4669312 116.5634059 53.3981168 24.6005327 [51] -64.6632379 -6.9095199 -2.6864187 -49.2149568 -14.5258282 [56] -37.1502689 0.7178616 60.6560419 104.1267206 17.8309590 [61] -84.0017898 -23.5319326 -52.7973109 -23.7543504 -55.6060547 [66] 17.9710412 -0.9077576 60.2207856 114.8289621 49.5254493 [71] 33.1436962 61.0291520 > postscript(file="/var/wessaorg/rcomp/tmp/28y7g1386152126.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/3eo2d1386152126.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/45v3g1386152126.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/50iwy1386152126.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/6h2vq1386152126.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/70o1v1386152126.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/86nrz1386152126.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/93kh01386152126.tab") > > try(system("convert tmp/1kgay1386152126.ps tmp/1kgay1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/28y7g1386152126.ps tmp/28y7g1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/3eo2d1386152126.ps tmp/3eo2d1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/45v3g1386152126.ps tmp/45v3g1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/50iwy1386152126.ps tmp/50iwy1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/6h2vq1386152126.ps tmp/6h2vq1386152126.png",intern=TRUE)) character(0) > try(system("convert tmp/70o1v1386152126.ps tmp/70o1v1386152126.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 24.612 6.275 30.916