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Type 'q()' to quit R. > x <- c(68.897,38.683,44.720,39.525,45.315,50.380,40.600,36.279,42.438,38.064,31.879,11.379,70.249,39.253,47.060,41.697,38.708,49.267,39.018,32.228,40.870,39.383,34.571,12.066,70.938,34.077,45.409,40.809,37.013,44.953,37.848,32.745,43.412,34.931,33.008,8.620,68.906,39.556,50.669,36.432,40.891,48.428,36.222,33.425,39.401,37.967,34.801,12.657,69.116,41.519,51.321,38.529,41.547,52.073,38.401,40.898,40.439,41.888,37.898,8.771,68.184,50.530,47.221,41.756,45.633,48.138,39.486,39.341,41.117,41.629,29.722,7.054,56.676,34.870,35.117,30.169,30.936,35.699,33.228,27.733,33.666,35.429,27.438,8.170,63.410,38.040,45.389,37.353,37.024,50.957,37.994,36.454,46.080,43.373,37.395,10.963,76.058,50.179,57.452,47.568,50.050,50.856,41.992,39.284,44.521,43.832,41.153,17.100) > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '1' > par1 = 'FALSE' > 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,] -0.3557028 -0.08065492 0.1528701 -0.2722908 0.1764863 -0.05337912 [2,] -0.2341332 0.00000000 0.1862263 -0.3954020 0.1756336 -0.05244445 [3,] -0.2552256 0.00000000 0.1936715 -0.3790880 0.1783715 0.00000000 [4,] -0.3010869 0.00000000 0.1996238 -0.3649927 0.0000000 0.00000000 [5,] 0.0000000 0.00000000 0.2259998 -0.5963710 0.0000000 0.00000000 [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 [13,] NA NA NA NA NA NA [14,] NA NA NA NA NA NA [,7] [1,] -0.9999404 [2,] -1.0000178 [3,] -1.0000331 [4,] -0.7870096 [5,] -0.8236037 [6,] NA [7,] NA [8,] NA [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.59945 0.8556 0.48792 0.68833 0.15940 0.67324 0.13585 [2,] 0.19539 NA 0.06819 0.02483 0.16125 0.67978 0.16491 [3,] 0.12973 NA 0.05116 0.02419 0.15662 NA 0.00353 [4,] 0.05652 NA 0.04185 0.02274 NA NA 0.00000 [5,] NA NA 0.03582 0.00000 NA NA 0.00000 [6,] NA NA NA NA NA NA NA [7,] NA NA NA NA NA NA NA [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 -0.3557 -0.0807 0.1529 -0.2723 0.1765 -0.0534 -0.9999 s.e. 0.6751 0.4421 0.2196 0.6768 0.1245 0.1262 0.6651 sigma^2 estimated as 9.62: log likelihood = -254.43, aic = 524.87 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.3557 -0.0807 0.1529 -0.2723 0.1765 -0.0534 -0.9999 s.e. 0.6751 0.4421 0.2196 0.6768 0.1245 0.1262 0.6651 sigma^2 estimated as 9.62: log likelihood = -254.43, aic = 524.87 [[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 -0.2341 0 0.1862 -0.3954 0.1756 -0.0524 -1.0000 s.e. 0.1796 0 0.1010 0.1736 0.1245 0.1267 0.7149 sigma^2 estimated as 9.623: log likelihood = -254.45, aic = 522.9 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.2552 0 0.1937 -0.3791 0.1784 0 -1.0000 s.e. 0.1671 0 0.0981 0.1657 0.1250 0 0.3348 sigma^2 estimated as 9.763: log likelihood = -254.54, aic = 521.07 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 -0.3011 0 0.1996 -0.3650 0 0 -0.7870 s.e. 0.1561 0 0.0969 0.1578 0 0 0.1478 sigma^2 estimated as 11.13: log likelihood = -255.26, aic = 520.53 [[3]][[6]] NULL [[3]][[7]] NULL $aic [1] 524.8690 522.9028 521.0706 520.5254 521.4577 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 > postscript(file="/var/wessaorg/rcomp/tmp/17ev21355573897.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 = 108 Frequency = 1 [1] 3.977768e-02 -5.614523e-03 1.426622e-03 -3.518223e-03 2.430687e-03 [6] 6.681567e-03 -3.382928e-03 -7.017150e-03 -4.090756e-04 -4.528548e-03 [11] -1.002593e-02 -6.091856e-02 -1.223179e-01 -4.941493e-01 1.009049e+00 [16] 6.371648e-01 -6.585342e+00 -4.399353e-01 8.086920e-01 -4.040211e-01 [21] 3.768625e-01 3.094535e+00 3.175976e+00 -3.752872e-01 -1.110345e+00 [26] -5.945602e+00 4.143967e-01 1.842645e+00 -2.584392e+00 -3.074341e+00 [31] 1.424078e+00 2.632429e+00 3.956588e+00 -3.112973e+00 2.913657e-01 [36] -2.056466e+00 1.111056e+00 3.590850e+00 5.173098e+00 -6.335456e+00 [41] -8.506171e-01 2.818852e-01 -1.317469e+00 9.289992e-02 -1.632669e+00 [46] 2.611281e+00 2.296328e+00 2.144149e+00 -2.507611e+00 2.196390e+00 [51] 2.395084e+00 -3.283482e+00 -1.460425e+00 2.626612e+00 -8.965159e-01 [56] 5.063092e+00 -4.606505e+00 1.808050e+00 6.559702e-01 -4.548101e+00 [61] -3.834779e+00 1.164989e+01 -3.158888e+00 -1.492996e+00 3.189358e-01 [66] -2.564849e+00 -1.211226e+00 2.318961e+00 -9.894907e-01 9.739818e-01 [71] -7.134996e+00 -2.622987e+00 -1.021750e+01 7.888083e-01 -4.347191e+00 [76] 1.635030e+00 -8.452021e-01 -1.750339e+00 5.830869e+00 1.402654e+00 [81] 1.183815e+00 2.698171e+00 5.768071e-01 3.903310e+00 6.560898e-01 [86] 1.082284e+00 2.133435e+00 1.209898e+00 -1.978392e+00 5.535423e+00 [91] -4.536143e-02 4.299496e-01 3.710178e+00 1.849005e+00 2.376955e-01 [96] -4.300436e+00 6.370358e+00 5.012148e+00 4.372959e+00 -1.880791e+00 [101] -2.238330e-01 -7.425099e+00 -3.804571e+00 -1.534310e+00 9.478000e-02 [106] 2.984636e-01 3.890391e+00 2.238504e+00 > postscript(file="/var/wessaorg/rcomp/tmp/2aozo1355573897.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/3z1bq1355573897.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/4mzjw1355573897.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/5irbh1355573897.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/6lrgy1355573897.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/7l5x41355573897.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/88ibz1355573897.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/97nxa1355573897.tab") > > try(system("convert tmp/17ev21355573897.ps tmp/17ev21355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/2aozo1355573897.ps tmp/2aozo1355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/3z1bq1355573897.ps tmp/3z1bq1355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/4mzjw1355573897.ps tmp/4mzjw1355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/5irbh1355573897.ps tmp/5irbh1355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/6lrgy1355573897.ps tmp/6lrgy1355573897.png",intern=TRUE)) character(0) > try(system("convert tmp/7l5x41355573897.ps tmp/7l5x41355573897.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 14.172 2.516 16.675