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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' > 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,] 0.7774345 0.06792064 -0.2379196 -0.6726655 -0.04168148 -0.05970800 [2,] 0.7703582 0.06495301 -0.2299208 -0.6724213 0.00000000 -0.04068115 [3,] 0.7573497 0.06618212 -0.2304213 -0.6613219 0.00000000 0.00000000 [4,] 0.8160662 0.00000000 -0.1998839 -0.6913504 0.00000000 0.00000000 [5,] 0.3729823 0.00000000 0.0000000 -0.2472642 0.00000000 0.00000000 [6,] 0.1176110 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,] -0.9999193 [2,] -0.9999628 [3,] -0.9999771 [4,] -1.0003278 [5,] -0.9972995 [6,] -0.9990820 [7,] -1.0000097 [8,] 0.0000000 [9,] NA [10,] NA [11,] NA [12,] NA [13,] NA [14,] NA [[2]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0.01522 0.68869 0.09626 0.02696 0.81485 0.74175 0.01467 [2,] 0.01852 0.69937 0.09513 0.03180 NA 0.80459 0.00351 [3,] 0.01795 0.69062 0.09259 0.03106 NA NA 0.00235 [4,] 0.00173 NA 0.07329 0.00888 NA NA 0.00315 [5,] 0.41830 NA NA 0.59627 NA NA 0.00827 [6,] 0.36459 NA NA NA NA NA 0.01439 [7,] NA NA NA NA NA NA 0.05766 [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 0.7774 0.0679 -0.2379 -0.6727 -0.0417 -0.0597 -0.9999 s.e. 0.3117 0.1688 0.1409 0.2971 0.1773 0.1804 0.3986 sigma^2 estimated as 59.18: log likelihood = -219.3, aic = 454.6 [[3]][[2]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7774 0.0679 -0.2379 -0.6727 -0.0417 -0.0597 -0.9999 s.e. 0.3117 0.1688 0.1409 0.2971 0.1773 0.1804 0.3986 sigma^2 estimated as 59.18: log likelihood = -219.3, aic = 454.6 [[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 0.7704 0.0650 -0.2299 -0.6724 0 -0.0407 -1.00 s.e. 0.3189 0.1675 0.1358 0.3065 0 0.1638 0.33 sigma^2 estimated as 60.38: log likelihood = -219.33, aic = 452.65 [[3]][[4]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.7573 0.0662 -0.2304 -0.6613 0 0 -1.000 s.e. 0.3120 0.1656 0.1350 0.3001 0 0 0.316 sigma^2 estimated as 61.13: log likelihood = -219.36, aic = 450.71 [[3]][[5]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.8161 0 -0.1999 -0.6914 0 0 -1.0003 s.e. 0.2500 0 0.1099 0.2565 0 0 0.3265 sigma^2 estimated as 61.26: log likelihood = -219.43, aic = 448.87 [[3]][[6]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.373 0 0 -0.2473 0 0 -0.9973 s.e. 0.458 0 0 0.4645 0 0 0.3666 sigma^2 estimated as 64.18: log likelihood = -220.67, aic = 449.34 [[3]][[7]] Call: arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, fixed = last.arma$next.vector, method = "ML") Coefficients: ar1 ar2 ar3 ma1 sar1 sar2 sma1 0.1176 0 0 0 0 0 -0.9991 s.e. 0.1289 0 0 0 0 0 0.3979 sigma^2 estimated as 64.33: log likelihood = -220.79, aic = 447.58 [[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 -1.0000 s.e. 0 0 0 0 0 0 0.5181 sigma^2 estimated as 65.18: log likelihood = -221.2, aic = 446.4 $aic [1] 454.5968 452.6511 450.7124 448.8682 449.3365 447.5762 446.4033 464.1784 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 log(s2) : NaNs produced 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 arima(series, order = order, seasonal = seasonal, include.mean = include.mean, : some AR parameters were fixed: setting transform.pars = FALSE 8: In max(i) : no non-missing arguments to max; returning -Inf 9: In max(i) : no non-missing arguments to max; returning -Inf 10: In max(try.data.frame[, 4], na.rm = TRUE) : no non-missing arguments to max; returning -Inf > postscript(file="/var/wessaorg/rcomp/tmp/1mc361386079603.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] 4.599995e-02 6.199994e-02 6.599993e-02 5.899994e-02 5.799994e-02 [6] 6.099994e-02 4.099996e-02 2.699997e-02 5.799994e-02 6.999993e-02 [11] 4.899995e-02 5.899994e-02 -1.414175e+00 -1.838465e+01 4.242668e+00 [16] -9.899408e+00 -1.414166e+00 -4.949681e+00 8.485271e+00 5.656847e+00 [21] 2.121352e+00 -1.272781e+01 -1.414172e+00 -5.656786e+00 5.715467e+00 [26] 1.143092e+01 4.082492e+00 -5.715427e+00 -4.898933e+00 5.307226e+00 [31] -8.981400e+00 -8.164800e-01 -3.674193e+00 2.449503e+00 -7.348414e+00 [36] -1.224737e+01 1.356768e+01 -7.505502e+00 -1.010356e+01 4.618794e+00 [41] -1.299030e+01 3.752776e+00 -1.414500e+01 -2.309381e+00 -1.125826e+01 [46] -4.330088e+00 1.299087e-05 1.645442e+01 7.826211e+00 4.024914e+00 [51] -8.720608e+00 -8.944115e-01 -2.235943e-01 -6.931764e+00 -2.012443e+00 [56] -7.155376e+00 2.236180e-01 8.273425e+00 1.520520e+01 2.906887e+00 [61] -1.278012e+01 -3.103737e+00 -7.120347e+00 -3.468883e+00 -8.398362e+00 [66] 2.556037e+00 1.825804e-01 1.058926e+01 1.570131e+01 6.755224e+00 [71] 5.112061e+00 8.763529e+00 > postscript(file="/var/wessaorg/rcomp/tmp/2odba1386079603.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/353pc1386079603.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/443dq1386079603.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/5thwh1386079603.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/6po2c1386079603.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/7ncv81386079603.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/8o1ci1386079603.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/96k9t1386079603.tab") > > try(system("convert tmp/1mc361386079603.ps tmp/1mc361386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/2odba1386079603.ps tmp/2odba1386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/353pc1386079603.ps tmp/353pc1386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/443dq1386079603.ps tmp/443dq1386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/5thwh1386079603.ps tmp/5thwh1386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/6po2c1386079603.ps tmp/6po2c1386079603.png",intern=TRUE)) character(0) > try(system("convert tmp/7ncv81386079603.ps tmp/7ncv81386079603.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 20.711 6.848 27.522