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Data:
62.4 67.4 76.1 67.4 74.5 72.6 60.5 66.1 76.5 76.8 77 71 74.8 73.7 80.5 71.8 76.9 79.9 65.9 69.5 75.1 79.6 75.2 68 72.8 71.5 78.5 76.8 75.3 76.7 69.7 67.8 77.5 82.5 75.3 70.9 76 73.7 79.7 77.8 73.3 78.3 71.9 67 82 83.7 74.8 80 74.3 76.8 89 81.9 76.8 88.9 75.8 75.5 89.1 88 85.9 89.3 82.9 81.2 90.5 86.4 81.8 91.3 73.4 76.6 91 87 89.7 90.7 86.5 86.6 98.8 84.4 91.4 95.7 78.5 81.7 94.3 98.5 95.4 91.7 92.8 90.5 102.2 91.8 95 102 88.9 89.6 97.9 108.6 100.8 95.1 101 100.9 102.5 105.4 98.4 105.3 96.5 88.1 107.9 107 92.5 95.7 85.2 85.5 94.7 86.2 88.8 93.4 83.4 82.9 96.7 96.2 92.8 92.8 90 95.4 108.3 96.3 95 109 92 92.3 107 105.5 105.4 103.9 99.2 102.2 121.5 102.3 110 105.9 91.9 100 111.7 104.9 103.3 101.8 100.8 104.2 116.5 97.9 100.7 107 96.3 96 104.5 107.4 102.4 94.9 98.8 96.8 108.2 103.8 102.3 107.2 102 92.6 105.2 113 105.6 101.6 101.7 102.7 109 105.5 103.3 108.6 98.2 90 112.4 111.9 102.1 102.4 101.7 98.7 114 105.1 98.3 110 96.5 92.2 112 111.4 107.5 103.4 103.5 107.4 117.6 110.2 104.3 115.9 98.9 101.9 113.5 109.5 110 114.2 106.9 109.2 124.2 104.7 111.9 119 102.9 106.3
Include mean?
112001150013313112additive121212FALSEFALSEFALSEFALSEFALSE
FALSE
TRUE
Box-Cox lambda transformation parameter (lambda)
Do not include Seasonal DummiesDo not include Seasonal Dummies5Do not include Seasonal DummiesDo not include Seasonal Dummies12Do not include Seasonal Dummies11Do not include Seasonal Dummies1Do not include Seasonal DummiesSingle12TripleTripleDouble11111
1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Degree of non-seasonal differencing (d)
No Linear TrendNo Linear Trend0No Linear TrendNo Linear Trend5No Linear Trend22No Linear Trend2No Linear Trendadditiveadditivemultiplicativeadditive00000
0
1
2
Degree of seasonal differencing (D)
00P1 P5 Q1 Q3 P95 P9900P1 P5 Q1 Q3 P95 P99P1 P5 Q1 Q3 P95 P990TRUE0TRUE1212121211111
0
1
Seasonal Period (s)
00001212121212
1
2
3
4
6
12
Maximum AR(p) order
1212121230330
0
1
2
3
Maximum MA(q) order
11111
0
1
Maximum SAR(P) order
22212
0
1
2
Maximum SMA(Q) order
11111
0
1
Chart options
R Code
par9 <- '1' par8 <- '1' 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]]$res par(mar=c(1,2,4,1)) acf(residus,main='') title('acf',line=.5) par(mar=c(1,2,4,1)) pacf(residus,main='') title('pacf',line=.5) par(mar=c(2,2,4,1)) qqnorm(residus,main='') title('qq-norm',line=.5) qqline(residus) residus } if (par2 == 0) x <- log(x) if (par2 != 0) x <- x^par2 (selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5))) bitmap(file='test1.png') resid <- arimaSelectplot(selection) dev.off() resid bitmap(file='test2.png') acf(resid,length(resid)/2, main='Residual Autocorrelation Function') dev.off() bitmap(file='test3.png') pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function') dev.off() bitmap(file='test4.png') cpgram(resid, main='Residual Cumulative Periodogram') dev.off() bitmap(file='test5.png') hist(resid, main='Residual Histogram', xlab='values of Residuals') dev.off() bitmap(file='test6.png') densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test7.png') qqnorm(resid, main='Residual Normal Q-Q Plot') qqline(resid) dev.off() ncols <- length(selection[[1]][1,]) nrows <- length(selection[[2]][,1])-1 load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Iteration', header=TRUE) for (i in 1:ncols) { a<-table.element(a,names(selection[[3]][[1]]$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='mytable.tab') a <-table.start() a <- table.row.start(a) a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE) a <- table.row.end(a) a <- table.row.start(a) a <- table.element(a,'Description',1,TRUE) a <- table.element(a,'Link',1,TRUE) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Histogram',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Central Tendency',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'QQ Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Kernel Density Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Spectral Analysis',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a <- table.row.start(a) a <- table.element(a,'Summary Statistics',1,header=TRUE) a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1) a <- table.row.end(a) a<-table.end(a) table.save(a,file='mytable7.tab')
Compute
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Raw Input
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Raw Output
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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