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Data:
358.59 362.96 362.42 364.97 364.04 361.06 358.48 352.96 359.59 360.39 357.40 362.93 364.55 365.73 364.70 364.65 359.43 362.14 356.97 354.82 353.17 357.06 356.18 355.01 355.65 357.31 357.07 357.91 358.48 358.97 351.77 352.16 359.08 360.35 359.53 359.30 358.41 359.68 355.31 357.08 349.71 354.13 345.49 341.69 344.25 340.17 342.47 344.43 333.23 339.72 342.61 346.36 339.09 339.73 341.12 335.94 333.46 335.66 341.12 342.21 342.62 346.06 344.43 346.65 343.74 335.67 342.75 341.77 345.84 346.52 350.79 345.44 345.87 338.48 337.21 340.81 339.86 342.86 343.33 341.73 351.38 351.13 345.99 347.55 346.02 345.29 347.03 348.01 345.48 349.40 351.05 349.70 350.86 354.45 355.30 357.48 355.24 351.79 355.22 351.02 350.28 350.17 348.16 340.30 343.75 344.71 344.13 342.14 345.04 346.02 346.43 347.07 339.33 339.10 337.19 339.58 327.85 326.81 321.73 320.45 327.69 323.95 320.47 322.13 316.34 314.78 308.90 308.62 314.41 306.88 310.60 321.60 321.50 325.68 324.35 320.01 326.88 332.39 331.48 332.62 324.79 327.12 328.91 328.37 324.83 325.90 326.18 328.94 333.78 328.06 325.87 325.41 318.86 319.13 310.16 311.73 306.54 311.16 311.98 306.72 308.05 300.76 301.90 293.09 292.76 294.58 289.90 296.69 297.21 293.31 296.25 298.60 296.87 301.02 304.73 301.92 295.72 293.18 298.35 297.99 299.85 299.85 304.45 299.45 298.14 298.78 297.02 301.33 294.96 296.69 300.73 301.96 297.38 293.87 285.96 285.41 283.70 284.76 277.11 274.73 274.73 274.73 274.73 274.69 275.42 264.15 276.24 268.88 277.97 280.49 281.09 276.16 272.58 270.94 284.31 283.94 284.18 282.83 283.84 282.71 279.29 280.70 274.47 273.44 275.49 279.46 280.19 288.21 284.80 281.41 283.39 287.97 290.77 290.60 289.67 289.84 298.55 296.07 297.14 295.34 296.25 294.30 296.15 296.49 298.05 301.03 300.52 301.50 296.93 289.84 291.44 286.88 286.74 288.93 292.19 295.39 295.86 293.36 292.86 292.73 296.73 285.02 285.24 288.62 283.36 285.84 291.48 291.41 287.77 284.97 286.05 278.19 281.21 277.92 280.08 269.24 268.48 268.83 269.54 262.37 265.12 265.34 263.32 267.18 260.75 261.78 257.27 255.63 251.39 259.49 261.18 261.65 262.01 265.23 268.10 262.27 263.59 257.85 265.69 271.15 266.69 265.77 262.32 270.48 273.03 269.13 280.65 282.75 281.44 281.99 282.86 287.21 283.11 280.66 282.39 280.83 284.71 279.99 283.50 284.88 288.60 284.80 287.20 286.22 286.54 279.58 283.08 288.88 280.18 284.16 290.57 286.82 273.00 278.69 264.54 271.92 283.60 269.25 263.58 264.16 268.85 269.67 249.41 268.99 268.65 260.16 256.55 251.47 234.93 232.96 215.49 213.68 236.07 235.41 214.77 225.85 224.64 238.26 232.44 222.50 225.28 220.49 216.86 234.70 230.06 238.27 238.56 242.70 249.14 234.89 227.78 234.04 230.70 230.17 218.23 232.20 220.76 215.60 217.69 204.35 191.44 203.84 211.86 210.57 219.57 219.98 226.01 207.04 212.52 217.92 210.45 218.53 223.32 218.76 217.63
Include mean?
FALSE
FALSE
TRUE
Box-Cox lambda transformation parameter (lambda)
1
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)
1
0
1
2
Degree of seasonal differencing (D)
0
0
1
Seasonal Period (s)
1
1
2
3
4
6
12
Maximum AR(p) order
3
0
1
2
3
Maximum MA(q) order
1
0
1
Maximum SAR(P) order
2
0
1
2
Maximum SMA(Q) order
1
0
1
Chart options
R Code
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,'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='mytable1.tab')
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Raw Output
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Computing time
0 seconds
R Server
Big Analytics Cloud Computing Center
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