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Type 'q()' to quit R. > x <- c(164,96,73,49,39,59,169,169,210,278,298,245,200,188,90,79,78,91,167,169,289,247,275,203,223,104,107,85,75,99,135,211,335,488,326,346,261,224,141,148,145,223,272,445,560,612,467,404,518,404,300,210,196,186,247,343,464,680,711,610,513,292,273,322,189,257,324,404,677,858,895,664,628,308,324,248,272) > par10 = 'FALSE' > par9 = '0' > par8 = '1' > par7 = '1' > par6 = '2' > par5 = '12' > par4 = '1' > par3 = '0' > par2 = '0.0' > par1 = '12' > par10 <- 'FALSE' > par9 <- '0' > par8 <- '1' > par7 <- '1' > par6 <- '2' > par5 <- '12' > par4 <- '1' > par3 <- '0' > par2 <- '0.0' > par1 <- '12' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 () > #Author: root > #To cite this work: Wessa P., (2013), ARIMA Forecasting (v1.0.9) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/ > #Source of accompanying publication: > # > par1 <- as.numeric(par1) #cut off periods > par2 <- as.numeric(par2) #lambda > 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) #p > par7 <- as.numeric(par7) #q > par8 <- as.numeric(par8) #P > par9 <- as.numeric(par9) #Q > if (par10 == 'TRUE') par10 <- TRUE > if (par10 == 'FALSE') par10 <- FALSE > if (par2 == 0) x <- log(x) > if (par2 != 0) x <- x^par2 > lx <- length(x) > first <- lx - 2*par1 > nx <- lx - par1 > nx1 <- nx + 1 > fx <- lx - nx > if (fx < 1) { + fx <- par5 + nx1 <- lx + fx - 1 + first <- lx - 2*fx + } > first <- 1 > if (fx < 3) fx <- round(lx/10,0) > (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML')) Call: arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, par4, par9), period = par5), include.mean = par10, method = "ML") Coefficients: ar1 ar2 ma1 sar1 0.1830 0.6183 0.4297 -0.5251 s.e. 0.4014 0.3065 0.4962 0.1349 sigma^2 estimated as 0.06029: log likelihood = -3.27, aic = 16.54 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 66 End = 77 Frequency = 1 [1] 5.558974 5.678933 6.143331 6.343070 6.590308 6.433134 6.289434 6.316176 [9] 5.917288 5.715596 5.603772 5.305663 $se Time Series: Start = 66 End = 77 Frequency = 1 [1] 0.2455319 0.2879552 0.3392384 0.3618270 0.3858150 0.3991518 0.4118618 [8] 0.4199152 0.4270532 0.4319468 0.4360860 0.4390648 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 66 End = 77 Frequency = 1 [1] 5.077731 5.114540 5.478424 5.633889 5.834110 5.650796 5.482185 5.493142 [9] 5.080263 4.868980 4.749043 4.445096 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 66 End = 77 Frequency = 1 [1] 6.040216 6.243325 6.808238 7.052251 7.346505 7.215471 7.096683 7.139210 [9] 6.754312 6.562211 6.458500 6.166230 > if (par2 == 0) { + x <- exp(x) + forecast$pred <- exp(forecast$pred) + lb <- exp(lb) + ub <- exp(ub) + } > if (par2 != 0) { + x <- x^(1/par2) + forecast$pred <- forecast$pred^(1/par2) + lb <- lb^(1/par2) + ub <- ub^(1/par2) + } > if (par2 < 0) { + olb <- lb + lb <- ub + ub <- olb + } > (actandfor <- c(x[1:nx], forecast$pred)) [1] 164.0000 96.0000 73.0000 49.0000 39.0000 59.0000 169.0000 169.0000 [9] 210.0000 278.0000 298.0000 245.0000 200.0000 188.0000 90.0000 79.0000 [17] 78.0000 91.0000 167.0000 169.0000 289.0000 247.0000 275.0000 203.0000 [25] 223.0000 104.0000 107.0000 85.0000 75.0000 99.0000 135.0000 211.0000 [33] 335.0000 488.0000 326.0000 346.0000 261.0000 224.0000 141.0000 148.0000 [41] 145.0000 223.0000 272.0000 445.0000 560.0000 612.0000 467.0000 404.0000 [49] 518.0000 404.0000 300.0000 210.0000 196.0000 186.0000 247.0000 343.0000 [57] 464.0000 680.0000 711.0000 610.0000 513.0000 292.0000 273.0000 322.0000 [65] 189.0000 259.5563 292.6369 465.6019 568.5389 728.0047 622.1204 538.8482 [73] 553.4524 371.4029 303.5650 271.4484 201.4746 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 66 End = 77 Frequency = 1 [1] 0.3153489 0.3869279 0.4817909 0.5266968 0.5766125 0.6053967 0.6335371 [8] 0.6517338 0.6681042 0.6794603 0.6891511 0.6961740 > postscript(file="/var/fisher/rcomp/tmp/15fy61386839133.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mar=c(4,4,2,2),las=1) > ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) > plot(x,ylim=ylim,type='n',xlim=c(first,lx)) > usr <- par('usr') > rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') > rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') > abline(h= (-3:3)*2 , col ='gray', lty =3) > polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) > lines(nx1:lx, lb , lty=2) > lines(nx1:lx, ub , lty=2) > lines(x, lwd=2) > lines(nx1:lx, forecast$pred , lwd=2 , col ='white') > box() > par(opar) > dev.off() null device 1 > prob.dec <- array(NA, dim=fx) > prob.sdec <- array(NA, dim=fx) > prob.ldec <- array(NA, dim=fx) > prob.pval <- array(NA, dim=fx) > perf.pe <- array(0, dim=fx) > perf.spe <- array(0, dim=fx) > perf.scalederr <- array(0, dim=fx) > perf.mase <- array(0, dim=fx) > perf.mase1 <- array(0, dim=fx) > perf.mape <- array(0, dim=fx) > perf.smape <- array(0, dim=fx) > perf.mape1 <- array(0, dim=fx) > perf.smape1 <- array(0,dim=fx) > perf.se <- array(0, dim=fx) > perf.mse <- array(0, dim=fx) > perf.mse1 <- array(0, dim=fx) > perf.rmse <- array(0, dim=fx) > perf.scaleddenom <- 0 > for (i in 2:fx) { + perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1]) + } > perf.scaleddenom = perf.scaleddenom / (fx-1) > for (i in 1:fx) { + locSD <- (ub[i] - forecast$pred[i]) / 1.96 + perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom + perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i] + perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+i] + forecast$pred[i]) + perf.se[i] = (x[nx+i] - forecast$pred[i])^2 + prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) + prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) + prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) + prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.smape[1] = abs(perf.spe[1]) > perf.mape1[1] = perf.mape[1] > perf.smape1[1] = perf.smape[1] > perf.mse[1] = perf.se[1] > perf.mase[1] = abs(perf.scalederr[1]) > perf.mase1[1] = perf.mase[1] > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.smape[i] = perf.smape[i-1] + abs(perf.spe[i]) + perf.smape1[i] = perf.smape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i]) + perf.mase1[i] = perf.mase[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/fisher/rcomp/tmp/23u6b1386839133.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:par1] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/fisher/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$pred[i],4)) + a<-table.element(a,round(lb[i],4)) + a<-table.element(a,round(ub[i],4)) + a<-table.element(a,round((1-prob.pval[i]),4)) + a<-table.element(a,round((1-prob.dec[i]),4)) + a<-table.element(a,round((1-prob.sdec[i]),4)) + a<-table.element(a,round((1-prob.ldec[i]),4)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/fisher/rcomp/tmp/36cqf1386839133.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',10,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'% S.E.',1,header=TRUE) > a<-table.element(a,'PE',1,header=TRUE) > a<-table.element(a,'MAPE',1,header=TRUE) > a<-table.element(a,'sMAPE',1,header=TRUE) > a<-table.element(a,'Sq.E',1,header=TRUE) > a<-table.element(a,'MSE',1,header=TRUE) > a<-table.element(a,'RMSE',1,header=TRUE) > a<-table.element(a,'ScaledE',1,header=TRUE) > a<-table.element(a,'MASE',1,header=TRUE) > a<-table.row.end(a) > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(perc.se[i],4)) + a<-table.element(a,round(perf.pe[i],4)) + a<-table.element(a,round(perf.mape1[i],4)) + a<-table.element(a,round(perf.smape1[i],4)) + a<-table.element(a,round(perf.se[i],4)) + a<-table.element(a,round(perf.mse1[i],4)) + a<-table.element(a,round(perf.rmse[i],4)) + a<-table.element(a,round(perf.scalederr[i],4)) + a<-table.element(a,round(perf.mase1[i],4)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/fisher/rcomp/tmp/4gf7m1386839133.tab") > > try(system("convert tmp/15fy61386839133.ps tmp/15fy61386839133.png",intern=TRUE)) character(0) > try(system("convert tmp/23u6b1386839133.ps tmp/23u6b1386839133.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 2.822 0.679 3.472