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Type 'q()' to quit R. > x <- c(26.81,28.24,27.58,27.98,27.84,27.49,26.97,27.71,27.46,27.04,28.00,27.32,26.36,26.15,25.94,24.00,24.32,23.10,22.92,23.56,22.17,22.36,19.86,20.07,19.21,19.99,20.47,21.17,21.25,21.18,21.21,21.11,21.94,22.56,23.23,19.50,19.32,19.00,18.98,19.88,19.48,19.52,19.52,19.75,19.64,20.23,20.40,20.91,21.95,21.83,22.27,21.99,21.66,20.32,20.62,20.28,20.79,22.86,22.59,23.29,21.87,21.52,22.00) > par10 = 'FALSE' > par9 = '1' > par8 = '0' > par7 = '0' > par6 = '1' > par5 = '4' > par4 = '0' > par3 = '1' > par2 = '0.0' > par1 = '4' > par10 <- 'FALSE' > par9 <- '1' > par8 <- '0' > par7 <- '0' > par6 <- '1' > par5 <- '4' > par4 <- '0' > par3 <- '1' > par2 <- '0.0' > par1 <- '4' > #'GNU S' R Code compiled by R2WASP v. 1.0.44 () > #Author: Prof. Dr. P. Wessa > #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/ > #Source of accompanying publication: > #Technical description: > 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 sma1 -0.0992 -0.2716 s.e. 0.1320 0.1597 sigma^2 estimated as 0.001578: log likelihood = 104.64, aic = -203.29 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 60 End = 63 Frequency = 1 [1] 3.123019 3.116415 3.095302 3.096999 $se Time Series: Start = 60 End = 63 Frequency = 1 [1] 0.03972164 0.05346225 0.06455014 0.07397587 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 60 End = 63 Frequency = 1 [1] 3.045165 3.011629 2.968783 2.952006 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 60 End = 63 Frequency = 1 [1] 3.200873 3.221201 3.221820 3.241991 > if (par2 == 0) { + x <- exp(x) + forecast$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] 26.81000 28.24000 27.58000 27.98000 27.84000 27.49000 26.97000 27.71000 [9] 27.46000 27.04000 28.00000 27.32000 26.36000 26.15000 25.94000 24.00000 [17] 24.32000 23.10000 22.92000 23.56000 22.17000 22.36000 19.86000 20.07000 [25] 19.21000 19.99000 20.47000 21.17000 21.25000 21.18000 21.21000 21.11000 [33] 21.94000 22.56000 23.23000 19.50000 19.32000 19.00000 18.98000 19.88000 [41] 19.48000 19.52000 19.52000 19.75000 19.64000 20.23000 20.40000 20.91000 [49] 21.95000 21.83000 22.27000 21.99000 21.66000 20.32000 20.62000 20.28000 [57] 20.79000 22.86000 22.59000 22.71485 22.56534 22.09390 22.13143 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 60 End = 63 Frequency = 1 [1] 0.04130882 0.05636375 0.06881133 0.07960772 > postscript(file="/var/wessaorg/rcomp/tmp/1qs1k1356012650.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$pred , lwd=2 , col ='white') > box() > par(opar) > dev.off() null device 1 > prob.dec <- array(NA, dim=fx) > prob.sdec <- array(NA, dim=fx) > prob.ldec <- array(NA, dim=fx) > prob.pval <- array(NA, dim=fx) > perf.pe <- array(0, dim=fx) > perf.mape <- array(0, dim=fx) > perf.mape1 <- array(0, dim=fx) > perf.se <- array(0, dim=fx) > perf.mse <- array(0, dim=fx) > perf.mse1 <- array(0, dim=fx) > perf.rmse <- array(0, dim=fx) > for (i in 1:fx) { + locSD <- (ub[i] - forecast$pred[i]) / 1.96 + perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$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$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.mse[1] = abs(perf.se[1]) > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/wessaorg/rcomp/tmp/2k3jw1356012650.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:par1] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$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/wessaorg/rcomp/tmp/3i5yl1356012650.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,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,'Sq.E',1,header=TRUE) > a<-table.element(a,'MSE',1,header=TRUE) > a<-table.element(a,'RMSE',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.se[i],4)) + a<-table.element(a,round(perf.mse1[i],4)) + a<-table.element(a,round(perf.rmse[i],4)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/42rio1356012650.tab") > > try(system("convert tmp/1qs1k1356012650.ps tmp/1qs1k1356012650.png",intern=TRUE)) character(0) > try(system("convert tmp/2k3jw1356012650.ps tmp/2k3jw1356012650.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.680 0.417 2.079