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Type 'q()' to quit R. > x <- c(2617.2,2506.13,2679.07,2589.73,2457.46,2517.3,2386.53,2453.37,2529.66,2475.14,2525.93,2480.93,2229.85,2169.14,2030.98,2071.37,1953.35,1748.74,1696.58,1900.09,1908.64,1881.46,2100.18,2672.2,3136,2994.38,3168.22,3751.41,3925.43,3719.52,3757.12,3722.23,4127.47,4162.5,4441.82,4325.29,4350.83,4384.47,4639.4,4697.86,4614.76,4471.65,4305.23,4433.57,4388.53,4140.3,4144.38,4070.78,3906.01,3795.91,3703.32,3675.8,3911.06,3912.28,3839.25,3744.63,3549.25,3394.14,3264.26,3328.8,3223.98,3228.01,3112.83,3051.67,3039.71,3125.67,3106.54) > par10 = 'FALSE' > par9 = '1' > par8 = '2' > par7 = '1' > par6 = '3' > par5 = '12' > par4 = '1' > par3 = '1' > par2 = '1' > par1 = '6' > #'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 ar2 ar3 ma1 sar1 sar2 sma1 0.9741 -0.2288 0.1783 -0.5220 -0.5833 -0.5911 -0.9992 s.e. 0.3951 0.2396 0.1745 0.3347 0.2109 0.1753 0.9444 sigma^2 estimated as 15291: log likelihood = -321.7, aic = 659.39 > (forecast <- predict(arima.out,par1)) $pred Time Series: Start = 62 End = 67 Frequency = 1 [1] 2883.674 2788.736 2970.290 2753.344 2396.881 2248.419 $se Time Series: Start = 62 End = 67 Frequency = 1 [1] 142.0776 249.6310 342.3992 437.4039 537.7003 640.5204 > (lb <- forecast$pred - 1.96 * forecast$se) Time Series: Start = 62 End = 67 Frequency = 1 [1] 2605.201 2299.459 2299.187 1896.033 1342.988 992.999 > (ub <- forecast$pred + 1.96 * forecast$se) Time Series: Start = 62 End = 67 Frequency = 1 [1] 3162.146 3278.013 3641.392 3610.656 3450.773 3503.839 > if (par2 == 0) { + x <- exp(x) + forecast$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] 2617.200 2506.130 2679.070 2589.730 2457.460 2517.300 2386.530 2453.370 [9] 2529.660 2475.140 2525.930 2480.930 2229.850 2169.140 2030.980 2071.370 [17] 1953.350 1748.740 1696.580 1900.090 1908.640 1881.460 2100.180 2672.200 [25] 3136.000 2994.380 3168.220 3751.410 3925.430 3719.520 3757.120 3722.230 [33] 4127.470 4162.500 4441.820 4325.290 4350.830 4384.470 4639.400 4697.860 [41] 4614.760 4471.650 4305.230 4433.570 4388.530 4140.300 4144.380 4070.780 [49] 3906.010 3795.910 3703.320 3675.800 3911.060 3912.280 3839.250 3744.630 [57] 3549.250 3394.140 3264.260 3328.800 3223.980 2883.674 2788.736 2970.290 [65] 2753.344 2396.881 2248.419 > (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) Time Series: Start = 62 End = 67 Frequency = 1 [1] 0.04926966 0.08951403 0.11527466 0.15886276 0.22433333 0.28487592 > postscript(file="/var/www/html/rcomp/tmp/1mxmb1292622071.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$pred[i]) / locSD) + } > perf.mape[1] = abs(perf.pe[1]) > perf.mse[1] = abs(perf.se[1]) > for (i in 2:fx) { + perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) + perf.mape1[i] = perf.mape[i] / i + perf.mse[i] = perf.mse[i-1] + perf.se[i] + perf.mse1[i] = perf.mse[i] / i + } > perf.rmse = sqrt(perf.mse1) > postscript(file="/var/www/html/rcomp/tmp/2i6111292622071.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) > dum <- forecast$pred > dum[1:par1] <- x[(nx+1):lx] > lines(dum, lty=1) > lines(ub,lty=3) > lines(lb,lty=3) > dev.off() null device 1 > > #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'time',1,header=TRUE) > a<-table.element(a,'Y[t]',1,header=TRUE) > a<-table.element(a,'F[t]',1,header=TRUE) > a<-table.element(a,'95% LB',1,header=TRUE) > a<-table.element(a,'95% UB',1,header=TRUE) > a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) > a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) > mylab <- paste('P(F[t]>Y[',nx,sep='') > mylab <- paste(mylab,'])',sep='') > a<-table.element(a,mylab,1,header=TRUE) > a<-table.row.end(a) > for (i in (nx-par5):nx) { + a<-table.row.start(a) + a<-table.element(a,i,header=TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.element(a,'-') + a<-table.row.end(a) + } > for (i in 1:fx) { + a<-table.row.start(a) + a<-table.element(a,nx+i,header=TRUE) + a<-table.element(a,round(x[nx+i],4)) + a<-table.element(a,round(forecast$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/www/html/rcomp/tmp/3ppyd1292622071.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/www/html/rcomp/tmp/4s8xj1292622071.tab") > > try(system("convert tmp/1mxmb1292622071.ps tmp/1mxmb1292622071.png",intern=TRUE)) character(0) > try(system("convert tmp/2i6111292622071.ps tmp/2i6111292622071.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 2.660 0.529 6.221