Forecast (12 maanden)

*The author of this computation has been verified*

R Software Module: /rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Sun, 20 Dec 2009 03:03:13 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj.htm/, Retrieved Sun, 20 Dec 2009 11:04:04 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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3030.29 2803.47 2767.63 2882.6 2863.36 2897.06 3012.61 3142.95 3032.93 3045.78 3110.52 3013.24 2987.1 2995.55 2833.18 2848.96 2794.83 2845.26 2915.02 2892.63 2604.42 2641.65 2659.81 2638.53 2720.25 2745.88 2735.7 2811.7 2799.43 2555.28 2304.98 2214.95 2065.81 1940.49 2042 1995.37 1946.81 1765.9 1635.25 1833.42 1910.43 1959.67 1969.6 2061.41 2093.48 2120.88 2174.56 2196.72 2350.44 2440.25 2408.64 2472.81 2407.6 2454.62 2448.05 2497.84 2645.64 2756.76 2849.27 2921.44

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Univariate ARIMA Extrapolation Forecast time Y[t] F[t] 95% LB 95% UB p-value (H0: Y[t] = F[t]) P(F[t]>Y[t-1]) P(F[t]>Y[t-s]) P(F[t]>Y[32]) 20 2892.63 - - - - - - - 21 2604.42 - - - - - - - 22 2641.65 - - - - - - - 23 2659.81 - - - - - - - 24 2638.53 - - - - - - - 25 2720.25 - - - - - - - 26 2745.88 - - - - - - - 27 2735.7 - - - - - - - 28 2811.7 - - - - - - - 29 2799.43 - - - - - - - 30 2555.28 - - - - - - - 31 2304.98 - - - - - - - 32 2214.95 - - - - - - - 33 2065.81 2235.7843 2041.9774 2429.5912 0.0428 0.5834 1e-04 0.5834 34 1940.49 2252.3131 1920.9792 2583.647 0.0325 0.865 0.0106 0.5875 35 2042 2257.3772 1856.2742 2658.4802 0.1463 0.9392 0.0246 0.5821 36 1995.37 2268.9303 1820.2801 2717.5805 0.116 0.8393 0.0532 0.5932 37 1946.81 2274.3988 1765.8464 2782.9512 0.1034 0.8589 0.0429 0.5906 38 1765.9 2277.1085 1729.9632 2824.2539 0.0335 0.8816 0.0466 0.5881 39 1635.25 2282.9389 1697.7853 2868.0925 0.015 0.9583 0.0647 0.5901 40 1833.42 2284.285 1659.5738 2908.9962 0.0786 0.9791 0.049 0.5861 41 1910.43 2286.1753 1631.0507 2941.2998 0.1305 0.9122 0.0623 0.5844 42 1959.67 2288.7207 1601.1493 2976.292 0.1741 0.8596 0.2237 0.5833 43 1969.6 2288.9029 1570.773 3007.0329 0.1917 0.8156 0.4825 0.58 44 2061.41 2290.2102 1545.0598 3035.3606 0.2736 0.8005 0.5785 0.5785 45 2093.48 2291.103 1517.7397 3064.4664 0.3082 0.7198 0.716 0.5765 46 2120.88 2291.1275 1491.7428 3090.5123 0.3382 0.686 0.805 0.5741 47 2174.56 2291.9212 1467.6788 3116.1636 0.3901 0.6579 0.7238 0.5726 48 2196.72 2292.1222 1442.8543 3141.3901 0.4129 0.6069 0.7533 0.5707 49 2350.44 2292.2014 1419.4974 3164.9055 0.448 0.5849 0.781 0.5689 50 2440.25 2292.607 1396.833 3188.381 0.3733 0.4497 0.8754 0.5675 51 2408.64 2292.5928 1374.1266 3211.0591 0.4022 0.3763 0.9197 0.5658 52 2472.81 2292.7036 1352.5197 3232.8875 0.3537 0.4045 0.8308 0.5644 53 2407.6 2292.8695 1331.1801 3254.5588 0.4076 0.3569 0.7821 0.5631 54 2454.62 2292.8283 1310.163 3275.4936 0.3735 0.4095 0.7468 0.5617 55 2448.05 2292.924 1289.8596 3295.9883 0.3809 0.376 0.7362 0.5605 56 2497.84 2292.9701 1269.7488 3316.1915 0.3474 0.3832 0.6713 0.5594 57 2645.64 2292.9507 1250.0624 3335.8389 0.2537 0.3501 0.6461 0.5583 58 2756.76 2293.0123 1230.8296 3355.195 0.1961 0.2576 0.6246 0.5573 59 2849.27 2293.0128 1211.8153 3374.2104 0.1566 0.2003 0.585 0.5563 60 2921.44 2293.013 1193.1984 3392.8276 0.1314 0.1608 0.5681 0.5553 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0442 -0.076 0 28891.2691 0 0 34 0.0751 -0.1384 0.1072 97233.6644 63062.4668 251.1224 35 0.0907 -0.0954 0.1033 46387.3383 57504.0906 239.8001 36 0.1009 -0.1206 0.1076 74835.2144 61836.8716 248.6702 37 0.1141 -0.144 0.1149 107314.4188 70932.381 266.3313 38 0.1226 -0.2245 0.1332 261334.1527 102666.0096 320.4154 39 0.1308 -0.2837 0.1547 419500.8738 147928.1331 384.6143 40 0.1395 -0.1974 0.16 203279.2461 154847.0222 393.5061 41 0.1462 -0.1644 0.1605 141184.5052 153328.9648 391.5724 42 0.1533 -0.1438 0.1588 108274.354 148823.5037 385.7765 43 0.1601 -0.1395 0.1571 101954.3717 144562.6735 380.214 44 0.166 -0.0999 0.1523 52349.5504 136878.2466 369.9706 45 0.1722 -0.0863 0.1472 39054.8504 129353.3699 359.6573 46 0.178 -0.0743 0.142 28984.2252 122184.1453 349.5485 47 0.1835 -0.0512 0.136 13773.6471 114956.7788 339.0528 48 0.189 -0.0416 0.1301 9101.5787 108340.8288 329.1517 49 0.1942 0.0254 0.1239 3391.7294 102167.3523 319.6363 50 0.1993 0.0644 0.1206 21798.4617 97702.414 312.5739 51 0.2044 0.0506 0.1169 13466.9433 93268.9681 305.3997 52 0.2092 0.0786 0.115 32438.3218 90227.4358 300.3788 53 0.214 0.05 0.1119 13163.0943 86557.7053 294.2069 54 0.2187 0.0706 0.11 26176.5597 83813.1078 289.5049 55 0.2232 0.0677 0.1082 24064.0843 81215.3241 284.983 56 0.2277 0.0893 0.1074 41971.6618 79580.1715 282.0996 57 0.2321 0.1538 0.1093 124389.7658 81372.5553 285.2588 58 0.2363 0.2022 0.1128 215061.9188 86514.4539 294.1334 59 0.2406 0.2426 0.1176 309422.0683 94770.2915 307.8478 60 0.2447 0.2741 0.1232 394920.4688 105489.9407 324.7921

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj/16jab1261303390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj/16jab1261303390.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj/21xjb1261303390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/20/t12613034425x5zcsu7tl4ptxj/21xjb1261303390.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods par1 <- 28 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 par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 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')) (forecast <- predict(arima.out,par1)) (lb <- forecast$pred - 1.96 * forecast$se) (ub <- forecast$pred + 1.96 * forecast$se) 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$pred)) (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) bitmap(file='test1.png') opar <- par(mar=c(4,4,2,2),las=1) ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) plot(x,ylim=ylim,type='n',xlim=c(first,lx)) usr <- par('usr') rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') abline(h= (-3:3)*2 , col ='gray', lty =3) polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) lines(nx1:lx, lb , lty=2) lines(nx1:lx, ub , lty=2) lines(x, lwd=2) lines(nx1:lx, forecast$pred , lwd=2 , col ='white') box() par(opar) dev.off() 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) bitmap(file='test2.png') 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() load(file='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<br />(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='mytable.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='mytable1.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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