forecasting (verkoopprijzen)

*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: Thu, 31 Dec 2009 08:08:41 -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/31/t12622721838al3drnwu09gemq.htm/, Retrieved Thu, 31 Dec 2009 16:09:45 +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/31/t12622721838al3drnwu09gemq.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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2072.65 2020.13 2032.76 2050.31 2128.98 2122.14 2122.89 2091.95 2002.97 1923.21 1834.44 1819.15 1792.00 1822.40 1900.70 1903.00 1958.80 1820.50 1719.80 1661.10 1664.40 1703.40 1774.90 1795.00 1816.30 1867.40 1900.00 1961.10 2065.70 2073.50 2080.80 2118.00 2099.00 2085.20 1937.70 1749.50 1750.30 1675.60 1697.50 1699.80 1655.90 1636.00 1614.20 1602.30 1548.70 1556.10 1526.90 1509.20 1566.30 1596.00 1654.50 1664.20 1687.70 1691.00 1664.60 1697.50 1685.10 1643.00 1559.60 1560.20 1590.16 1604.93 1661.80 1670.73 1692.40 1688.17 1658.04 1613.46 1595.11 1558.83 1526.65 1475.19

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[48]) 36 1749.5 - - - - - - - 37 1750.3 - - - - - - - 38 1675.6 - - - - - - - 39 1697.5 - - - - - - - 40 1699.8 - - - - - - - 41 1655.9 - - - - - - - 42 1636 - - - - - - - 43 1614.2 - - - - - - - 44 1602.3 - - - - - - - 45 1548.7 - - - - - - - 46 1556.1 - - - - - - - 47 1526.9 - - - - - - - 48 1509.2 - - - - - - - 49 1566.3 1514.1074 1449.5588 1587.0541 0.0804 0.5525 0 0.5525 50 1596 1510.6051 1404.5407 1641.4985 0.1005 0.2021 0.0067 0.5084 51 1654.5 1533.7073 1388.7636 1728.3842 0.112 0.2653 0.0496 0.5974 52 1664.2 1545.5064 1369.1875 1800.5217 0.1808 0.2011 0.1178 0.6099 53 1687.7 1566.5799 1359.8666 1888.1649 0.2302 0.2759 0.2931 0.6367 54 1691 1542.1627 1322.9527 1898.6048 0.2066 0.2118 0.3029 0.5719 55 1664.6 1521.3805 1292.046 1909.0974 0.2345 0.1956 0.3195 0.5245 56 1697.5 1508.6006 1268.8585 1929.8602 0.1897 0.234 0.3314 0.4989 57 1685.1 1486.0319 1241.576 1927.4627 0.1884 0.1739 0.3904 0.459 58 1643 1483.7138 1228.2815 1963.1901 0.2575 0.2052 0.3837 0.4585 59 1559.6 1460.9276 1203.9579 1952.7972 0.3471 0.2341 0.3963 0.4237 60 1560.2 1432.5792 1177.6656 1925.8392 0.306 0.3069 0.3804 0.3804 61 1590.16 1431.3714 1165.8041 1966.9923 0.2806 0.3187 0.3107 0.3879 62 1604.93 1426.0005 1152.1519 1999.1694 0.2703 0.2873 0.2805 0.388 63 1661.8 1444.6673 1152.1524 2096.5443 0.2569 0.315 0.2641 0.4231 64 1670.73 1454.2217 1147.3155 2176.7602 0.2785 0.2867 0.2845 0.4407 65 1692.4 1471.8539 1146.9221 2289.4846 0.2985 0.3168 0.3024 0.4643 66 1688.17 1451.0872 1127.4008 2279.1402 0.2873 0.2839 0.2851 0.4453 67 1658.04 1433.385 1110.1991 2274.8255 0.3004 0.2764 0.2951 0.4299 68 1613.46 1422.476 1097.045 2290.9972 0.3332 0.2975 0.2674 0.4224 69 1595.11 1403.1756 1080.3057 2273.5964 0.3328 0.3179 0.2628 0.4057 70 1558.83 1401.1867 1072.5824 2318.2348 0.3681 0.3393 0.3026 0.4087 71 1526.65 1381.6242 1056.7571 2292.718 0.3775 0.3515 0.3509 0.3919 72 1475.19 1357.1831 1039.0718 2244.0437 0.3971 0.354 0.3268 0.3684 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 49 0.0246 0.0345 0 2724.0704 0 0 50 0.0442 0.0565 0.0455 7292.2956 5008.183 70.7685 51 0.0648 0.0788 0.0566 14590.8722 8202.4128 90.5672 52 0.0842 0.0768 0.0616 14088.1689 9673.8518 98.3557 53 0.1047 0.0773 0.0648 14670.0838 10673.0982 103.3107 54 0.1179 0.0965 0.0701 22152.5343 12586.3375 112.1888 55 0.13 0.0941 0.0735 20511.8317 13718.551 117.1262 56 0.1425 0.1252 0.08 35682.9656 16464.1028 128.3125 57 0.1516 0.134 0.086 39628.1073 19037.8811 137.9778 58 0.1649 0.1074 0.0881 25372.0992 19671.3029 140.2544 59 0.1718 0.0675 0.0862 9736.2378 18768.1152 136.9968 60 0.1757 0.0891 0.0865 16287.074 18561.3618 136.2401 61 0.1909 0.1109 0.0884 25213.824 19073.0896 138.1054 62 0.2051 0.1255 0.091 32015.7682 19997.5667 141.4128 63 0.2302 0.1503 0.095 47146.6066 21807.5027 147.6736 64 0.2535 0.1489 0.0983 46875.8345 23374.2734 152.8865 65 0.2834 0.1498 0.1014 48640.5724 24860.5263 157.6722 66 0.2911 0.1634 0.1048 56208.2418 26602.066 163.1014 67 0.2995 0.1567 0.1075 50469.8467 27858.265 166.908 68 0.3115 0.1343 0.1089 36474.9012 28289.0968 168.1936 69 0.3165 0.1368 0.1102 36838.8128 28696.2261 169.3996 70 0.3339 0.1125 0.1103 24851.3961 28521.4611 168.883 71 0.3364 0.105 0.1101 21032.4881 28195.8536 167.9162 72 0.3334 0.0869 0.1091 13925.6292 27601.2609 166.1363

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/31/t12622721838al3drnwu09gemq/11dzo1262272118.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t12622721838al3drnwu09gemq/11dzo1262272118.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t12622721838al3drnwu09gemq/2sv3x1262272118.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t12622721838al3drnwu09gemq/2sv3x1262272118.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = -1.7 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = -1.7 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

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

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')) (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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