*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: Mon, 27 Dec 2010 23:57:39 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t12934941296xci25fdwej56vk.htm/, Retrieved Tue, 28 Dec 2010 00:55:31 +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/2010/Dec/28/t12934941296xci25fdwej56vk.htm/}, year = {2010}, } @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 = {2010}, 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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224 215 196 159 187 208 131 93 210 228 176 195 188 188 190 188 176 225 93 79 235 247 195 197 211 156 209 180 185 303 129 85 249 231 212 240 234 217 287 221 208 241 156 96 320 242 227 200 215 238 279 208 262 259 167 123 302 246 235

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[35]) 23 195 - - - - - - - 24 197 - - - - - - - 25 211 - - - - - - - 26 156 - - - - - - - 27 209 - - - - - - - 28 180 - - - - - - - 29 185 - - - - - - - 30 303 - - - - - - - 31 129 - - - - - - - 32 85 - - - - - - - 33 249 - - - - - - - 34 231 - - - - - - - 35 212 - - - - - - - 36 240 199.9633 148.2372 251.6894 0.0646 0.3242 0.5447 0.3242 37 234 212.4758 159.9433 265.0084 0.211 0.1522 0.522 0.5071 38 217 154.8105 102.2528 207.3682 0.0102 0.0016 0.4823 0.0165 39 287 209.7942 157.2357 262.3527 0.002 0.3941 0.5118 0.4672 40 221 179.6532 127.0947 232.2117 0.0615 0 0.4948 0.1139 41 208 185.3759 132.8174 237.9344 0.1994 0.092 0.5056 0.1604 42 241 306.1603 253.6018 358.7188 0.0076 0.9999 0.5469 0.9998 43 156 130.4966 77.9381 183.0551 0.1708 0 0.5223 0.0012 44 96 85.2558 32.6973 137.8143 0.3443 0.0042 0.5038 0 45 320 249.549 196.9905 302.1075 0.0043 1 0.5082 0.9193 46 242 230.3331 177.7746 282.8916 0.3318 4e-04 0.4901 0.7529 47 227 212.6761 160.1175 265.2346 0.2966 0.1371 0.5101 0.5101 48 200 200.0821 124.8479 275.3164 0.4991 0.2416 0.1492 0.3781 49 215 212.5162 136.6791 288.3532 0.4744 0.6268 0.2894 0.5053 50 238 154.7882 78.9323 230.6441 0.0158 0.0599 0.054 0.0697 51 279 209.8107 133.9542 285.6672 0.0369 0.2332 0.0231 0.4774 52 208 179.6462 103.7897 255.5028 0.2319 0.0051 0.1426 0.2016 53 262 185.3835 109.527 261.2401 0.0239 0.2795 0.2795 0.2458 54 259 306.2244 230.3679 382.081 0.1112 0.8734 0.954 0.9925 55 167 130.527 54.6705 206.3835 0.173 5e-04 0.2552 0.0176 56 123 85.261 9.4045 161.1175 0.1648 0.0173 0.3907 5e-04 57 302 249.5602 173.7036 325.4167 0.0877 0.9995 0.0344 0.8341 58 246 230.3196 154.463 306.1761 0.3427 0.032 0.3814 0.682 59 235 212.6898 136.8332 288.5463 0.2822 0.1947 0.3558 0.5071 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 36 0.132 0.2002 0 1602.9373 0 0 37 0.1261 0.1013 0.1508 463.2901 1033.1137 32.1421 38 0.1732 0.4017 0.2344 3867.5325 1977.92 44.4738 39 0.1278 0.368 0.2678 5960.7299 2973.6225 54.5309 40 0.1493 0.2301 0.2603 1709.5571 2720.8094 52.1614 41 0.1447 0.122 0.2372 511.85 2352.6495 48.5041 42 0.0876 -0.2128 0.2338 4245.8662 2623.109 51.2163 43 0.2055 0.1954 0.229 650.4226 2376.5232 48.7496 44 0.3145 0.126 0.2175 115.4379 2125.2915 46.1009 45 0.1075 0.2823 0.224 4963.342 2409.0966 49.0825 46 0.1164 0.0507 0.2082 136.1168 2202.462 46.9304 47 0.1261 0.0674 0.1965 205.1753 2036.0215 45.1223 48 0.1918 -4e-04 0.1814 0.0067 1879.405 43.3521 49 0.1821 0.0117 0.1693 6.1694 1745.6024 41.7804 50 0.25 0.5376 0.1938 6924.2008 2090.8423 45.7257 51 0.1845 0.3298 0.2023 4787.1618 2259.3623 47.5327 52 0.2154 0.1578 0.1997 803.9363 2173.749 46.6235 53 0.2088 0.4133 0.2116 5870.0825 2379.1008 48.776 54 0.1264 -0.1542 0.2086 2230.1485 2371.2612 48.6956 55 0.2965 0.2794 0.2121 1330.2806 2319.2122 48.1582 56 0.4539 0.4426 0.2231 1424.2331 2276.5942 47.7137 57 0.1551 0.2101 0.2225 2749.9377 2298.1098 47.9386 58 0.168 0.0681 0.2158 245.8763 2208.8822 46.9987 59 0.182 0.1049 0.2112 497.746 2137.5849 46.234

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t12934941296xci25fdwej56vk/1gnl11293494257.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934941296xci25fdwej56vk/1gnl11293494257.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934941296xci25fdwej56vk/2cfja1293494257.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934941296xci25fdwej56vk/2cfja1293494257.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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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