*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, 21 Dec 2009 09:27:37 -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/21/t12614129111jf1g1lh7xipywu.htm/, Retrieved Mon, 21 Dec 2009 17:28:33 +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/21/t12614129111jf1g1lh7xipywu.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 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293 etc...

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 1 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[95]) 83 4199.75 - - - - - - - 84 4290.89 - - - - - - - 85 4443.91 - - - - - - - 86 4502.64 - - - - - - - 87 4356.98 - - - - - - - 88 4591.27 - - - - - - - 89 4696.96 - - - - - - - 90 4621.4 - - - - - - - 91 4562.84 - - - - - - - 92 4202.52 - - - - - - - 93 4296.49 - - - - - - - 94 4435.23 - - - - - - - 95 4105.18 - - - - - - - 96 4116.68 4024.2231 3798.9034 4249.5428 0.2106 0.2406 0.0102 0.2406 97 3844.49 4004.3654 3644.5065 4364.2243 0.1919 0.2704 0.0083 0.2915 98 3720.98 3999.4946 3534.7159 4464.2732 0.1201 0.7433 0.0169 0.3279 99 3674.4 3998.2998 3446.4781 4550.1216 0.125 0.8377 0.1013 0.3521 100 3857.62 3998.0068 3370.7259 4625.2876 0.3305 0.844 0.0319 0.3689 101 3801.06 3997.9349 3303.259 4692.6108 0.2893 0.6539 0.0243 0.3811 102 3504.37 3997.9173 3241.8106 4754.0239 0.1004 0.6951 0.053 0.3905 103 3032.6 3997.9129 3185.0002 4810.8257 0.01 0.883 0.0866 0.398 104 3047.03 3997.9119 3131.9103 4863.9134 0.0157 0.9855 0.3217 0.4041 105 2962.34 3997.9116 3081.8926 4913.9306 0.0134 0.9791 0.2615 0.4092 106 2197.82 3997.9115 3034.4683 4961.3548 1e-04 0.9824 0.1868 0.4136 107 2014.45 3997.9115 2989.2713 5006.5517 1e-04 0.9998 0.4174 0.4174 108 1862.83 3997.9115 2946.0145 5049.8085 0 0.9999 0.4124 0.4208 109 1905.41 3997.9115 2904.4677 5091.3554 1e-04 0.9999 0.6083 0.4238 110 1810.99 3997.9115 2864.4427 5131.3804 1e-04 0.9999 0.684 0.4264 111 1670.07 3997.9115 2825.7836 5170.0394 0 0.9999 0.7057 0.4288 112 1864.44 3997.9115 2788.3595 5207.4635 3e-04 0.9999 0.5899 0.431 113 2052.02 3997.9115 2752.0591 5243.7639 0.0011 0.9996 0.6216 0.433 114 2029.6 3997.9115 2716.7869 5279.0362 0.0013 0.9985 0.7749 0.4348 115 2070.83 3997.9115 2682.46 5313.363 0.002 0.9983 0.9248 0.4365 116 2293.41 3997.9115 2649.0065 5346.8165 0.0066 0.9974 0.9165 0.4381 117 2443.27 3997.9115 2616.3628 5379.4603 0.0137 0.9922 0.9291 0.4395 118 2513.17 3997.9115 2584.4728 5411.3503 0.0198 0.9845 0.9937 0.4409 119 2466.92 3997.9115 2553.2865 5442.5365 0.0189 0.978 0.9964 0.4421 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 96 0.0286 0.023 0 8548.2838 0 0 97 0.0459 -0.0399 0.0315 25560.1432 17054.2135 130.5918 98 0.0593 -0.0696 0.0442 77570.3675 37226.2648 192.9411 99 0.0704 -0.081 0.0534 104911.0957 54147.4725 232.6961 100 0.0801 -0.0351 0.0497 19708.4444 47259.6669 217.3929 101 0.0887 -0.0492 0.0497 38759.7201 45843.0091 214.1098 102 0.0965 -0.1235 0.0602 243588.8903 74092.4207 272.1992 103 0.1037 -0.2415 0.0829 931829.0479 181309.4991 425.8045 104 0.1105 -0.2378 0.1001 904176.3243 261628.0352 511.4959 105 0.1169 -0.259 0.116 1072408.552 342706.0869 585.411 106 0.123 -0.4503 0.1464 3240329.5617 606126.4028 778.5412 107 0.1287 -0.4961 0.1755 3934119.6288 883459.1716 939.9251 108 0.1342 -0.534 0.2031 4558573.1102 1166160.2438 1079.889 109 0.1395 -0.5234 0.226 4378562.6202 1395617.5564 1181.3626 110 0.1447 -0.547 0.2474 4782625.743 1621418.1022 1273.3492 111 0.1496 -0.5823 0.2683 5418846.1509 1858757.3552 1363.3625 112 0.1544 -0.5336 0.2839 4551700.7345 2017165.7893 1420.2696 113 0.159 -0.4867 0.2952 3786493.8148 2115461.7907 1454.4627 114 0.1635 -0.4923 0.3056 3874250.247 2208029.6042 1485.944 115 0.1679 -0.482 0.3144 3713643.1918 2283310.2836 1511.0626 116 0.1721 -0.4263 0.3197 2905325.438 2312930.0529 1520.832 117 0.1763 -0.3889 0.3229 2416910.2614 2317656.426 1522.3851 118 0.1804 -0.3714 0.325 2204457.3867 2312734.7286 1520.7678 119 0.1844 -0.3829 0.3274 2343935.04 2314034.7416 1521.1952

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614129111jf1g1lh7xipywu/1sjzk1261412855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614129111jf1g1lh7xipywu/1sjzk1261412855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614129111jf1g1lh7xipywu/21yt91261412855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t12614129111jf1g1lh7xipywu/21yt91261412855.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

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