Opgave 10: Inschr PW's

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 17:51:15 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t1211845898phjo7n47x68fao1.htm/, Retrieved Tue, 27 May 2008 01:51:39 +0200

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41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

Text written by user:

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.567279661944919 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 39690 41086 -1396 3 43129 40294.0775919249 2834.92240807511 4 37863 41902.2714172178 -4039.27141721782 5 35953 39610.8748931547 -3657.87489315472 6 29133 37535.8368603291 -8402.83686032911 7 24693 32769.0784068233 -8076.07840682331 8 22205 28187.6833783599 -5982.68337835992 9 21725 24793.8287739604 -3068.82877396042 10 27192 23052.9446245013 4139.05537549868 11 21790 25400.9465586855 -3610.94655868551 12 13253 23352.5300155732 -10099.5300155732 13 37702 17623.2720425363 20078.7279574637 14 30364 29013.5260505303 1350.47394946971 15 32609 29779.6224560509 2829.37754394911 16 30212 31384.6707926969 -1172.67079269688 17 29965 30719.4385018431 -754.438501843117 18 28352 30291.4608835593 -1939.46088355932 19 25814 29191.2441691784 -3377.2441691784 20 22414 27275.4022385814 -4861.40223858143 21 20506 24517.6276201007 -4011.62762010068 22 28806 22241.9128599211 6564.08714007893 23 22228 25965.5859937220 -3737.58599372203 24 13971 23845.3294747133 -9874.32947471334 25 36845 18243.8231883652 18601.1768116348 26 35338 28795.8924818471 6542.10751815295 27 35022 32507.0970231522 2514.90297684783 28 34777 33933.7503336827 843.249666317322 29 26887 34412.1087193263 -7525.10871932633 30 23970 30143.2675889281 -6173.26758892813 31 22780 26641.2984379855 -3861.29843798546 32 17351 24450.8623654166 -7099.86236541663 33 21382 20423.2548429076 958.74515709237 34 24561 20967.1314715143 3593.86852848568 35 17409 23005.8599954282 -5596.85999542816 36 11514 19830.8751492686 -8316.87514926863 37 31514 15112.8810261534 16401.1189738466 38 27071 24416.9022531555 2654.0977468445 39 29462 25922.5179257542 3539.48207424578 40 26105 27930.3941202925 -1825.39412029247 41 22397 26894.8851608167 -4497.88516081671 42 23843 24343.3263873215 -500.326387321544 43 21705 24059.5014034597 -2354.50140345966 44 18089 22723.8406432562 -4634.84064325623 45 20764 20094.5898099813 669.410190018734 46 25316 20474.3325962776 4841.66740372242 47 17704 23220.9120443110 -5516.91204431096 48 15548 20091.2800448344 -4543.28004483439 49 28029 17513.9696768796 10515.0303231204 50 29383 23478.9325239199 5904.06747608007 51 36438 26828.1899258506 9609.81007414938 52 32034 32279.6397360690 -245.639736068955 53 22679 32140.2933096315 -9461.29330963152 54 24319 26773.0940393820 -2454.09403938203 55 18004 25380.9364023404 -7376.93640234035 56 17537 21196.1504138316 -3659.15041383155 57 20366 19120.3888040676 1245.61119593242 58 22782 19826.9987022109 2955.00129778907 59 19169 21503.3108394675 -2334.31083946751 60 13807 20179.1037755800 -6372.10377558002 61 29743 16564.3388998910 13178.6611001090 62 25591 24040.3253136475 1550.67468635250 63 29096 24919.9915255081 4176.00847449191 64 26482 27288.956201197 -806.956201196976 65 22405 26831.1863601776 -4426.1863601776 66 27044 24320.3008580708 2723.69914192916 67 17970 25865.3999865441 -7895.39998654408 68 18730 21386.5001512574 -2656.50015125744 69 19684 19879.5216434955 -195.521643495493 70 19785 19768.6061916705 16.3938083295470 71 18479 19777.9060657176 -1298.90606571763 72 10698 19041.0630718591 -8343.06307185913 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 14308.2130728697 1802.31109659009 26814.1150491494 74 14308.2130728697 -69.8013532381556 28686.2274989776 75 14308.2130728697 -1724.78457056607 30341.2107163056 76 14308.2130728697 -3224.23478906528 31840.6609348048 77 14308.2130728697 -4605.1801348157 33221.6062805552 78 14308.2130728697 -5891.93933312892 34508.3654788684 79 14308.2130728697 -7101.50135359156 35717.9274993310 80 14308.2130728697 -8246.2895024405 36862.71564818 81 14308.2130728697 -9335.7142873792 37952.1404331187 82 14308.2130728697 -10377.1067673466 38993.5329130861 83 14308.2130728697 -11376.3100920798 39992.7362378193 84 14308.2130728697 -12338.0708107768 40954.4969565163

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/1a77m1211845868.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/1a77m1211845868.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/2crid1211845868.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/2crid1211845868.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/3uovd1211845868.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211845898phjo7n47x68fao1/3uovd1211845868.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

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

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) 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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.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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