Inschrijvingen nieuwe personenwagens - Elisa Somers

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 10:13:28 -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/25/t1211732087zr801ng3ubj7wjq.htm/, Retrieved Sun, 25 May 2008 18:14:51 +0200

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Dataseries X:

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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:

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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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.567279660412336 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 39690 41086 -1396 3 43129 40294.0775940644 2834.92240593562 4 37863 41902.2714137989 -4039.27141379887 5 35953 39610.8748978658 -3657.87489786579 6 29133 37535.8368679737 -8402.83686797367 7 24693 32769.0784230093 -8076.07842300931 8 22205 28187.6833977412 -5982.6833977412 9 21725 24793.8287915160 -3068.82879151605 10 27192 23052.9446368012 4139.05536319878 11 21790 25400.9465576645 -3610.94655766448 12 13253 23352.5300206655 -10099.5300206655 13 37702 17623.2720602182 20078.7279397818 14 30364 29013.5260274093 1350.47397259071 15 32609 29779.6224439762 2829.37755602376 16 30212 31384.6707831357 -1172.67078313569 17 29965 30719.438499503 -754.438499503005 18 28352 30291.4608837029 -1939.46088370295 19 25814 29191.2441722129 -3377.24417221293 20 22414 27275.4022450704 -4861.40224507044 21 20506 24517.6276303591 -4011.62763035911 22 28806 22241.9128705083 6564.08712949175 23 22228 25965.5859882433 -3737.58598824331 24 13971 23845.3294780707 -9874.32947807074 25 36845 18243.8232049513 18601.1767950487 26 35338 28795.8924605163 6542.10753948367 27 35022 32507.0970038956 2514.90299610439 28 34777 33933.7503214957 843.249678504326 29 26887 34412.1087127604 -7525.10871276042 30 23970 30143.2675976198 -6173.26759761978 31 22780 26641.2984512076 -3861.29845120756 32 17351 24450.8623770559 -7099.86237705586 33 21382 20423.2548588253 958.74514117471 34 24561 20967.1314769329 3593.86852306714 35 17409 23005.8599922650 -5596.85999226497 36 11514 19830.8751564775 -8316.87515647751 37 31514 15112.8810420192 16401.1189579808 38 27071 24416.9022348849 2654.09776511515 39 29462 25922.5179137805 3539.48208621949 40 26105 27930.3941096867 -1825.39410968665 41 22397 26894.8851590249 -4497.88515902493 42 23843 24343.3263934396 -500.32639343958 43 21705 24059.5014068738 -2354.50140687385 44 18089 22723.8406483421 -4634.84064834208 45 20764 20094.5898192853 669.410180714702 46 25316 20474.3325992777 4841.6674007223 47 17704 23220.9120381889 -5516.91203818892 48 15548 20091.2800506404 -4543.28005064038 49 28029 17513.9696863550 10515.0303136450 50 29383 23478.9325119049 5904.06748809506 51 36438 26828.189911603 9609.81008839698 52 32034 32279.6397151759 -245.639715175901 53 22679 32140.2933009671 -9461.29330096713 54 24319 26773.094050133 -2454.09405013299 55 18004 25380.9364107536 -7376.93641075361 56 17537 21196.1504287779 -3659.15042877791 57 20366 19120.3888161431 1245.61118385688 58 22782 19826.9987055273 2955.00129447274 59 19169 21503.3108363738 -2334.31083637377 60 13807 20179.1037778188 -6372.10377781882 61 29743 16564.3389106256 13178.6610893744 62 25591 24040.3252980952 1550.67470190483 63 29096 24919.9915164017 4176.00848359826 64 26482 27288.9561908564 -806.956190856396 65 22405 26831.1863569397 -4426.18635693975 66 27044 24320.3008634533 2723.69913654675 67 17970 25865.3999846989 -7895.39998469887 68 18730 21386.5001625593 -2656.50016255933 69 19684 19879.5216524574 -195.521652457359 70 19785 19768.6061958481 16.3938041519104 71 18479 19777.9060675003 -1298.90606750025 72 10698 19041.0630746212 -8343.06307462119 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 14308.2130868514 1802.31111087188 26814.1150628309 74 14308.2130868514 -69.8013294544653 28686.2275031572 75 14308.2130868514 -1724.78453923805 30341.2107129408 76 14308.2130868514 -3224.23475139642 31840.6609250992 77 14308.2130868514 -4605.18009162325 33221.606265326 78 14308.2130868514 -5891.93928500615 34508.3654587089 79 14308.2130868514 -7101.50130099023 35717.927474693 80 14308.2130868514 -8246.2894457172 36862.7156194200 81 14308.2130868514 -9335.71422682334 37952.1404005261 82 14308.2130868514 -10377.1067031984 38993.5328769012 83 14308.2130868514 -11376.3100245423 39992.7361982450 84 14308.2130868514 -12338.0707400241 40954.4969137269

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/1nhic1211732003.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/1nhic1211732003.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/2v7bg1211732003.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/2v7bg1211732003.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/3iabe1211732003.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732087zr801ng3ubj7wjq/3iabe1211732003.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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