*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:36:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5.htm/, Retrieved Wed, 18 May 2011 16:32:44 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

70938 34077 45409 40809 37013 44953 19848 32745 43412 34931 33008 8620 68906 39556 50669 36432 40891 48428 36222 33425 39401 37967 34801 12657 69116 41519 51321 38529 41547 52073 38401 40898 40439 41888 37898 8771 68184 50530 47221 41756 45633 48138 39486 39341 41117 41629 29722 7054 56676 34870 35117 30169 30936 35699 33228 27733 33666 35429 27438 8170 63410 38040 45389 37353 37024 50957 37994 36454 46080 43373 37395 10963 75001

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.344206838588595 beta 0 gamma 0.800062194590154 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 68906 67427.0202991453 1478.97970085469 14 39556 38146.0789092969 1409.9210907031 15 50669 50153.7420735709 515.257926429127 16 36432 36405.2893918018 26.7106081982274 17 40891 40942.8420487901 -51.8420487901385 18 48428 48489.6480107205 -61.648010720477 19 36222 22874.7870268288 13347.2129731712 20 33425 40492.9310246098 -7067.93102460975 21 39401 48550.2095142503 -9149.20951425026 22 37967 37153.7643814158 813.235618584171 23 34801 35802.0443257 -1001.0443257 24 12657 11033.6700393808 1623.32996061923 25 69116 72097.9408045413 -2981.94080454131 26 41519 41245.2867222375 273.713277762494 27 51321 52392.4517088857 -1071.45170888566 28 38529 37841.5140012541 687.485998745928 29 41547 42565.2954263186 -1018.2954263186 30 52073 49774.2965803529 2298.70341964708 31 38401 32007.1830730635 6393.81692693647 32 40898 36520.5984738087 4377.40152619125 33 40439 47425.4432482943 -6986.44324829426 34 41888 42000.4861018366 -112.486101836563 35 37898 39378.2183963945 -1480.21839639451 36 8771 15821.8535258243 -7050.85352582433 37 68184 71484.1391221893 -3300.13912218931 38 50530 42230.1203370697 8299.87966293028 39 47221 55434.1718168137 -8213.17181681374 40 41756 39347.8764061758 2408.12359382416 41 45633 43768.9316501195 1864.06834988049 42 48138 53710.4095446217 -5572.40954462174 43 39486 35382.6101008767 4103.38989912329 44 39341 38049.6814679566 1291.31853204345 45 41117 41929.9465243306 -812.946524330575 46 41629 42236.5448056764 -607.544805676371 47 29722 38726.2591351341 -9004.25913513411 48 7054 9657.29324208409 -2603.29324208409 49 56676 68818.3667677855 -12142.3667677855 50 34870 42607.036279409 -7737.03627940897 51 35117 41627.0811200571 -6510.0811200571 52 30169 31699.7326989933 -1530.7326989933 53 30936 34479.5543137396 -3543.55431373957 54 35699 38657.9551183166 -2958.95511831662 55 33228 26306.3776903325 6921.62230966755 56 27733 28468.0794929526 -735.079492952631 57 33666 30546.7885581965 3119.21144180351 58 35429 32314.6317135209 3114.36828647914 59 27438 25679.9052384661 1758.09476153389 60 8170 3673.84395806354 4496.15604193646 61 63410 60273.6800618941 3136.31993810585 62 38040 41632.7461880415 -3592.74618804153 63 45389 42723.037105081 2665.96289491898 64 37353 38566.6869910395 -1213.68699103955 65 37024 40399.5600900091 -3375.56009000906 66 50957 44942.5104227803 6014.48957721968 67 37994 40863.7491081566 -2869.74910815663 68 36454 35637.9114724363 816.088527563712 69 46080 40272.7944919672 5807.20550803276 70 43373 42963.3225029234 409.677497076569 71 37395 34686.0197217196 2708.98027828045 72 10963 14443.8529061886 -3480.85290618864 73 75001 67584.4755412208 7416.52445877917 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 46886.2424383856 37594.8310901928 56177.6537865784 75 52496.9713279909 42670.5478134247 62323.3948425571 76 45387.422024536 35053.6485930196 55721.1954560524 77 46503.7730345552 35686.4190336819 57321.1270354284 78 57135.3415099947 45855.1189134985 68415.5641064909 79 46325.011013349 34600.1785594161 58049.8434672818 80 44020.8286716264 31867.6410108071 56174.0163324457 81 50993.5243175777 38426.5738296754 63560.4748054799 82 48853.2227652656 35885.7049298554 61820.7406006757 83 41641.2936010668 28285.2165925297 54997.370609604 84 17219.0245666213 3485.37729780493 30952.6718354378 85 77275.3654877053 63174.2541290016 91376.476846409

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/14gxl1305729409.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/14gxl1305729409.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/22pl11305729409.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/22pl11305729409.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/3dpqg1305729409.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729161wyzuatx70w43at5/3dpqg1305729409.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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