*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Aug 2009 11:07:26 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63.htm/, Retrieved Sun, 16 Aug 2009 19:08:40 +0200

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/Aug/16/t1250442516lqrx1ah9q834g63.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:

» Textbox « » Textfile « » CSV «

72,84 73,96 73,26 73,86 73,04 212,8 157,92 111,55 99,01 89,5 100,95 116,06 131,5 137,43 138,53 137,26 136,81 182,98 149,45 109,34 93,37 84,09 83,83 82,94 82,88 81,41 79,87 79,66 76,07 182,69 165,78 142,5 120,6 105,73 98,72 98,41 96,08 97,3 97,5 97,02 98,75 232,81 240,83 193,4 148,28 138,34 135,34 134,02 133,86 131,67 132,43 130,21 129,98 206,16 195,17 159,16 136,33 125,18 121,21 119,38 119,26 119,75 118,78 116,97 121,69 223,51 228,58 205,22 189,4 180,14 177,59 176,39 171,16 173,11 171,74 175,97 179,64 254,62 240,5 212,01 176,36 153,24 146,69 141,52 142,6 143,19 142,32 142,03 144,92 177,31 194,4 189,19 180,44 175,84 178,54 176,55

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.929989159847248 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 131.5 113.305714174274 18.1942858257257 14 137.43 137.974551701713 -0.544551701712805 15 138.53 140.340439005924 -1.81043900592434 16 137.26 139.292529560728 -2.03252956072808 17 136.81 139.387640893203 -2.57764089320281 18 182.98 188.245230333321 -5.26523033332143 19 149.45 184.803288962658 -35.3532889626577 20 109.34 103.736795169832 5.60320483016845 21 93.37 93.3794968619423 -0.00949686194233834 22 84.09 81.665020226247 2.42497977375298 23 83.83 91.7655111862668 -7.93551118626677 24 82.94 97.1210791226548 -14.1810791226548 25 82.88 98.5752185079875 -15.6952185079875 26 81.41 88.5952534687052 -7.18525346870516 27 79.87 84.1426336785468 -4.27263367854684 28 79.66 81.119372501963 -1.45937250196295 29 76.07 81.4832106853364 -5.41321068533644 30 182.69 105.825899270878 76.8641007291216 31 165.78 176.216490802454 -10.4364908024540 32 142.5 115.847018188818 26.6529818111824 33 120.6 119.791116015651 0.808883984348782 34 105.73 105.369052697395 0.360947302604799 35 98.72 114.332266471431 -15.6122664714306 36 98.41 114.050955619058 -15.6409556190585 37 96.08 116.449692253561 -20.3696922535607 38 97.3 103.344233617483 -6.04423361748266 39 97.5 100.34415490479 -2.84415490479013 40 97.02 98.7867686268537 -1.76676862685372 41 98.75 98.5661583306535 0.183841669346549 42 232.81 140.93937568456 91.8706243154399 43 240.83 216.949158999637 23.8808410003633 44 193.4 168.759011032804 24.6409889671965 45 148.28 160.826969898315 -12.5469698983152 46 138.34 130.127155229314 8.21284477068582 47 135.34 147.037480061412 -11.6974800614124 48 134.02 155.141438975657 -21.1214389756574 49 133.86 157.497848228690 -23.6378482286904 50 131.67 144.560722945706 -12.8907229457061 51 132.43 135.931789495187 -3.5017894951867 52 130.21 133.748952916699 -3.53895291669934 53 129.98 132.069884988681 -2.08988498868149 54 206.16 190.351485060288 15.8085149397118 55 195.17 192.644734398672 2.52526560132816 56 159.16 138.121713365665 21.0382866343348 57 136.33 130.557867088628 5.77213291137218 58 125.18 119.862731573144 5.31726842685615 59 121.21 131.954380405339 -10.7443804053388 60 119.38 138.391881533937 -19.0118815339374 61 119.26 140.253698745492 -20.9936987454921 62 119.75 129.628314538365 -9.87831453836537 63 118.78 124.229876447978 -5.44987644797848 64 116.97 120.260059049991 -3.29005904999086 65 121.69 118.880945098856 2.80905490114449 66 223.51 179.016840310821 44.4931596891794 67 228.58 206.002537173279 22.5774628267214 68 205.22 161.929461231110 43.2905387688905 69 189.4 166.052109338176 23.3478906618239 70 180.14 165.217018751686 14.9229812483140 71 177.59 187.194932773089 -9.6049327730889 72 176.39 200.763514177480 -24.3735141774796 73 171.16 206.059970511165 -34.8999705111648 74 173.11 186.989177727086 -13.8791777270861 75 171.74 179.381107528609 -7.64110752860947 76 175.97 173.449511924002 2.52048807599792 77 179.64 178.247833517453 1.39216648254717 78 254.62 266.870582063894 -12.2505820638935 79 240.5 236.833171960790 3.66682803921034 80 212.01 172.673712156756 39.3362878432438 81 176.36 170.770165824129 5.58983417587052 82 153.24 154.464255749855 -1.22425574985505 83 146.69 158.876839049809 -12.1868390498092 84 141.52 165.384332148669 -23.864332148669 85 142.6 165.15956205409 -22.5595620540901 86 143.19 156.848670740075 -13.6586707400753 87 142.32 149.137645674677 -6.81764567467673 88 142.03 144.599200734974 -2.56920073497403 89 144.92 144.398710283295 0.521289716704558 90 177.31 214.913996051311 -37.6039960513109 91 194.4 168.111082203988 26.2889177960116 92 189.19 140.347532800055 48.8424671999452 93 180.44 150.104225600533 30.3357743994673 94 175.84 156.079593518720 19.7604064812797 95 178.54 179.691595421468 -1.15159542146847 96 176.55 198.797301018429 -22.2473010184293 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 205.259082949355 162.400179191347 248.117986707364 98 223.676991638419 162.843328577126 284.510654699713 99 231.407744271001 157.327138946502 305.488349595499 100 233.941863898399 149.512909719481 318.370818077318 101 236.993026804595 143.110132423085 330.875921186105 102 345.021288263484 204.387210569578 485.65536595739 103 328.425851119435 189.407657235446 467.444045003424 104 240.505297334114 131.195733644992 349.814861023237 105 192.787573944479 96.5167579893626 289.058389899595 106 168.016308700406 75.2316744704573 260.800942930354 107 171.662811817287 69.36537295357 273.960250681004 108 189.509901875503 75.7845693001444 303.235234450861

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/1lsdh1250442443.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/1lsdh1250442443.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/2eelh1250442443.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/2eelh1250442443.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/3ss011250442443.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442516lqrx1ah9q834g63/3ss011250442443.ps (open in new window)

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = Unknown ;

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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