Exponential Smoothing

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Dec 2009 11:09:40 -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/03/t1259863813619gsly29qyl2em.htm/, Retrieved Thu, 03 Dec 2009 19:10:17 +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/03/t1259863813619gsly29qyl2em.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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5560 3922 3759 4138 4634 3996 4308 4429 5219 4929 5755 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5526 4247 3830 4394 4826 4409 4569 4106 4794 3914 3793 4405 4022 4100 4788 3163 3585 3903 4178 3863 4187

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.136400379311296 beta 0.764143764094036 gamma 0.532919558253932 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4163 3804.99851942050 358.001480579503 14 4962 4619.58026217785 342.419737822145 15 5208 4981.75591859466 226.244081405342 16 4755 4696.32685219716 58.6731478028414 17 4491 4606.84339277074 -115.843392770738 18 5732 6053.94153285779 -321.941532857792 19 5731 5164.57701725345 566.422982746551 20 5040 5590.1229855836 -550.122985583603 21 6102 6501.5443895458 -399.544389545799 22 4904 6076.11507828765 -1172.11507828765 23 5369 6849.45840771214 -1480.45840771214 24 5578 6194.96725752462 -616.96725752462 25 4619 4437.27060010126 181.729399898736 26 4731 4995.53102873729 -264.531028737289 27 5011 4855.59017182273 155.409828177272 28 5299 4172.7003702016 1126.29962979840 29 4146 3966.68293802328 179.317061976718 30 4625 4988.03121163714 -363.031211637135 31 4736 4378.29640626406 357.703593735944 32 4219 4106.43064278002 112.569357219979 33 5116 4799.29332900233 316.70667099767 34 4205 4197.89174511871 7.10825488129285 35 4121 4818.03501444208 -697.035014442075 36 5103 4731.8580955895 371.141904410494 37 4300 3831.01667102751 468.983328972488 38 4578 4353.20337485126 224.796625148739 39 3809 4714.65886382585 -905.658863825853 40 5526 4478.61104419984 1047.38895580016 41 4247 3974.55105242518 272.448947574816 42 3830 4894.23934140712 -1064.23934140712 43 4394 4591.87346856672 -197.873468566718 44 4826 4145.53482018947 680.465179810531 45 4409 5105.9198748165 -696.919874816502 46 4569 4201.86143670517 367.13856329483 47 4106 4564.54500082431 -458.545000824312 48 4794 5059.56625581318 -265.566255813183 49 3914 4082.84941219792 -168.849412197923 50 3793 4306.68283092809 -513.682830928088 51 4405 3886.98621259734 518.013787402663 52 4022 4659.15224601824 -637.152246018236 53 4100 3507.96398467972 592.036015320284 54 4788 3676.24787308608 1111.75212691392 55 3163 4119.94164016574 -956.94164016574 56 3585 3963.46161866683 -378.461618666835 57 3903 3990.49342470667 -87.493424706674 58 4178 3642.44519888634 535.554801113656 59 3863 3615.82003964365 247.179960356350 60 4187 4226.08359918485 -39.0835991848535 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 3487.72670805667 2799.90973148786 4175.54368462548 62 3618.45899558128 2872.71547901424 4364.20251214832 63 3839.05702656775 2971.64043732906 4706.47361580644 64 4052.96786056963 2993.2048673035 5112.73085383576 65 3688.73142366956 2495.36892381734 4882.09392352178 66 4037.82782078263 2516.70063302386 5558.9550085414 67 3354.14820932174 1811.20209724205 4897.09432140144 68 3608.04107720640 1697.0913864528 5518.99076796001 69 3884.34865237854 1524.19376531099 6244.50353944608 70 3913.38138564548 1192.88062443812 6633.88214685284 71 3705.40062296169 777.086115053747 6633.71513086963 72 4139.26143821402 542.566114842396 7735.95676158564

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/19xs21259863777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/19xs21259863777.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/2ferj1259863777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/2ferj1259863777.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/3ghb71259863777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259863813619gsly29qyl2em/3ghb71259863777.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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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