*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: Tue, 21 Dec 2010 15:34:15 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9.htm/, Retrieved Tue, 21 Dec 2010 16:32:14 +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/2010/Dec/21/t1292945534itwae5d4j2ramn9.htm/}, year = {2010}, } @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 = {2010}, 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 «

3010 2910 3840 3580 3140 3550 3250 2820 2260 2060 2120 2210 2190 2180 2350 2440 2370 2440 2610 3040 3190 3120 3170 3600 3420 3650 4180 2960 2710 2950 3030 3770 4740 4450 5550 5580 5890 7480 10450 6360 6710 6200 4490 3480 2520 1920 2010 1950 2240 2370 2840 2700 2980 3290 3300 3000 2330 2190 1970 2170 2830 3190 3550 3240 3450 3570 3230 3260 2700

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.917611569721477 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 3840 2910 930 4 3580 3763.37875984097 -183.378759840974 5 3140 3595.10828816972 -455.10828816972 6 3550 3177.49565746905 372.504342530951 7 3250 3519.30995194694 -269.309951946942 8 2820 3272.18802419929 -452.188024199293 9 2260 2857.25506150453 -597.255061504527 10 2060 2309.20690699326 -249.206906993260 11 2120 2080.53176588174 39.4682341182593 12 2210 2116.74827414513 93.2517258548687 13 2190 2202.31713668605 -12.3171366860543 14 2180 2191.01478955709 -11.0147895570899 15 2350 2180.90749122146 169.092508778543 16 2440 2336.06873362988 103.931266370122 17 2370 2431.43726610691 -61.4372661069065 18 2440 2375.06171991515 64.938280084848 19 2610 2434.64983703882 175.350162961178 20 3040 2595.55317532455 444.446824675455 21 3190 3003.38272377272 186.617276227284 22 3120 3174.62489554878 -54.6248955487804 23 3170 3124.50045939839 45.4995406016078 24 3600 3166.25136427144 433.74863572856 25 3420 3564.26413076687 -144.264130766873 26 3650 3431.88569527938 218.114304720622 27 4180 3632.02990481278 547.970095187223 28 2960 4134.85360401795 -1174.85360401795 29 2710 3056.79434424210 -346.794344242104 30 2950 2738.57184165158 211.428158348423 31 3030 2932.58076591699 97.4192340830054 32 3770 3021.97378222497 748.026217775035 33 4740 3708.37129411033 1031.62870588967 34 4450 4655.00573029149 -205.005730291487 35 5550 4466.89010031682 1083.10989968318 36 5580 5460.76427554597 119.235724454025 37 5890 5570.17635582911 319.823644170890 38 7480 5863.6502319908 1616.34976800920 39 10450 7346.83147983267 3103.16852016733 40 6360 10194.3348167337 -3834.33481673369 41 6710 6675.90482671298 34.0951732870244 42 6200 6707.19095219281 -507.190952192808 43 4490 6241.78666640264 -1751.78666640264 44 3480 4634.32695362776 -1154.32695362776 45 2520 3575.10318573758 -1055.10318573758 46 1920 2606.92829525479 -686.928295254788 47 2010 1976.59494395994 33.4050560400565 48 1950 2007.24780986949 -57.2478098694937 49 2240 1954.71655719203 285.283442807969 50 2370 2216.4959449626 153.504055037401 51 2840 2357.35304186408 482.646958135919 52 2700 2800.23547474048 -100.235474740478 53 2980 2708.25824342209 271.741756577910 54 3290 2957.61162323442 332.388376765583 55 3300 3262.61504339546 37.3849566045424 56 3000 3296.91991210932 -296.919912109321 57 2330 3024.46276547712 -694.462765477124 58 2190 2387.21569713454 -197.215697134542 59 1970 2206.2482917132 -236.248291713199 60 2170 1989.46412591023 180.535874089767 61 2830 2155.12593272478 674.874067275217 62 3190 2774.39818496151 415.601815038487 63 3550 3155.75921883807 394.240781161926 64 3240 3517.51912088829 -277.51912088829 65 3450 3262.86436474226 187.135635257738 66 3570 3434.58218876194 135.417811238059 67 3230 3558.84313910034 -328.843139100343 68 3260 3257.09287003834 2.90712996166076 69 2700 3259.76048612584 -559.760486125843 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 70 2746.11778778385 1162.39028115570 4329.84529441201 71 2746.11778778385 596.671640989021 4895.56393457868 72 2746.11778778385 151.499384108342 5340.73619145936 73 2746.11778778385 -227.763612576989 5719.99918814469 74 2746.11778778385 -563.851472818528 6056.08704838623 75 2746.11778778385 -868.82653113078 6361.06210669848 76 2746.11778778385 -1150.00186535485 6642.23744092256 77 2746.11778778385 -1412.20811025423 6904.44368582193 78 2746.11778778385 -1658.83399367922 7151.06956924692 79 2746.11778778385 -1892.36538236296 7384.60095793066 80 2746.11778778385 -2114.68996838751 7606.92554395522 81 2746.11778778385 -2327.28126661510 7819.5168421828

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/1vg1q1292945651.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/1vg1q1292945651.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/2oqib1292945651.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/2oqib1292945651.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/3oqib1292945651.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945534itwae5d4j2ramn9/3oqib1292945651.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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