*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Jun 2010 10:28:11 +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/Jun/05/t1275733736vfusfwwr7aiyabm.htm/, Retrieved Sat, 05 Jun 2010 12:28:56 +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/2010/Jun/05/t1275733736vfusfwwr7aiyabm.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

7089 77102 35123 23109 11115 48105 7896 79102 2494 76101 9484 8183 9092 49109 27127 31116 77120 80115 67117 18110 3099 3105 5786 7387 5089 288 65108 44100 68102 8798 8183 288 3680 9374 2271 4671 3466 8068 2780 9883 6479 3373 6468 460 5553 6157 2345 3744 6144 9948 2049 9549 6049 745 9643 9938 5535 6932 1827 9726 7624 9529 7631 6132 7534 2137 8738 8836 3230 633 9126 123

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 beta 0 gamma 0.769366005522916 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 9092 6099.76957811147 2992.23042188853 14 49109 33007.0120293955 16101.9879706045 15 27127 19441.1766657392 7685.82333426077 16 31116 24225.1139393889 6890.8860606111 17 77120 66085.3443844594 11034.6556155406 18 80115 69059.1700769884 11055.8299230116 19 67117 6678.95211761443 60438.0478823856 20 18110 69241.2740108332 -51131.2740108332 21 3099 2293.78721472168 805.212785278321 22 3105 69990.6959818707 -66885.6959818707 23 5786 7898.92425550947 -2112.92425550947 24 7387 6057.87065445871 1329.12934554129 25 5089 8401.889945404 -3312.88994540400 26 288 45395.3341953175 -45107.3341953175 27 65108 25354.3878635743 39753.6121364257 28 44100 29526.7274223548 14573.2725776452 29 68102 74575.0332977089 -6473.03329770888 30 8798 77565.1497825966 -68767.1497825966 31 8183 53177.9315984881 -44994.9315984881 32 288 29902.6099678208 -29614.6099678208 33 3680 2913.29055892724 766.709441072758 34 9374 18531.1152376787 -9157.11523767867 35 2271 6273.31216107567 -4002.31216107567 36 4671 7080.4575898611 -2409.4575898611 37 3466 5853.06504137149 -2387.06504137149 38 8068 10691.2846656788 -2623.28466567885 39 2780 55939.4656380834 -53159.4656380834 40 9883 40738.9079328143 -30855.9079328143 41 6479 69594.9015258338 -63115.9015258338 42 3373 24658.0424431642 -21285.0424431642 43 6468 18560.3608057825 -12092.3608057825 44 460 7118.13579175937 -6658.13579175937 45 5553 3503.1707390021 2049.82926099790 46 6157 11485.9420651528 -5328.9420651528 47 2345 3194.06924085309 -849.069240853092 48 3744 5226.70282847279 -1482.70282847279 49 6144 4016.53834556811 2127.46165443189 50 9948 8673.018621096 1274.98137890401 51 2049 15040.3799043785 -12991.3799043785 52 9549 16999.4212997621 -7450.42129976212 53 6049 21035.6724839253 -14986.6724839253 54 745 8282.05436128123 -7537.05436128123 55 9643 9256.90947529575 386.090524704254 56 9938 1995.59245342431 7942.4075465757 57 5535 5080.23968954004 454.760310459956 58 6932 7386.03519482315 -454.035194823153 59 1827 2540.82423060557 -713.824230605574 60 9726 4085.96167595315 5640.03832404685 61 7624 5653.33502054155 1970.66497945845 62 9529 9653.94595169947 -124.945951699468 63 7631 5045.25384111612 2585.74615888388 64 6132 11267.3204249013 -5135.32042490129 65 7534 9505.4361388875 -1971.4361388875 66 2137 2483.30095393322 -346.300953933217 67 8738 9553.9544000577 -815.954400057704 68 8836 8106.21082176831 729.789178231689 69 3230 5430.11681306898 -2200.11681306898 70 633 7036.71595061524 -6403.71595061524 71 9126 1991.63213365909 7134.3678663409 72 123 8425.21543232124 -8302.21543232124 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 7169.4976640114 -26616.7049340432 40955.700262066 74 9557.81678393419 -24228.3858141204 43344.0193819888 75 7034.63903467283 -26751.5635633818 40820.8416327274 76 7316.37946251474 -26469.8231355399 41102.5820605693 77 7988.6801915681 -25797.5224064865 41774.8827896227 78 2216.86877229684 -31569.3338257578 36003.0713703514 79 8926.18682259646 -24860.0157754581 42712.3894206511 80 8667.68580669828 -25118.5167913563 42453.8884047529 81 3737.42172891429 -30048.7808691403 37523.6243269689 82 2109.91458918701 -31676.2880088676 35896.1171872416 83 7480.57224091685 -26305.6303571378 41266.7748389714 84 2037.77310816554 NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/1icwt1275733687.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/1icwt1275733687.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/2blve1275733687.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/2blve1275733687.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/3blve1275733687.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275733736vfusfwwr7aiyabm/3blve1275733687.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=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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