Retail sales and food services - Isabelle Hoes

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 27 May 2010 10:45:09 +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/May/27/t1274957153arol7ybm26vr8tv.htm/, Retrieved Thu, 27 May 2010 12:45:54 +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/May/27/t1274957153arol7ybm26vr8tv.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 «

357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293009 294822 338844 335407 345080 350608 351285 355147 332791 335615 343202 404868 317902 313552 361505 351436 373350 366310 361669 375078 345547 348117 356089 416856 328087 322747 373626 358275 391287 376371 371848 387261 353159 367855 376822 425283 342191 344062 373587 370144 399979 380431 385909 384798 352554 352479 338788 387964 313593 304056 334149 336155 354668 351418 354316 359483 330411 344726 347175

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.609943620608653 beta 0.0462444503125317 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 386918 376360.299665169 10557.7003348314 14 293009 289731.696569409 3277.30343059078 15 294822 293478.974616221 1343.02538377937 16 338844 338379.351246054 464.648753945658 17 335407 335908.876911778 -501.87691177841 18 345080 345972.14221899 -892.142218990135 19 350608 342181.790690353 8426.20930964651 20 351285 355281.568763131 -3996.56876313133 21 355147 352151.436263208 2995.56373679161 22 332791 340899.140389615 -8108.14038961509 23 335615 342896.785248752 -7281.78524875152 24 343202 343402.26748632 -200.267486320168 25 404868 414078.702641918 -9210.70264191797 26 317902 306803.830044844 11098.1699551563 27 313552 314423.957074853 -871.957074853068 28 361505 360156.302375839 1348.69762416102 29 351436 357366.985262714 -5930.98526271351 30 373350 364109.144154601 9240.85584539914 31 366310 369945.869336141 -3635.8693361411 32 361669 370513.342069944 -8844.34206994408 33 375078 366647.4073439 8430.59265609964 34 345547 353091.213458242 -7544.21345824172 35 348117 355653.086272872 -7536.08627287159 36 356089 358710.381447685 -2621.38144768518 37 416856 426514.604984097 -9658.60498409742 38 328087 322716.942131211 5370.05786878947 39 322747 321506.41636454 1240.58363545983 40 373626 370113.706071517 3512.29392848274 41 358275 365068.816707848 -6793.81670784816 42 391287 377028.845898754 14258.1541012464 43 376371 380304.41728973 -3933.4172897301 44 371848 378199.162177427 -6351.16217742715 45 387261 382466.89280015 4794.10719984985 46 353159 359304.322000702 -6145.32200070168 47 367855 362493.575268288 5361.42473171209 48 376822 375752.043364205 1069.95663579466 49 425283 446851.918075464 -21568.9180754641 50 342191 337711.949702172 4479.05029782781 51 344062 333893.379549709 10168.620450291 52 373587 391451.394660793 -17864.3946607932 53 370144 368582.329060007 1561.67093999306 54 399979 394159.361088204 5819.63891179592 55 380431 384442.248971058 -4011.24897105753 56 385909 380781.022678237 5127.97732176317 57 384798 396551.243097282 -11753.2430972824 58 352554 358227.375240229 -5673.37524022942 59 352479 365613.750351211 -13134.7503512112 60 338788 364578.213513894 -25790.2135138935 61 387964 403581.811297175 -15617.8112971753 62 313593 312959.721236728 633.278763271926 63 304056 307691.410354691 -3635.41035469063 64 334149 339013.438628454 -4864.43862845434 65 336155 330236.976426515 5918.0235734848 66 354668 355689.184978092 -1021.18497809226 67 351418 337962.467385161 13455.532614839 68 354316 346829.130041056 7486.86995894386 69 359483 355431.995505037 4051.00449496263 70 330411 330179.588057195 231.411942805222 71 344726 336851.399300696 7874.60069930443 72 347175 342944.736818311 4230.26318168867 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 405916.737669491 389639.951184706 422193.524154277 74 328618.97028998 310301.144704528 346936.795875432 75 321820.044157382 300796.643294615 342843.445020149 76 357901.479217663 332677.759701704 383125.198733622 77 357418.372030887 329592.686698973 385244.057362802 78 378902.98322812 347184.870629806 410621.095826434 79 367668.330534595 334188.979826332 401147.681242857 80 366597.460273037 330674.996465697 402519.924080377 81 369869.040521126 331148.102502673 408589.978539579 82 340155.506141098 301696.013171721 378614.999110475 83 350250.268980912 308275.894278327 392224.643683497 84 350222.167644986 308831.778803132 391612.556486839

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/1plyk1274957105.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/1plyk1274957105.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/2plyk1274957105.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/2plyk1274957105.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/34vwb1274957105.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/27/t1274957153arol7ybm26vr8tv/34vwb1274957105.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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