Exponential Smoothing - Consumptie wijn - Veronika Kaplova

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 28 May 2010 15:27:14 +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/28/t127506050844ypym524i49at8.htm/, Retrieved Fri, 28 May 2010 17:28:32 +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/28/t127506050844ypym524i49at8.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 «

2550 2867 3458 2961 3163 2880 3331 3062 3534 3622 4464 5411 2564 2820 3508 3088 3299 2939 3320 3418 3604 3495 4163 4882 2211 3260 2992 2425 2707 3244 3965 3315 3333 3583 4021 4904 2252 2952 3573 3048 3059 2731 3563 3092 3478 3478 4308 5029 2075 3264 3308 3688 3136 2824 3644 4694 2914 3686 4358 5587 2265 3685 3754 3708 3210 3517 3905 3670 4221 4404 5086 5725 2367 3819 4067 4022 3937 4365 4290

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 0.0219538867872071 beta 0.849748700445273 gamma 0.31528236748219 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2564 2540.43602621567 23.5639737843312 14 2820 2786.89098463547 33.1090153645282 15 3508 3455.56989823856 52.4301017614375 16 3088 3050.56973081324 37.4302691867629 17 3299 3283.39819595327 15.6018040467293 18 2939 2961.14590175454 -22.1459017545403 19 3320 3366.75875814298 -46.7587581429775 20 3418 3100.59931681039 317.400683189611 21 3604 3599.56837945171 4.43162054829372 22 3495 3694.90035916793 -199.900359167934 23 4163 4546.02210889468 -383.022108894679 24 4882 5493.2020492742 -611.202049274198 25 2211 2599.88516127479 -388.885161274794 26 3260 2829.75306104031 430.246938959695 27 2992 3514.04923030427 -522.049230304274 28 2425 3070.94469955403 -645.944699554028 29 2707 3249.40172859017 -542.401728590168 30 3244 2870.35214456770 373.647855432297 31 3965 3232.17887781673 732.821122183275 32 3315 3080.69145459866 234.308545401342 33 3333 3443.40913219231 -110.409132192313 34 3583 3446.36955696997 136.630443030027 35 4021 4185.26716669707 -164.267166697068 36 4904 4995.02349954517 -91.0234995451665 37 2252 2332.71711674191 -80.7171167419096 38 2952 2791.13887019654 160.861129803455 39 3573 3144.28423347904 428.715766520959 40 3048 2716.65581452568 331.34418547432 41 3059 2963.79533803315 95.2046619668545 42 2731 2920.88139677717 -189.881396777173 43 3563 3399.23070619969 163.769293800309 44 3092 3106.31236676567 -14.3123667656746 45 3478 3367.92849927736 110.07150072264 46 3478 3470.47216221219 7.52783778780577 47 4308 4130.19080414777 177.809195852225 48 5029 5002.94381004437 26.0561899556269 49 2075 2341.88088511256 -266.880885112562 50 3264 2893.34757275042 370.652427249584 51 3308 3364.69995854097 -56.6999585409685 52 3688 2896.39343174623 791.60656825377 53 3136 3106.59651997808 29.4034800219247 54 2824 2987.66349368554 -163.663493685535 55 3644 3624.47889309474 19.5211069052552 56 4694 3273.89766748418 1420.10233251582 57 2914 3673.86917067579 -759.869170675788 58 3686 3763.76039016466 -77.760390164658 59 4358 4570.98991837248 -212.989918372482 60 5587 5498.17264158295 88.8273584170529 61 2265 2496.17060320570 -231.170603205705 62 3685 3347.35915372792 337.640846272082 63 3754 3747.33898683811 6.66101316189406 64 3708 3539.20744667407 168.792553325934 65 3210 3504.03572867123 -294.035728671233 66 3517 3298.69945035517 218.300549644833 67 3905 4100.03008792936 -195.030087929355 68 3670 4190.1011634476 -520.1011634476 69 4221 3806.95905597092 414.040944029085 70 4404 4159.40935432775 244.590645672249 71 5086 5015.05920873687 70.9407912631259 72 5725 6160.50026357569 -435.500263575693 73 2367 2694.56000863673 -327.560008636734 74 3819 3825.67730976688 -6.67730976687517 75 4067 4131.41753902044 -64.4175390204364 76 4022 3939.85923129124 82.1407687087567 77 3937 3725.88583305532 211.11416694468 78 4365 3679.12360994954 685.876390050455 79 4290 4429.40676732055 -139.406767320545 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 80 4422.69523593488 4191.14601114111 4654.24446072865 81 4343.32522124694 4110.12578300933 4576.52465948454 82 4668.34678357059 4430.88942459568 4905.8041425455 83 5544.839680593 5296.0800743669 5793.59928681909 84 6629.07501932279 6356.60615170544 6901.54388694014 85 2859.88705468780 2615.75914260311 3104.01496677250 86 4241.30154429076 3969.00497576137 4513.59811282014 87 4575.15167462803 4278.008072942 4872.29527631407 88 4428.69191307064 4114.4905308867 4742.89329525458 89 4244.56764548917 3914.14174975514 4574.9935412232 90 4357.91690051763 3997.35064722494 4718.48315381033 91 4886.56018785983 4536.78910148962 5236.33127423003

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/1q5qv1275060432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/1q5qv1275060432.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/2q5qv1275060432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/2q5qv1275060432.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/3je8g1275060432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t127506050844ypym524i49at8/3je8g1275060432.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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