Exponential smoothing witte wijn verkoop Australië

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 13:58:50 +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/06/t127583277059wbuwfdm273cta.htm/, Retrieved Sun, 06 Jun 2010 15:59:34 +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/06/t127583277059wbuwfdm273cta.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 «

1954 2302 3054 2414 2226 2725 2589 3470 2400 3180 4009 3924 2072 2434 2956 2828 2687 2629 3150 4119 3030 3055 3821 4001 2529 2472 3134 2789 2758 2993 3282 3437 2804 3076 3782 3889 2271 2452 3084 2522 2769 3438 2839 3746 2632 2851 3871 3618 2389 2344 2678 2492 2858 2246 2800 3869 3007 3023 3907 4209 2353 2570 2903 2910 3782 2759 2931 3641 2794 3070 3576 4106 2452 2206 2488 2416 2534 2521 3093 3903 2907 3025 3812 4209

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.369649244277171 beta 0.00993226516517318 gamma 0.570305179539606 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2072 2006.68440258248 65.3155974175247 14 2434 2364.80808988699 69.1919101130079 15 2956 2875.65737218089 80.3426278191091 16 2828 2782.88890432896 45.1110956710413 17 2687 2692.76062571217 -5.76062571216744 18 2629 2657.54308286388 -28.5430828638755 19 3150 2813.98415850912 336.015841490876 20 4119 3954.81928031406 164.180719685939 21 3030 2797.84170833199 232.158291668007 22 3055 3833.43262096272 -778.432620962715 23 3821 4448.03815236594 -627.038152365939 24 4001 4136.17590677012 -135.175906770116 25 2529 2184.31225076755 344.687749232453 26 2472 2686.94799112296 -214.947991122958 27 3134 3132.94575940254 1.05424059746383 28 2789 2986.57353373055 -197.573533730553 29 2758 2781.72444066096 -23.7244406609598 30 2993 2728.01963951761 264.980360482394 31 3282 3137.64321765883 144.356782341169 32 3437 4182.95408726275 -745.954087262747 33 2804 2757.90169803649 46.0983019635109 34 3076 3298.86754297183 -222.867542971832 35 3782 4142.85719190746 -360.857191907457 36 3889 4102.49717875758 -213.497178757575 37 2271 2291.3499594395 -20.3499594394980 38 2452 2442.28447537688 9.71552462311502 39 3084 3026.03531927356 57.9646807264371 40 2522 2831.01685839742 -309.016858397422 41 2769 2647.93666754506 121.063332454938 42 3438 2744.35961559261 693.640384407395 43 2839 3273.33897787271 -434.338977872713 44 3746 3736.29201683936 9.70798316063838 45 2632 2849.36695828950 -217.366958289504 46 2851 3188.29601732302 -337.296017323021 47 3871 3912.52244562161 -41.5224456216129 48 3618 4039.31927743104 -421.319277431045 49 2389 2245.53854743103 143.461452568965 50 2344 2467.71088386613 -123.710883866128 51 2678 3010.28585660102 -332.285856601022 52 2492 2552.69802575038 -60.6980257503751 53 2858 2610.56924010095 247.430759899048 54 2246 2933.04347847209 -687.04347847209 55 2800 2559.03307821820 240.966921781798 56 3869 3345.70983198529 523.290168014706 57 3007 2615.62594789321 391.374052106793 58 3023 3139.50463909946 -116.504639099456 59 3907 4099.96328287365 -192.963282873648 60 4209 4026.27903115901 182.720968840985 61 2353 2517.87690113672 -164.876901136724 62 2570 2531.38136064977 38.6186393502262 63 2903 3088.85754423609 -185.857544236093 64 2910 2760.56295689399 149.437043106009 65 3782 3026.60819327319 755.391806726809 66 2759 3154.27350131302 -395.273501313020 67 2931 3269.86980707291 -338.869807072906 68 3641 4051.65694382411 -410.656943824106 69 2794 2874.95772752598 -80.957727525978 70 3070 3035.06948128551 34.9305187144878 71 3576 4018.10535899468 -442.105358994679 72 4106 3979.73902662874 126.260973371255 73 2452 2376.65624769638 75.3437523036196 74 2206 2550.92778697610 -344.927786976104 75 2488 2857.33546422964 -369.335464229642 76 2416 2588.9893835527 -172.989383552701 77 2534 2878.32776861777 -344.327768617773 78 2521 2306.5684216494 214.431578350598 79 3093 2612.56512273000 480.434877270003 80 3903 3594.92481758455 308.075182415454 81 2907 2811.03752163595 95.9624783640547 82 3025 3079.33402369482 -54.3340236948206 83 3812 3848.93253200061 -36.9325320006142 84 4209 4175.34960117933 33.6503988206687 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 2471.07481034546 2034.35948904420 2907.79013164672 86 2458.75044604526 1969.06047973908 2948.44041235143 87 2905.90190972403 2332.08099969688 3479.72281975118 88 2835.85704427651 2226.48088442140 3445.23320413161 89 3166.12863070004 2473.22136480856 3859.03589659151 90 2871.16413740044 2184.09031920512 3558.23795559576 91 3235.36115711707 2451.27595883966 4019.44635539448 92 4042.71359985493 3074.53345724137 5010.89374246849 93 3010.76221990253 2212.78859366489 3808.73584614017 94 3196.65347715677 2327.88492030864 4065.4220340049 95 4032.75511971334 2947.96372307536 5117.54651635131 96 4417.44255352766 3296.43142553109 5538.45368152422

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/19vf61275832727.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/19vf61275832727.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/29vf61275832727.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/29vf61275832727.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/3k4er1275832727.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127583277059wbuwfdm273cta/3k4er1275832727.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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