lynn.pelgrims@student.kdg.be

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 20:13:31 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8.htm/, Retrieved Thu, 19 May 2011 22:13:17 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4734 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6923 9858 11331 4016 3957 4510 4276 4968 4677 3523 1821 5222 6872 10803 13916 2639 2899 3370 3740 2927 3986 4217 1738 5221 6424 9842 13076 3934 3162 4286 4676 5010 4874 4633 1659 5951 6981 9851 12670

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' @ 216.218.223.82 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.308920174800032 beta 0 gamma 0.63304779631648 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2541 2393.50833868648 147.491661313524 14 2475 2389.82957954486 85.1704204551402 15 3031 2978.46749248468 52.5325075153246 16 3266 3224.68452592027 41.3154740797308 17 3776 3723.54556511424 52.4544348857607 18 3230 3146.04134513217 83.9586548678344 19 3028 2495.93638764876 532.063612351243 20 1759 2615.42697148435 -856.426971484353 21 3595 3129.98059337787 465.019406622129 22 4474 4811.19275455775 -337.192754557747 23 6838 6258.55829948475 579.441700515249 24 8357 7934.86975076983 422.130249230167 25 3113 2940.90516043429 172.094839565706 26 3006 2897.68831373255 108.311686267446 27 4047 3580.46589940871 466.534100591291 28 3523 3995.51499634823 -472.514996348226 29 3937 4423.94954379872 -486.949543798717 30 3986 3610.75875581215 375.24124418785 31 3260 3148.73441559458 111.26558440542 32 1573 2417.2388004176 -844.238800417595 33 3528 3625.06086969704 -97.0608696970385 34 5211 4817.25400517526 393.745994824736 35 7614 7041.6915738063 572.308426193701 36 9254 8751.14534360582 502.854656394184 37 5375 3252.8736881419 2122.1263118581 38 3088 3743.2519181274 -655.2519181274 39 3718 4484.22248389336 -766.222483893357 40 4514 4085.57228718524 428.427712814763 41 4520 4862.05195726191 -342.051957261911 42 4539 4410.93535956836 128.064640431644 43 3663 3653.32724170051 9.6727582994904 44 1643 2264.46469501254 -621.464695012545 45 4734 4149.69369766263 584.306302337369 46 5428 6067.62647796335 -639.626477963354 47 8314 8359.27994241763 -45.2799424176301 48 10651 10011.6052518353 639.394748164725 49 3633 4499.57305081962 -866.57305081962 50 4292 3012.53813717407 1279.46186282593 51 4154 4324.06523554391 -170.06523554391 52 4121 4656.288978844 -535.288978843996 53 4647 4799.96689031067 -152.966890310666 54 4753 4607.06030980049 145.939690199511 55 3965 3774.97903745214 190.020962547855 56 1723 2059.85167444573 -336.851674445727 57 5048 4770.79937146954 277.200628530462 58 6923 6117.09990459278 805.900095407219 59 9858 9488.97632961112 369.02367038888 60 11331 11853.5444537716 -522.544453771616 61 4016 4563.31949339721 -547.319493397212 62 3957 3996.87204542113 -39.8720454211334 63 4510 4266.86126847803 243.13873152197 64 4276 4564.85778587997 -288.857785879971 65 4968 4974.17235853488 -6.17235853488091 66 4677 4953.99768781614 -276.997687816143 67 3523 3980.72313410983 -457.72313410983 68 1821 1867.19289066026 -46.1928906602607 69 5222 5009.48685230371 212.513147696287 70 6872 6581.45741871882 290.542581281177 71 10803 9580.8148104008 1222.18518959919 72 13916 11851.2739311343 2064.72606886566 73 2639 4698.39199842502 -2059.39199842502 74 2899 3891.23363939581 -992.233639395808 75 3370 3952.59002165526 -582.590021655264 76 3740 3766.1311848531 -26.1311848531027 77 2927 4299.77610625762 -1372.77610625762 78 3986 3773.76575338307 212.234246616928 79 4217 3055.86933497662 1161.13066502338 80 1738 1733.60236826915 4.39763173084611 81 5221 4830.86842062341 390.131579376592 82 6424 6427.33679785996 -3.33679785996355 83 9842 9546.13288845202 295.867111547977 84 13076 11678.2450754074 1397.75492459262 85 3934 3308.1346526193 625.865347380701 86 3162 3785.80690373151 -623.806903731512 87 4286 4199.67146838314 86.3285316168594 88 4676 4505.69936087628 170.30063912372 89 5010 4415.17155919637 594.828440803634 90 4874 5415.26988008695 -541.269880086954 91 4633 4676.44951397193 -43.4495139719284 92 1659 2060.96806905497 -401.968069054974 93 5951 5568.76517552133 382.234824478671 94 6981 7129.87966154635 -148.879661546348 95 9851 10660.3884204093 -809.388420409317 96 12670 13071.0034899073 -401.003489907263 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 3629.69257528739 2668.82693621589 4590.55821435889 98 3364.11570380035 2335.75515871177 4392.47624888892 99 4292.92276662416 3112.29238737278 5473.55314587553 100 4610.10830334885 3329.48554071608 5890.73106598162 101 4642.27216964661 3300.56105880802 5983.98328048519 102 4941.39296431942 3498.2680794252 6384.51784921364 103 4592.81587806067 3161.56050742819 6024.07124869315 104 1853.29345270853 790.339974286499 2916.24693113056 105 6031.38922364695 3853.53727607732 8209.24117121658 106 7277.06845881118 4698.45262837149 9855.68428925086 107 10674.5896268213 7008.0364459173 14341.1428077252 108 13682.0400723341 9142.93903315879 18221.1411115094

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/1mu0g1305836008.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/1mu0g1305836008.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/2tu461305836008.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/2tu461305836008.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/3uje41305836008.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305835993euagxqvsptu9nq8/3uje41305836008.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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