Exponential Smoothing-Consumentenprijzen Kabeljauw-Toon Baeten

*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 17:56:42 +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/t13058276703ec8b1w03da0ojb.htm/, Retrieved Thu, 19 May 2011 19:54:33 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

12,32 12,34 12,36 12,54 12,77 12,79 12,96 12,96 13 13,19 13,25 13,61 13,8 13,83 14,04 14,16 14,2 14,27 14,31 14,69 14,9 14,92 15,01 15,09 15,14 15,24 15,33 15,36 15,44 15,5 15,58 15,65 15,72 15,82 15,87 16,07 16,18 16,19 16,39 16,54 16,61 16,62 16,66 16,71 16,72 16,79 16,82 16,83 16,91 16,97 17,02 17,03 17,04 17,07 17,11 17,12 17,14 17,18 17,24 17,26 17,26 17,29 17,36 17,44 17,48 17,48 17,52 17,54 17,58 17,64 17,69 17,69 17,76 17,79 17,82 17,89 17,95 18 18,03 18,06 18,08 18,13 18,16 18,18 18,18 18,27 18,31 18,35 18,45 18,5

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 1 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.1650321679672 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 12.36 12.36 0 4 12.54 12.38 0.16 5 12.77 12.5864051468748 0.183594853125248 6 12.79 12.8467042035136 -0.0567042035136307 7 12.96 12.8573461858749 0.102653814125079 8 12.96 13.0442873673701 -0.0842873673700861 9 13 13.0303772404008 -0.030377240400755 10 13.19 13.0653640185606 0.124635981439443 11 13.25 13.2759329647842 -0.0259329647842268 12 13.61 13.3316531913841 0.278346808615931 13 13.8 13.7375893686567 0.062410631343294 14 13.83 13.9378891304515 -0.107889130451493 15 14.04 13.950083953353 0.0899160466470121 16 14.16 14.1749229934662 -0.0149229934661825 17 14.2 14.2924602195019 -0.0924602195019002 18 14.27 14.3172013090268 -0.0472013090267769 19 14.31 14.3794115746672 -0.069411574667198 20 14.69 14.4079564320179 0.282043567982145 21 14.9 14.8345026935032 0.0654973064968498 22 14.92 15.0553118559903 -0.13531185599034 23 15.01 15.0529810470446 -0.0429810470445879 24 15.09 15.1358877916693 -0.045887791669319 25 15.14 15.2083148299269 -0.0683148299269032 26 15.24 15.2470406854398 -0.00704068543975644 27 15.33 15.3458787458577 -0.015878745857659 28 15.36 15.4332582420042 -0.0732582420041687 29 15.44 15.4511682755048 -0.0111682755047546 30 15.5 15.5293251507858 -0.0293251507857502 31 15.58 15.5844855575756 -0.00448555757561309 32 15.65 15.6637452962844 -0.0137452962843678 33 15.72 15.7314768802392 -0.0114768802392078 34 15.82 15.7995828258118 0.020417174188168 35 15.87 15.9029523163319 -0.032952316331869 36 16.07 15.9475141241281 0.122485875871922 37 16.18 16.1677282337686 0.0122717662314145 38 16.19 16.2797534699545 -0.089753469954541 39 16.39 16.2749412602254 0.115058739774636 40 16.54 16.4939296534939 0.0460703465060526 41 16.61 16.6515327426568 -0.041532742656841 42 16.62 16.7146785040946 -0.0946785040945564 43 16.66 16.7090535053039 -0.0490535053039416 44 16.71 16.7409580989772 -0.0309580989772407 45 16.72 16.7858490167869 -0.0658490167868848 46 16.79 16.784981810788 0.00501818921196318 47 16.82 16.855809973433 -0.0358099734329542 48 16.83 16.8799001758825 -0.0499001758824704 49 16.91 16.8816650416746 0.0283349583253631 50 16.97 16.9663412212763 0.00365877872366482 51 17.02 17.0269450374612 -0.006945037461211 52 17.03 17.0757988828724 -0.0457988828723757 53 17.04 17.0782405939415 -0.0382405939414738 54 17.07 17.081929665819 -0.011929665818954 55 17.11 17.1099608872057 3.91127942691583e-05 56 17.12 17.149967342075 -0.0299673420749613 57 17.14 17.1550217666441 -0.0150217666441179 58 17.18 17.1725426919281 0.00745730807185652 59 17.24 17.2137733876464 0.0262266123535575 60 17.26 17.2781016223416 -0.0181016223415789 61 17.26 17.2951142723628 -0.0351142723628293 62 17.29 17.2893192878682 0.000680712131796213 63 17.36 17.3194316272671 0.0405683727329276 64 17.44 17.3961267137701 0.043873286229914 65 17.48 17.4833672173125 -0.00336721731245859 66 17.48 17.5228115181394 -0.0428115181393665 67 17.52 17.5157462404869 0.00425375951314066 68 17.54 17.5564482476413 -0.0164482476413248 69 17.58 17.5737337576738 0.00626624232618411 70 17.64 17.6147678892299 0.0252321107700908 71 17.69 17.6789319991727 0.0110680008273114 72 17.69 17.7307585753443 -0.0407585753442845 73 17.76 17.724032099292 0.0359679007080373 74 17.79 17.799967959923 -0.009967959923042 75 17.82 17.8283229258867 -0.008322925886727 76 17.89 17.8569493753838 0.0330506246161875 77 17.95 17.9324037916169 0.0175962083831074 78 18 17.9953077320344 0.00469226796564115 79 18.03 18.0460821071894 -0.0160821071894084 80 18.06 18.0734280421745 -0.0134280421744641 81 18.08 18.1012119832629 -0.0212119832628552 82 18.13 18.1177113236781 0.0122886763218979 83 18.16 18.169739350573 -0.00973935057294995 84 18.18 18.1981320444333 -0.0181320444333046 85 18.18 18.2151396738308 -0.0351396738307983 86 18.27 18.2093404972768 0.0606595027231585 87 18.31 18.3093512665191 0.00064873348094352 88 18.35 18.3494583284118 0.000541671588152326 89 18.45 18.3895477216484 0.0604522783516295 90 18.5 18.4995242922033 0.000475707796706359 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 91 18.5496027992923 18.4129466785889 18.6862589199957 92 18.5992055985846 18.3893906089811 18.8090205881881 93 18.6488083978769 18.3712123817257 18.9264044140282 94 18.6984111971692 18.3537319334166 19.0430904609219 95 18.7480139964615 18.3353733362382 19.1606546566849 96 18.7976167957538 18.3154525586087 19.279781032899 97 18.8472195950461 18.2936392930385 19.4007998970537 98 18.8968223943384 18.2697690021859 19.5238757864909 99 18.9464251936307 18.2437631029553 19.6490872843061 100 18.996027992923 18.2155905729263 19.7764654129198 101 19.0456307922153 18.1852478194878 19.9060137649429 102 19.0952335915077 18.152747444166 20.0377197388493

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/197q81305827801.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/197q81305827801.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/2bydr1305827801.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/2bydr1305827801.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/3b0y31305827801.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058276703ec8b1w03da0ojb/3b0y31305827801.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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