Exponential Smoothing - Prijzen van stof voor jurken

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 10:16:54 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88.htm/, Retrieved Wed, 28 May 2008 18:19:23 +0200

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Dataseries X:

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20.66 20.66 20.67 20.71 20.73 20.73 20.74 20.74 20.75 20.75 20.77 20.78 20.78 20.8 20.84 20.85 20.86 20.86 20.86 20.86 20.9 20.92 20.95 20.95 20.95 20.96 21.1 21.18 21.19 21.19 21.19 21.19 21.19 21.21 21.22 21.22 21.22 21.23 21.41 21.42 21.43 21.44 21.44 21.44 21.48 21.53 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.57 21.6 21.61 21.6 21.6 21.71 21.75 21.84 21.85 21.92 21.92 21.93 22 22 21.99 22.01 22.01

Text written by user:

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.957264156086689 beta 0.000728381616693922 gamma 0.0436617754682502 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 20.78 20.6843109662098 0.0956890337901655 14 20.8 20.8035987033585 -0.00359870335853785 15 20.84 20.8466009164802 -0.00660091648018124 16 20.85 20.8546382827958 -0.00463828279578848 17 20.86 20.8632994673315 -0.00329946733154429 18 20.86 20.8632377301432 -0.00323773014320139 19 20.86 20.8636470812610 -0.00364708126102542 20 20.86 20.8640757840295 -0.00407578402951358 21 20.9 20.9003471252069 -0.000347125206889842 22 20.92 20.9131080625231 0.0068919374769223 23 20.95 20.9398873063327 0.0101126936672671 24 20.95 20.9397701731196 0.0102298268803942 25 20.95 20.9860023929698 -0.0360023929698094 26 20.96 20.9790976480829 -0.0190976480829228 27 21.1 21.0074421275515 0.0925578724484808 28 21.18 21.1103949481767 0.0696050518233235 29 21.19 21.1901405564534 -0.000140556453377627 30 21.19 21.1929577864363 -0.00295778643629774 31 21.19 21.1934960734358 -0.00349607343584069 32 21.19 21.1939370234997 -0.00393702349964897 33 21.19 21.230790213948 -0.0407902139479859 34 21.21 21.2048440403121 0.00515595968786542 35 21.22 21.2300589066462 -0.0100589066461723 36 21.22 21.2103199121532 0.0096800878468315 37 21.22 21.2562222506461 -0.036222250646091 38 21.23 21.2493084655983 -0.0193084655983071 39 21.41 21.2780762706042 0.131923729395847 40 21.42 21.4186885885673 0.00131141143273794 41 21.43 21.4328956824652 -0.00289568246520133 42 21.44 21.4329220424188 0.00707795758118479 43 21.44 21.4429234571782 -0.00292345717816644 44 21.44 21.4437742090780 -0.00377420907803128 45 21.48 21.4810105358994 -0.00101053589935063 46 21.53 21.4932229680535 0.036777031946535 47 21.54 21.5487940549371 -0.00879405493711616 48 21.54 21.5299617251912 0.0100382748087569 49 21.54 21.5764832131057 -0.0364832131056687 50 21.54 21.5695812629633 -0.0295812629633403 51 21.54 21.5893029495434 -0.0493029495433639 52 21.54 21.5561103661355 -0.0161103661354751 53 21.54 21.5535373732239 -0.0135373732239437 54 21.54 21.543243287304 -0.00324328730401646 55 21.54 21.5431954985783 -0.00319549857825407 56 21.54 21.5436361267929 -0.00363612679290881 57 21.57 21.5810351530419 -0.0110351530418917 58 21.6 21.5836134901029 0.0163865098970604 59 21.61 21.6194851074222 -0.00948510742223618 60 21.6 21.5998310315448 0.000168968455238172 61 21.6 21.6367606437960 -0.0367606437960362 62 21.71 21.6295234928109 0.0804765071890543 63 21.75 21.7547601494398 -0.00476014943981085 64 21.84 21.7642298458755 0.0757701541245268 65 21.85 21.8496092884565 0.00039071154353465 66 21.92 21.8525218568999 0.067478143100054 67 21.92 21.9200367206734 -3.67206734281922e-05 68 21.93 21.9233719797981 0.00662802020194775 69 22 21.9711307833457 0.0288692166542965 70 22 22.0120269381526 -0.0120269381526299 71 21.99 22.0208334448575 -0.0308334448574996 72 22.01 21.9803858639892 0.0296141360108244 73 22.01 22.0459357368618 -0.0359357368617808 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 22.0400491409490 21.9740889513344 22.1060093305635 75 22.0886419735042 21.9953520016362 22.1819319453721 76 22.1028533211521 21.9886313672149 22.2170752750893 77 22.1155359273941 21.9836519333000 22.2474199214882 78 22.1180530754471 21.9706473476190 22.2654588032753 79 22.1207003928136 21.9592566354794 22.2821441501477 80 22.1239416949812 21.9495814267901 22.2983019631722 81 22.1655922766963 21.9789237747106 22.3522607786821 82 22.1787070568031 21.9806797342357 22.3767343793706 83 22.1989852916556 21.9901448059261 22.4078257773851 84 22.1878915447423 21.9690354776472 22.4067476118374 85 22.2251020549114 18.5174640958123 25.9327400140105

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/14xhr1211991408.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/14xhr1211991408.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/243kc1211991408.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/243kc1211991408.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/39a3o1211991408.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211991563nien4mvkqlmxv88/39a3o1211991408.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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