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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 30 May 2010 01:03:56 +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/30/t127518160387stgt9f0qijylh.htm/, Retrieved Sun, 30 May 2010 03:06:43 +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/30/t127518160387stgt9f0qijylh.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 «

18288.3 16049 16764.5 17880.2 16555.9 16087.1 16373.5 17842.2 22321.5 22786.7 18274.1 22392.9 23899.3 21343.5 22952.3 21374.4 21164.1 20906.5 17877.4 20664.3 22160 19813.6 17735.4 19640.2 20844.4 19823.1 18594.6 21350.6 18574.1 18924.2 17343.4 19961.2 19932.1 19464.6 16165.4 17574.9 19795.4 19439.5 17170 21072.4 17751.8 17515.5 18040.3 19090.1 17746.5 19202.1 15141.6 16258.1 18586.5 17209.4 17838.7 19123.5 16583.6 15991.2 16704.5 17422 17872 17823.2 13866.5 15912.8 17870.5 15420.3 16379.4 17903.9 15305.8 14583.3 14861 14968.9 16726.5 16283.6 11703.7 15101.8 15469.7 14956.9 15370.6 15998.1 14725.1 14768.9 13659.6 15070.3 16942.6 15761.3 12083 15023.6 15106.5

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.326901016459753 beta 0.0446229444979951 gamma 0.91238775163749 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 23899.3 21615.7486912393 2283.55130876068 14 21343.5 19874.1573879974 1469.34261200265 15 22952.3 22121.8258216281 830.474178371886 16 21374.4 21227.5285458716 146.871454128443 17 21164.1 21495.2199672658 -331.119967265779 18 20906.5 21545.3420321796 -638.842032179575 19 17877.4 19280.1713032421 -1402.77130324211 20 20664.3 20084.9503596855 579.349640314478 21 22160 24532.7045728378 -2372.70457283775 22 19813.6 24041.7304430732 -4228.1304430732 23 17735.4 17970.5554293756 -235.15542937558 24 19640.2 21777.4410602050 -2137.24106020496 25 20844.4 23850.6933789375 -3006.29337893752 26 19823.1 19714.5998937978 108.500106202198 27 18594.6 20939.9911905536 -2345.39119055362 28 21350.6 18356.2841552187 2994.31584478128 29 18574.1 19071.3998930772 -497.299893077179 30 18924.2 18685.9323628415 238.267637158515 31 17343.4 16058.84983214 1284.55016786001 32 19961.2 18819.1022081686 1142.09779183138 33 19932.1 21505.8020214568 -1573.70202145675 34 19464.6 20016.1299424397 -551.529942439676 35 16165.4 17532.2407550719 -1366.84075507191 36 17574.9 19717.7529811395 -2142.85298113946 37 19795.4 21172.0784989800 -1376.67849898003 38 19439.5 19421.9755150343 17.5244849656592 39 17170 19049.6862691411 -1879.68626914107 40 21072.4 19843.3327505371 1229.06724946287 41 17751.8 17757.1947173780 -5.39471737795611 42 17515.5 17911.5433523241 -396.043352324094 43 18040.3 15637.6814563228 2402.6185436772 44 19090.1 18610.2841249505 479.815875049546 45 17746.5 19337.3121830273 -1590.81218302726 46 19202.1 18394.2165274608 807.88347253915 47 15141.6 15798.2725234051 -656.672523405095 48 16258.1 17693.9847830826 -1435.88478308255 49 18586.5 19814.8758977416 -1228.37589774163 50 17209.4 18936.5629197668 -1727.16291976681 51 17838.7 16770.4461412036 1068.25385879642 52 19123.5 20421.5914093451 -1298.09140934514 53 16583.6 16698.9853570465 -115.385357046503 54 15991.2 16523.6449667608 -532.44496676078 55 16704.5 15868.113105563 836.38689443701 56 17422 17069.205713296 352.794286703993 57 17872 16402.5664394611 1469.43356053891 58 17823.2 17897.0986252003 -73.8986252002796 59 13866.5 14064.7385634458 -198.238563445804 60 15912.8 15589.7283407549 323.071659245112 61 17870.5 18396.6698562816 -526.169856281551 62 15420.3 17435.4422031367 -2015.14220313669 63 16379.4 16881.5777051103 -502.177705110318 64 17903.9 18532.8531405357 -628.953140535705 65 15305.8 15731.8250137122 -426.025013712208 66 14583.3 15170.7810438640 -587.481043864043 67 14861 15309.0644964530 -448.064496453022 68 14968.9 15745.7142638718 -776.814263871778 69 16726.5 15331.5185426636 1394.98145733641 70 16283.6 15788.7789360675 494.821063932515 71 11703.7 12009.1385039417 -305.438503941714 72 15101.8 13760.8367102897 1340.96328971034 73 15469.7 16335.4353143074 -865.735314307407 74 14956.9 14300.2811613617 656.618838638276 75 15370.6 15539.4408733427 -168.840873342739 76 15998.1 17217.1607413557 -1219.06074135574 77 14725.1 14334.5740031767 390.525996823339 78 14768.9 13939.9425679843 828.95743201572 79 13659.6 14646.1784245800 -986.578424580044 80 15070.3 14716.3355113673 353.964488632695 81 16942.6 16033.4887465577 909.111253442334 82 15761.3 15799.9543649097 -38.6543649097457 83 12083 11367.5268237749 715.473176225085 84 15023.6 14492.0224358100 531.577564189965 85 15106.5 15462.9916007743 -356.491600774285 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 14552.8107790734 12052.6975542549 17052.9240038918 87 15084.3873670457 12442.5184668802 17726.2562672113 88 16188.7993194076 13400.9723036746 18976.6263351406 89 14727.4651605765 11789.6512128949 17665.2791082581 90 14502.9756426821 11411.3020906068 17594.6491947574 91 13839.7147201253 10590.4496868918 17088.9797533587 92 15086.5010794512 11676.0400249482 18496.9621339542 93 16654.5621739534 13079.4160931364 20229.7082547704 94 15554.2166678874 11811.0017337425 19297.4316020324 95 11610.5464054532 7695.97486585012 15525.1179450564 96 14390.7718280814 10301.6439885672 18479.8996675956 97 14637.3800118069 10370.577158009 18904.1828656049

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/1stck1275181432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/1stck1275181432.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/2lkbn1275181432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/2lkbn1275181432.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/3lkbn1275181432.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t127518160387stgt9f0qijylh/3lkbn1275181432.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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