Exponential Smoothing (double) - Verhandelde kapitalen Euronext

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 26 May 2010 13:24:47 +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/26/t1274880545q3oq5tj4bebhy74.htm/, Retrieved Wed, 26 May 2010 15:29:09 +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/26/t1274880545q3oq5tj4bebhy74.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 «

3592,21 5955,74 4652,25 4211,65 4787,85 3599,73 4174,27 5106,33 5325,75 6604,61 5711,90 6919,30 7048,76 8655,98 6658,53 7247,03 8779,57 6602,49 9832,48 9369,49 8582,76 8206,94 6515,83 8618,10 8505,39 9881,64 9375,29 15642,50 12232,73 6288,93 12473,94 11142,82 10236,32 10581,51 8763,71 10819,04 11636,25 14650,13 10671,38 17468,63 13873,19 13077,58 16866,81 14186,64 19919,87 17681,78 9984,28 17423,09 13514,45 12334,57 12274,56 11752,23 13054,00 12460,98 8626,68 13722,62 12066,22 6798,83 6593,82 6606,19 6315,28 7232,95 6747,44 7803,61 6700,31 5369,53 8081,19 10718,39 9447,21 6815,10 5497,80 6805,31

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 0.46970488241959 beta 0.220607460394909 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 4652.25 8319.27 -3667.02 4 4211.65 8580.4047182938 -4368.7547182938 5 4787.85 8059.23909638813 -3271.38909638813 6 3599.73 7714.5288140925 -4114.79881409250 7 4174.27 6547.2877653495 -2373.0177653495 8 5106.33 5952.27672629837 -845.946726298374 9 5325.75 5986.88107087961 -661.131070879613 10 6604.61 6039.78756431809 564.822435681908 11 5711.9 6727.05753282585 -1015.15753282585 12 6919.3 6567.01216512138 352.287834878615 13 7048.76 7085.76676987385 -37.0067698738485 14 8655.98 7417.83314173134 1238.14685826866 15 6658.53 8477.1426728173 -1818.61267281729 16 7247.03 7912.23195290176 -665.201952901763 17 8779.57 7820.15538629656 959.414613703439 18 6602.49 8590.58408031849 -1988.09408031849 19 9832.48 7770.54644346737 2061.93355653262 20 9369.49 9066.48494404933 303.005055950665 21 8582.76 9567.64364555806 -984.883645558057 22 8206.94 9361.82069742208 -1154.88069742208 23 6515.83 8956.48010277087 -2440.65010277087 24 8618.1 7694.30619781219 923.793802187813 25 8505.39 8108.1519060904 397.238093909603 26 9881.64 8315.8337980054 1565.80620199459 27 9375.29 9234.6473026514 140.642697348596 28 15642.5 9498.6280036505 6143.8719963495 29 12232.73 13218.9852981385 -986.255298138454 30 6288.93 13488.0908204085 -7199.16082040846 31 12473.94 10092.9843520137 2380.95564798626 32 11142.82 11444.4209425648 -301.600942564832 33 10236.32 11504.5955944826 -1268.27559448258 34 10581.51 10979.2992166929 -397.789216692929 35 8763.71 10821.6554623859 -2057.94546238590 36 10819.04 9670.98307934336 1148.05692065665 37 11636.25 10145.1477874361 1491.10221256395 38 14650.13 10934.9511535929 3715.17884640715 39 10671.38 13154.3824963053 -2483.00249630528 40 17468.63 12205.2080852625 5263.42191473749 41 13873.19 15439.9649321112 -1566.7749321112 42 13077.58 15304.1951249811 -2226.61512498115 43 16866.81 14627.7724049732 2239.03759502684 44 14186.64 16280.8985447441 -2094.25854474408 45 19919.87 15681.6464199761 4238.22358002393 46 17681.78 18495.9584949773 -814.178494977332 47 9984.28 18852.7671450685 -8868.48714506849 48 17423.09 14507.4715012834 2915.61849871662 49 13514.45 15999.3453720487 -2484.89537204871 50 12334.57 14697.0856546356 -2362.51565463564 51 12274.56 13207.5034679181 -932.943467918087 52 11752.23 12292.7263405878 -540.496340587813 53 13054 11506.2770973726 1547.72290262742 54 12460.98 11861.0502964455 599.929703554539 55 8626.68 11832.8053589912 -3206.12535899124 56 13722.62 9684.61777975887 4038.00222024113 57 12066.22 11357.4517036547 708.768296345341 58 6798.83 11539.9710540372 -4741.14105403718 59 6593.82 8671.36243541919 -2077.54243541919 60 6606.19 6838.58331200908 -232.393312009085 61 6315.28 5848.39905241974 466.88094758026 62 7232.95 5235.04571783208 1997.90428216792 63 6747.44 5547.84516196726 1199.59483803274 64 7803.61 5609.97726095967 2193.63273904033 65 6700.31 6366.31891997047 333.991080029528 66 5369.53 6283.78610191817 -914.256101918173 67 8081.19 5520.20990391648 2560.98009608352 68 10718.39 6654.33890081583 4064.05109918417 69 9447.21 8915.58629207526 531.62370792474 70 6815.1 9572.72235279432 -2757.62235279431 71 5497.8 8399.13754463364 -2901.33754463364 72 6805.31 6857.41124866409 -52.1012486640857 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 6648.58639978656 1465.46817057974 11831.7046289934 74 6464.23376178672 489.688022630242 12438.7795009432 75 6279.88112378688 -648.762245195107 13208.5244927689 76 6095.52848578704 -1927.83265352139 14118.8896250955 77 5911.17584778719 -3328.77950161712 15151.1311971915 78 5726.82320978735 -4836.81037692102 16290.4567964957 79 5542.47057178751 -6440.51595142701 17525.4570950020 80 5358.11793378766 -8131.08190167112 18847.3177692465 81 5173.76529578782 -9901.60853269376 20249.1391242694 82 4989.41265778798 -11746.5970391545 21725.4223547304 83 4805.06001978813 -13661.5798662883 23271.6999058645 84 4620.70738178829 -15642.8585271066 24884.2732906832

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/1sp1g1274880283.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/1sp1g1274880283.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/23hij1274880283.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/23hij1274880283.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/33hij1274880283.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274880545q3oq5tj4bebhy74/33hij1274880283.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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