Isabelle Regnard, oef 10, Exponential Smoothing, Koffie, thee, cacao

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 12:15:22 +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/18/t1305720804txrk3nz5fk9oj2s.htm/, Retrieved Wed, 18 May 2011 14:13:37 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

106,42 106,22 106,32 105,81 105,92 107,54 107,34 107,24 107,74 105,71 105,41 106,22 106,32 106,12 106,22 105,92 105,71 105,71 105,92 105,71 105,41 104,49 101,35 99,72 99,01 97,89 95,86 94,95 95,35 95,15 95,46 95,56 95,05 94,64 93,63 93,12 93,53 97,18 96,27 95,15 97,08 101,95 103,07 103,68 102,87 102,56 103,38 103,27 102,89 102,69 101,54 102,9 101,53 101,96 101,99 101,11 101,75 101,71 104,11 103,57 103,32 103,64 103,68 103,79 103,01 101,54 101,9 103,68 104,62 104,11 105,04 104,83 105,05 104,68 107,32 109,9 109,77 110,69 110,54 110,89 110,95 109,73 110,85 110,39 110,58 110,4 111,07 110,86 111,38 111,44 110,36 110,06 108,34 107,94 107,39 107,1 107,61 107,74 106,9 106,71 106,6 108,21 110,54 110,91 109,51 110,27 111,39 112,13 111,64

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999924063401756 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 106.22 106.42 -0.200000000000003 3 106.32 106.22001518732 0.0999848126803471 4 105.81 106.319992407493 -0.509992407493442 5 105.92 105.810038727089 0.109961272911448 6 107.54 105.919991649915 1.620008350085 7 107.34 107.539876982077 -0.199876982076773 8 107.24 107.340015177978 -0.100015177978094 9 107.74 107.240007594812 0.499992405187612 10 105.71 107.739962032278 -2.02996203227761 11 105.41 105.710154148411 -0.300154148411295 12 106.22 105.410022792685 0.809977207315029 13 106.32 106.219938493086 0.100061506913775 14 106.12 106.31999240167 -0.199992401669547 15 106.22 106.120015186743 0.0999848132573362 16 105.92 106.219992407493 -0.299992407493392 17 105.71 105.920022780403 -0.210022780402937 18 105.71 105.710015948416 -1.5948415509115e-05 19 105.92 105.710000001211 0.20999999878893 20 105.71 105.919984053314 -0.209984053314471 21 105.41 105.710015945475 -0.300015945474698 22 104.49 105.41002278219 -0.920022782190316 23 101.35 104.4900698634 -3.14006986340038 24 99.72 101.350238446224 -1.63023844622367 25 99.01 99.720123794762 -0.710123794761927 26 97.89 99.0100539243853 -1.12005392438532 27 95.86 97.8900850530849 -2.03008505308487 28 94.95 95.860154157753 -0.910154157753084 29 95.35 94.9500691140106 0.399930885989377 30 95.15 95.349969630609 -0.199969630608976 31 95.46 95.1500151850135 0.309984814986493 32 95.56 95.4599764608076 0.100023539192364 33 95.05 95.5599924045527 -0.50999240455269 34 94.64 95.0500387270883 -0.41003872708832 35 93.63 94.640031136946 -1.01003113694608 36 93.12 93.6300766983287 -0.510076698328646 37 93.53 93.1200387334893 0.409961266510678 38 97.18 93.529968868936 3.650031131064 39 96.27 97.1797228290524 -0.909722829052427 40 95.15 96.270069081257 -1.12006908125697 41 97.08 95.1500850542358 1.92991494576417 42 101.95 97.0798534488241 4.87014655117588 43 103.07 101.949630177638 1.12036982236204 44 103.68 103.069914922927 0.610085077073094 45 102.87 103.679953672215 -0.809953672214604 46 102.56 102.870061505127 -0.310061505126598 47 103.38 102.560023545016 0.819976454984044 48 103.27 103.379937733777 -0.109937733777372 49 102.89 103.270008348298 -0.380008348297523 50 102.69 102.890028856541 -0.20002885654128 51 101.54 102.690015189511 -1.15001518951091 52 102.9 101.540087328241 1.35991267175858 53 101.53 102.899896732858 -1.36989673285781 54 101.96 101.530104025298 0.429895974702148 55 101.99 101.959967355162 0.0300326448379167 56 101.11 101.989997719423 -0.879997719423102 57 101.75 101.110066824033 0.639933175966732 58 101.71 101.749951405652 -0.0399514056515073 59 104.11 101.710003033774 2.39999696622615 60 103.57 104.109817752395 -0.539817752394583 61 103.32 103.570040991924 -0.250040991923782 62 103.64 103.320018987262 0.319981012737671 63 103.68 103.63997570173 0.0400242982696142 64 103.79 103.679996960691 0.110003039309063 65 103.01 103.789991646743 -0.779991646743397 66 101.54 103.010059229912 -1.47005922991232 67 101.9 101.540111631297 0.359888368702869 68 103.68 101.899972671302 1.78002732869847 69 104.62 103.67986483078 0.940135169220127 70 104.11 104.619928609333 -0.509928609333357 71 105.04 104.110038722244 0.929961277756078 72 104.83 105.039929381904 -0.209929381904075 73 105.05 104.830015941323 0.219984058676872 74 104.68 105.049983295159 -0.369983295158903 75 107.32 104.680028095273 2.63997190472715 76 109.9 107.319799529514 2.58020047048592 77 109.77 109.899804068353 -0.129804068353494 78 110.69 109.770009856879 0.919990143120614 79 110.54 110.689930139078 -0.149930139078108 80 110.89 110.540011385185 0.34998861481526 81 110.95 110.889973423055 0.0600265769448356 82 109.73 110.949995441786 -1.21999544178594 83 110.85 109.730092642304 1.11990735769628 84 110.39 110.849914958045 -0.459914958044905 85 110.58 110.390034924377 0.189965075622595 86 110.4 110.579985574698 -0.179985574698364 87 111.07 110.400013667492 0.669986332507719 88 110.86 111.069949123517 -0.209949123517035 89 111.38 110.860015942822 0.519984057177751 90 111.44 111.37996051418 0.0600394858204396 91 110.36 111.439995440806 -1.07999544080567 92 110.06 110.36008201118 -0.300082011179882 93 108.34 110.060022787207 -1.72002278720711 94 107.94 108.340130612679 -0.400130612679376 95 107.39 107.940030384558 -0.550030384557573 96 107.1 107.390041767436 -0.290041767436335 97 107.61 107.100022024785 0.509977975214838 98 107.74 107.609961274007 0.13003872599262 99 106.9 107.739990125302 -0.839990125301497 100 106.71 106.900063785993 -0.190063785992692 101 106.6 106.710014432797 -0.110014432797357 102 108.21 106.600008354122 1.60999164587822 103 110.54 108.209877742711 2.33012225728879 104 110.91 110.539823058442 0.370176941557702 105 109.51 110.909971890022 -1.3999718900223 106 110.27 109.510106309103 0.759893690897016 107 111.39 110.269942296258 1.12005770374192 108 112.13 111.389914946628 0.740085053371857 109 111.64 112.129943800459 -0.489943800458633 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 111.640037204666 109.442602820961 113.83747158837 111 111.640037204666 108.532513686428 114.747560722903 112 111.640037204666 107.834161883257 115.445912526074 113 111.640037204666 107.245418733419 116.034655675912 114 111.640037204666 106.726723042765 116.553351366566 115 111.640037204666 106.257784832355 117.022289576976 116 111.640037204666 105.826550716769 117.453523692562 117 111.640037204666 105.425167158505 117.854907250826 118 111.640037204666 105.048179026854 118.231895382477 119 111.640037204666 104.691614449673 118.588459959658 120 111.640037204666 104.352474969748 118.927599439584 121 111.640037204666 104.028431074977 119.251643334354

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/1tpn81305720919.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/1tpn81305720919.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/2v4kp1305720919.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/2v4kp1305720919.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/35r191305720919.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305720804txrk3nz5fk9oj2s/35r191305720919.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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