Tijdreeks 1 - stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 13 Aug 2010 15:29:15 +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/Aug/13/t12817133790zip2ss6juwhsvo.htm/, Retrieved Fri, 13 Aug 2010 17:29:39 +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/Aug/13/t12817133790zip2ss6juwhsvo.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:

Reuben Vermoet

Dataseries X:

» Textbox « » Textfile « » CSV «

210 209 208 206 226 225 210 200 201 201 202 204 197 196 187 196 221 218 200 191 194 192 199 196 182 178 169 177 207 213 191 182 188 189 194 195 171 165 156 170 201 208 189 175 184 187 193 199 179 188 171 182 212 216 192 182 183 183 187 190 167 167 158 171 201 208 181 169 173 180 181 192 169 168 156 161 195 208 176 164 170 175 170 175 148 151 143 139 166 186 149 142 138 137 130 138 118 113 99 93 125 146 109 97 97 94 92 103 78 72 57 40 70 89 53 46 43 38 29 34

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 0.113784222520231 beta 0.171310491544316 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 208 208 0 4 206 207 -1 5 226 205.86672334639 20.1332766536102 6 225 207.530526653901 17.4694733460994 7 210 209.231753678496 0.768246321504307 8 200 209.047619559445 -9.04761955944534 9 201 207.570234671978 -6.57023467197789 10 201 206.246667251226 -5.24666725122609 11 202 204.971430620551 -2.97143062055133 12 204 203.897159614338 0.102840385662120 13 197 203.174696753514 -6.17469675351367 14 196 201.617589358997 -5.61758935899741 15 187 200.014371522755 -13.0143715227546 16 196 197.315834838771 -1.31583483877122 17 221 195.922758236079 25.0772417639212 18 218 198.021613741549 19.9783862584507 19 200 199.929727255018 0.0702727449822191 20 191 199.573981337151 -8.57398133715074 21 194 198.0675279489 -4.06752794890016 22 192 196.994551847505 -4.99455184750499 23 199 195.718739094837 3.28126090516312 24 196 195.448543014036 0.551456985963938 25 182 194.878487553954 -12.8784875539545 26 178 192.529283264720 -14.5292832647204 27 169 189.709033416174 -20.7090334161736 28 177 185.781956094471 -8.78195609447053 29 207 183.04081031875 23.9591896812501 30 213 184.492113213374 28.5078867866265 31 191 187.016674090320 3.98332590967979 32 182 186.828371581037 -4.82837158103661 33 188 185.543320223368 2.45667977663160 34 189 185.135079431708 3.86492056829152 35 194 184.962410921494 9.03758907850568 36 195 185.554475058402 9.44552494159836 37 171 186.377072104361 -15.3770721043614 38 165 184.075512726154 -19.0755127261544 39 156 180.98130103994 -24.9813010399400 40 170 176.728157533014 -6.72815753301447 41 201 174.420785621500 26.5792143784997 42 208 176.421360631827 31.5786393681727 43 189 179.606335779450 9.39366422054977 44 175 180.450116130771 -5.45011613077128 45 184 179.498672462445 4.501327537555 46 187 179.767287891712 7.23271210828793 47 193 180.487674933128 12.5123250668722 48 199 182.052694264385 16.9473057356153 49 179 184.452688612138 -5.4526886121381 50 188 184.197630861548 3.80236913845209 51 171 185.069770079898 -14.0697700798982 52 182 183.634087808782 -1.63408780878163 53 212 183.581537632385 28.4184623676149 54 216 187.502438431943 28.4975615680574 55 192 191.987826227621 0.0121737723792421 56 182 193.232263616200 -11.2322636161996 57 183 192.978317314319 -9.97831731431887 58 183 192.672548654837 -9.67254865483696 59 187 192.213030156427 -5.21303015642684 60 190 192.159319872079 -2.15931987207907 61 167 192.410983244430 -25.4109832444302 62 167 189.521652337837 -22.5216523378369 63 158 186.522079945827 -28.5220799458273 64 171 182.283788885768 -11.2837888857681 65 201 179.786994894266 21.2130051057339 66 208 181.401316381721 26.5986836182789 67 181 184.146916118982 -3.14691611898203 68 169 183.446594871146 -14.4465948711457 69 173 181.178949206756 -8.17894920675616 70 180 179.465035127521 0.534964872479264 71 181 178.753054752812 2.24694524718845 72 192 178.279669159402 13.7203308405978 73 169 179.379216428855 -10.3792164288551 74 168 177.534299288157 -9.53429928815686 75 156 175.599673715542 -19.5996737155419 76 161 172.137722050047 -11.1377220500465 77 195 169.421505696254 25.578494303746 78 208 171.381602511762 36.6183974882377 79 176 175.311647717480 0.688352282520299 80 164 175.166838323780 -11.1668383237804 81 170 173.455426457595 -3.45542645759534 82 175 172.554096933026 2.44590306697356 83 170 172.371922197232 -2.37192219723195 84 175 171.595320429531 3.40467957046872 85 148 171.542370284688 -23.5423702846881 86 151 167.964372992394 -16.9643729923941 87 143 164.804171136206 -21.8041711362058 88 139 160.668260307724 -21.6682603077236 89 166 156.125446916305 9.87455308369456 90 186 155.364187068258 30.6358129317418 91 149 157.562397503018 -8.5623975030175 92 142 155.133568095981 -13.1335680959811 93 138 151.928606425941 -13.9286064259412 94 137 148.361679536717 -11.3616795367167 95 130 144.865361672413 -14.8653616724135 96 138 140.680618022316 -2.68061802231563 97 118 137.830054192974 -19.8300541929741 98 113 132.641619137428 -19.6416191374277 99 99 127.091762110641 -28.0917621106413 100 93 120.032835398327 -27.0328353983267 101 125 112.567462157511 12.4325378424886 102 146 109.834966114541 36.1650338854593 103 109 110.507798113161 -1.50779811316109 104 97 106.864665561865 -9.86466556186487 105 97 102.078367031523 -5.0783670315234 106 94 97.7376840387952 -3.73768403879524 107 92 93.4766930694786 -1.4766930694786 108 103 89.4441828618331 13.5558171381669 109 78 87.3863709721254 -9.38637097212543 110 72 82.5351368560166 -10.5351368560166 111 57 77.3478358777625 -20.3478358777625 112 40 70.6473757818176 -30.6473757818176 113 70 62.1775986850595 7.82240131494055 114 89 58.2375528843718 30.7624471156282 115 53 57.5073572402528 -4.50735724025282 116 46 52.6761549786559 -6.67615497865594 117 43 47.4680432617241 -4.46804326172409 118 38 42.4240867943552 -4.42408679435516 119 29 37.2988956724757 -8.29889567247572 120 34 31.5710467829666 2.42895321703341 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 27.1112040418685 -2.83848843077944 57.0608965145164 122 22.3749847474322 -7.83953011163862 52.589499606503 123 17.6387654529959 -12.9202115478730 48.1977424538649 124 12.9025461585596 -18.0888753586297 43.893967675749 125 8.16632686412337 -23.3527139216694 39.6853676499161 126 3.43010756968709 -28.7176431366806 35.5778582760548 127 -1.30611172474919 -34.1882294312025 31.5760059817041 128 -6.04233101918546 -39.7676764902309 27.68301445186 129 -10.7785503136217 -45.4578710863497 23.9007704591063 130 -15.5147696080580 -51.2594807993418 20.2299415832257 131 -20.2509889024943 -57.1720915505868 16.6701137455982 132 -24.9872081969306 -63.1943704051331 13.2199540112720

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/1rdfg1281713351.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/1rdfg1281713351.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/2j4e11281713351.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/2j4e11281713351.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/3j4e11281713351.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t12817133790zip2ss6juwhsvo/3j4e11281713351.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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