Opgave 10 oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 18 Jan 2010 08:56:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1.htm/, Retrieved Mon, 18 Jan 2010 16:57:08 +0100

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/Jan/18/t12638302246qiwwyg1q05azt1.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 «

102,5 77,7 82,8 77,3 103,1 99,7 99,5 107,2 96,7 97,1 105,2 151,2 102,7 75,4 87,2 83,7 105,8 111,5 99,7 111,2 101,5 110,9 116,3 164,9 118,1 83,7 84 107,2 113,7 120,7 111,2 112,4 112,5 130,4 130,7 174,3 132,2 91,8 104,2 104,8 131,4 141,2 132,7 135,7 136,9 151,2 144 201,5 149,6 108,7 122,8 126,7 139,9 162,5 142,7 151,6 148,1 159 157,8 226,7 153,7 122,3 117,6 166 154,5 183,9 164,4 173,3 160,2 166,4 170,3 238,4 166,8 122,5 141,8 140,5 173,8 188,8 168 187,4 177,7 183,8 196,1 264,6 193,7 141,3 170,1 163,7 190,1 230,7 195,9 210,3 204,7 210,3 221,2 288,2 203,2 162,4 149,2 195,3 213,7 227,9 212,1 226,8 212,6 220,9 228,1 311,6

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.152389418657338 beta 0.0403497841851909 gamma 0.289315718348342 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 102.7 99.8541577664804 2.84584223351962 14 75.4 73.8640764756996 1.53592352430037 15 87.2 85.8149277185064 1.38507228149356 16 83.7 82.3683955652689 1.33160443473115 17 105.8 103.864666659206 1.93533334079383 18 111.5 109.259412450623 2.24058754937664 19 99.7 103.552937819575 -3.85293781957476 20 111.2 111.592282860904 -0.392282860904231 21 101.5 101.023680942444 0.476319057555585 22 110.9 101.566028598322 9.33397140167772 23 116.3 111.768503544399 4.5314964556013 24 164.9 161.579583081682 3.32041691831793 25 118.1 110.948829503986 7.15117049601382 26 83.7 82.4572231403725 1.24277685962748 27 84 95.7097150921302 -11.7097150921302 28 107.2 89.9618009442243 17.2381990557757 29 113.7 116.677877146881 -2.97787714688113 30 120.7 122.089478988153 -1.38947898815346 31 111.2 113.617386421764 -2.41738642176409 32 112.4 123.875711719721 -11.4757117197207 33 112.5 110.887389959913 1.61261004008730 34 130.4 114.050028037679 16.3499719623206 35 130.7 125.036964849872 5.66303515012832 36 174.3 180.148818447016 -5.84881844701641 37 132.2 124.053471661732 8.14652833826754 38 91.8 91.1656178112643 0.634382188735714 39 104.2 102.117804952949 2.08219504705104 40 104.8 105.946193936461 -1.14619393646073 41 131.4 126.678095736289 4.72190426371127 42 141.2 134.348723530008 6.85127646999155 43 132.7 125.996073195731 6.70392680426896 44 135.7 136.595426964986 -0.8954269649862 45 136.9 127.467068820498 9.4329311795017 46 151.2 136.598214189012 14.6017858109880 47 144 145.803742351963 -1.80374235196251 48 201.5 204.568736053253 -3.06873605325254 49 149.6 144.845913269667 4.75408673033252 50 108.7 104.550847946836 4.14915205316417 51 122.8 118.229514187950 4.57048581205039 52 126.7 122.229940517904 4.47005948209616 53 139.9 149.170215243516 -9.27021524351608 54 162.5 156.493127134652 6.00687286534759 55 142.7 146.699640439811 -3.99964043981112 56 151.6 154.930791018806 -3.33079101880574 57 148.1 147.138413480555 0.961586519445149 58 159 157.295052453372 1.70494754662803 59 157.8 160.765946370615 -2.9659463706154 60 226.7 225.115937538779 1.58406246122121 61 153.7 161.762691979094 -8.06269197909418 62 122.3 115.408306488251 6.89169351174898 63 117.6 130.795358567693 -13.1953585676933 64 166 132.127241269681 33.8727587303188 65 154.5 162.577769569462 -8.07776956946228 66 183.9 175.16068090111 8.73931909889018 67 164.4 161.857668684000 2.54233131599972 68 173.3 172.337859915849 0.9621400841514 69 160.2 165.534649711094 -5.33464971109444 70 166.4 176.118688701466 -9.71868870146588 71 170.3 176.877063656989 -6.57706365698888 72 238.4 248.438145850133 -10.0381458501329 73 166.8 174.649207746374 -7.84920774637393 74 122.5 128.014099723703 -5.51409972370283 75 141.8 137.104677118695 4.69532288130526 76 140.5 153.763910712417 -13.2639107124170 77 173.8 167.017464508736 6.78253549126444 78 188.8 186.655886766621 2.1441132333795 79 168 169.776545813552 -1.77654581355222 80 187.4 179.275099179089 8.1249008209109 81 177.7 171.352571927643 6.34742807235699 82 183.8 182.956011553245 0.84398844675485 83 196.1 186.102252174173 9.99774782582668 84 264.6 264.70569713596 -0.105697135960042 85 193.7 186.969350415060 6.7306495849397 86 141.3 138.837126842074 2.46287315792557 87 170.1 153.039422816513 17.0605771834873 88 163.7 168.661514288136 -4.96151428813573 89 190.1 190.946882434901 -0.846882434900749 90 230.7 210.648994398385 20.0510056016149 91 195.9 193.253189790938 2.64681020906161 92 210.3 207.908450492858 2.39154950714226 93 204.7 197.554378952217 7.14562104778307 94 210.3 209.504306414633 0.79569358536736 95 221.2 215.876172877374 5.32382712262589 96 288.2 302.03938884432 -13.8393888443202 97 203.2 213.908324541505 -10.7083245415054 98 162.4 156.129498200061 6.27050179993947 99 149.2 176.639134446847 -27.439134446847 100 195.3 180.506300744108 14.793699255892 101 213.7 209.054707856130 4.6452921438696 102 227.9 237.096744304260 -9.19674430425965 103 212.1 208.857531579631 3.24246842036882 104 226.8 224.443507990124 2.35649200987592 105 212.6 214.325818835862 -1.72581883586176 106 220.9 223.761351406124 -2.86135140612356 107 228.1 230.891271727254 -2.79127172725376 108 311.6 315.294264877466 -3.69426487746625 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 223.972630086684 217.537735902683 230.407524270686 110 168.283969247903 161.569803264235 174.998135231571 111 179.897323263878 172.595500523373 187.199146004382 112 199.781434347138 191.714430661169 207.848438033106 113 225.147416182435 216.111379710796 234.183452654075 114 250.501208821895 240.383009309149 260.619408334642 115 224.851043074167 214.913794158129 234.788291990204 116 240.616902366314 229.736149297275 251.497655435353 117 228.211020791761 217.233978052832 239.188063530690 118 238.125826675523 226.317468962718 249.934184388328 119 246.102538660923 233.500227836307 258.70484948554 120 336.558436973491 319.414273267573 353.702600679409

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/1i6wg1263830168.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/1i6wg1263830168.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/2jn7k1263830168.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/2jn7k1263830168.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/3sa601263830168.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/18/t12638302246qiwwyg1q05azt1/3sa601263830168.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=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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