Exponential Smoothing - Olieprijzen in constante dollar - Bram Op de Beeck

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 10:43:42 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v.htm/, Retrieved Sun, 25 May 2008 18:44:32 +0200

User-defined keywords:

Dataseries X:

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23.11 18.64 14.94 16.90 15.46 11.15 13.13 12.48 12.95 12.59 10.58 10.58 12.39 15.53 13.06 10.22 16.33 19.72 21.31 18.84 24.84 15.67 15.57 12.73 13.56 15.54 17.22 12.14 11.07 12.02 11.55 6.92 10.33 8.38 12.11 11.46 12.75 13.32 13.00 11.90 11.79 12.55 11.84 11.25 11.15 10.99 11.70 14.01 17.51 17.27 16.90 15.79 15.45 16.24 16.71 16.77 16.64 17.80 16.87 16.13 15.76 15.66 15.54 15.30 15.05 14.69 14.39 14.18 13.70 13.66 13.27 13.56 13.14 14.19 22.57 23.09 23.31 22.91 22.36 43.06 64.67 64.68 56.90 48.79 45.21 41.40 22.17 25.52 20.28 22.87 27.63 22.95 21.35 18.38 17.15 18.27 19.40 20.52

Text written by user:

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.874143869308098 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 12.39 12.4368674516908 -0.0468674516908294 14 15.53 14.9300652227919 0.599934777208135 15 13.06 12.2240778636064 0.835922136393592 16 10.22 9.4910440743538 0.728955925646206 17 16.33 15.9020064277532 0.427993572246763 18 19.72 19.368634385036 0.351365614963981 19 21.31 21.1274451499091 0.182554850090881 20 18.84 18.7678576862619 0.0721423137381407 21 24.84 24.6571704475338 0.182829552466245 22 15.67 15.3936564466171 0.276343553382862 23 15.57 15.6743871362962 -0.104387136296246 24 12.73 13.2831377610683 -0.553137761068253 25 13.56 15.0128838888891 -1.45288388888910 26 15.54 16.3584250371190 -0.818425037118974 27 17.22 12.4422875976858 4.77771240231422 28 12.14 13.1414832500866 -1.00148325008658 29 11.07 18.0019148495259 -6.93191484952586 30 12.02 15.0252798830406 -3.00527988304063 31 11.55 13.8286536947063 -2.2786536947063 32 6.92 9.30371977593065 -2.38371977593065 33 10.33 13.0601864152357 -2.73018641523568 34 8.38 1.26204667527671 7.11795332472329 35 12.11 7.47541131133276 4.63458868866724 36 11.46 9.1702305830165 2.28976941698349 37 12.75 13.2718480252907 -0.521848025290724 38 13.32 15.5110990019581 -2.19109900195810 39 13 11.0993552365491 1.90064476345090 40 11.9 8.55623264753018 3.34376735246982 41 11.79 16.4686572473630 -4.67865724736305 42 12.55 15.9558846833017 -3.40588468330166 43 11.84 14.5005226253269 -2.66052262532692 44 11.25 9.62855711152015 1.62144288847985 45 11.15 16.8425071888646 -5.69250718886455 46 10.99 3.69432166789827 7.29567833210173 47 11.7 9.7504968653858 1.94950313461420 48 14.01 8.80305518072043 5.20694481927957 49 17.51 15.1008443243377 2.40915567566235 50 17.27 19.6921287480355 -2.42212874803547 51 16.9 15.5934027845622 1.30659721543778 52 15.79 12.7126229985381 3.07737700146188 53 15.45 19.3825127872921 -3.93251278729207 54 16.24 19.6821640587835 -3.44216405878350 55 16.71 18.2888969917302 -1.57889699173023 56 16.77 14.9013395057424 1.86866049425762 57 16.64 21.4108878807541 -4.77088788075414 58 17.8 10.7029730021859 7.09702699781405 59 16.87 15.9126494293192 0.957350570680763 60 16.13 14.5078926698596 1.62210733014036 61 15.76 17.3198991837725 -1.55989918377251 62 15.66 17.8336118713092 -2.17361187130917 63 15.54 14.421408434219 1.11859156578101 64 15.3 11.5991481543286 3.70085184567144 65 15.05 17.9318070504269 -2.88180705042688 66 14.69 19.2116396939056 -4.52163969390565 67 14.39 17.1092592018479 -2.71925920184786 68 14.18 13.1587573266194 1.02124267338062 69 13.7 18.0919127407484 -4.3919127407484 70 13.66 9.20892650343385 4.45107349656615 71 13.27 11.3329429801577 1.93705701984229 72 13.56 10.8682543205511 2.69174567944886 73 13.14 14.2148036122114 -1.07480361221137 74 14.19 15.0753201154468 -0.885320115446817 75 22.57 13.2036130046666 9.36638699533338 76 23.09 17.9161058220931 5.17389417790685 77 23.31 24.7079476638188 -1.39794766381879 78 22.91 27.0785039015258 -4.16850390152578 79 22.36 25.5116555321751 -3.15165553217508 80 43.06 21.6539421485418 21.4060578514582 81 64.67 43.7250799823098 20.9449200176902 82 64.68 58.1030748000591 6.57692519994091 83 56.9 61.76898712409 -4.86898712409003 84 48.79 55.4498188963999 -6.65981889639988 85 45.21 50.1477120257345 -4.93771202573446 86 41.4 47.6553384813228 -6.25533848132279 87 22.17 42.3797029278897 -20.2097029278897 88 25.52 20.7107871368709 4.80921286312914 89 20.28 26.3567384573136 -6.07673845731362 90 22.87 24.2886669191698 -1.41866691916982 91 27.63 25.2535482908091 2.37645170919089 92 22.95 29.3189347461984 -6.36893474619842 93 21.35 27.0526960571734 -5.70269605717339 94 18.38 16.3285404178415 2.05145958215847 95 17.15 14.5980064789821 2.55199352101793 96 18.27 14.5404558288841 3.72954417111595 97 19.4 18.5368846970835 0.863115302916533 98 20.52 20.9494374315293 -0.429437431529294 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 99 19.0102352484592 8.60646154673654 29.4140089501819 100 18.1562913079572 4.33795104455971 31.9746315713548 101 18.2282349758067 1.68572766786181 34.7707422837516 102 22.0583539657892 3.18078610253451 40.9359218290439 103 24.7409932734932 3.78698199092103 45.6950045560654 104 25.6283585359059 2.7858847375508 48.470832334261 105 29.0133353328115 4.42702553188943 53.5996451337336 106 24.2500645159343 -1.96433324608366 50.4644622779523 107 20.7892550250225 -6.9578650133467 48.5363750633917 108 18.6490968525277 -10.5504012736738 47.8485949787293 109 19.0246099019773 -11.5583708425549 49.6075906465094 110 20.52 -11.3865311749616 52.4265311749616

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/14c2z1211733813.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/14c2z1211733813.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/2l3ty1211733813.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/2l3ty1211733813.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/3uboy1211733813.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211733872inrq0sz5siz4r4v/3uboy1211733813.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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