SHWWS9klasmeth4

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 01 Dec 2009 13:08:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r.htm/, Retrieved Tue, 01 Dec 2009 21:10:17 +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/2009/Dec/01/t1259698212ho4peklyueldk9r.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.842600131373437 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 157 159.110261095247 -2.11026109524690 14 147 147.376317860187 -0.376317860186532 15 137 136.942349195449 0.0576508045512298 16 132 131.798915314866 0.201084685134447 17 125 124.945866367617 0.0541336323827721 18 123 123.202432657572 -0.202432657571890 19 117 119.012778976411 -2.0127789764107 20 114 112.478180075192 1.52181992480821 21 111 108.803961042407 2.19603895759332 22 112 111.583452723806 0.416547276193768 23 144 147.65632556169 -3.65632556168995 24 150 152.442613463198 -2.44261346319828 25 149 150.166197685816 -1.16619768581583 26 134 139.967343091050 -5.96734309105042 27 123 125.691651374911 -2.69165137491068 28 116 118.739134379916 -2.73913437991634 29 117 110.185659692264 6.81434030773566 30 111 114.211978842517 -3.21197884251697 31 105 107.576244852594 -2.57624485259416 32 102 101.521243438505 0.478756561494507 33 95 97.5583497079523 -2.55834970795232 34 93 95.9275457434062 -2.92754574340616 35 124 122.673689144122 1.32631085587785 36 130 130.668405813068 -0.668405813067722 37 124 130.045927592127 -6.04592759212676 38 115 116.510700197770 -1.51070019776968 39 106 107.681781828694 -1.68178182869393 40 105 102.166319011649 2.83368098835147 41 105 100.206154876492 4.79384512350848 42 101 101.271933222193 -0.271933222192985 43 95 97.5271174949162 -2.52711749491621 44 93 92.2832595698534 0.716740430146629 45 84 88.4467733713745 -4.44677337137453 46 87 85.0800535773441 1.91994642265587 47 116 114.532654873331 1.46734512666924 48 120 121.874612313483 -1.8746123134828 49 117 119.396960447348 -2.39696044734755 50 109 110.044188100603 -1.04418810060261 51 105 101.948436098719 3.05156390128073 52 107 101.165435732381 5.83456426761897 53 109 101.973937623378 7.02606237662158 54 109 104.026281016554 4.97371898344583 55 108 104.078101930881 3.92189806911853 56 107 104.470038017158 2.52996198284212 57 99 100.578272000367 -1.57827200036694 58 103 100.917215917477 2.08278408252264 59 131 135.489710732080 -4.48971073207952 60 137 138.081153983579 -1.08115398357867 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 136.088233901037 130.030701245877 142.145766556197 62 127.854359537270 120.121479949049 135.587239125490 63 120.182004035668 111.219118837270 129.144889234067 64 116.835685142666 106.693087337638 126.978282947694 65 112.51361905379 101.439526704451 123.587711403129 66 108.164723897094 96.3033115772464 120.026136216942 67 103.872356722968 91.3342502005528 116.410463245382 68 100.843371120951 87.5957999063578 114.090942335544 69 94.5407584269163 81.0393985627605 108.042118291072 70 96.6688036921573 81.9371638851851 111.400443499130 71 126.460310090694 106.671627275678 146.248992905711 72 133.119499344974 100.078566257659 166.160432432288

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/1evj91259698118.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/1evj91259698118.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/20bf21259698118.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/20bf21259698118.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/3jeic1259698118.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259698212ho4peklyueldk9r/3jeic1259698118.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=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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