KDGP2W62

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 03:33:53 -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/19/t1263897309wy3fw0z9lihkbd5.htm/, Retrieved Tue, 19 Jan 2010 11:35:14 +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/19/t1263897309wy3fw0z9lihkbd5.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

46.5 47 47.5 48.3 49.1 50.1 51.1 52 53.2 53.9 54.5 55.2 55.6 55.7 56.1 56.8 57.5 58.3 58.9 59.4 59.8 60 60 60.3 60.1 59.7 59.5 59.4 59.3 59.2 59.1 59 59.3 59.5 59.5 59.5 59.7 59.7 60.5 60.7 61.3 61.4 61.8 62.4 62.4 62.9 63.2 63.4 63.9 64.5 65 65.4 66.3 67.7 69 70 71.4 72.5 73.4 74.6 75.2 75.9 76.8 77.9 79.2 80.5 82.6 84.4 85.9 87.6

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.983484861538448 beta 0.23196686548946 gamma 0.942906046720505 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 55.6 51.4044871794872 4.19551282051281 14 55.7 56.5915872243153 -0.89158722431533 15 56.1 56.922198331552 -0.822198331552023 16 56.8 57.487646074217 -0.687646074216943 17 57.5 58.0743805019632 -0.574380501963169 18 58.3 58.7831397589259 -0.483139758925937 19 58.9 58.8214113814092 0.0785886185908211 20 59.4 59.8800632447548 -0.480063244754845 21 59.8 60.6006031302821 -0.800603130282092 22 60 60.3315839080673 -0.331583908067337 23 60 60.3565251305174 -0.356525130517433 24 60.3 60.388100856527 -0.0881008565269639 25 60.1 60.4539022893204 -0.353902289320388 26 59.7 59.766336626544 -0.066336626543972 27 59.5 59.7767516741339 -0.276751674133855 28 59.4 59.8722711205326 -0.472271120532625 29 59.3 59.7132600061644 -0.413260006164435 30 59.2 59.6593296768512 -0.459329676851169 31 59.1 58.8126274731411 0.28737252685886 32 59 59.1984087610925 -0.198408761092544 33 59.3 59.3857086112982 -0.0857086112982515 34 59.5 59.1849226660486 0.315077333951415 35 59.5 59.3508253526875 0.149174647312513 36 59.5 59.5046657042383 -0.00466570423825630 37 59.7 59.2881563670693 0.411843632930747 38 59.7 59.172633539368 0.527366460632038 39 60.5 59.7135802195463 0.786419780453734 40 60.7 61.0441258657622 -0.344125865762223 41 61.3 61.2337549785384 0.0662450214615546 42 61.4 61.981777863726 -0.581777863725961 43 61.8 61.3294273944567 0.470572605543332 44 62.4 62.232762865013 0.167237134986983 45 62.4 63.2097862400401 -0.809786240040147 46 62.9 62.5662952642739 0.333704735726137 47 63.2 63.0153570513097 0.184642948690289 48 63.4 63.4771987033318 -0.077198703331824 49 63.9 63.4548072545878 0.445192745412186 50 64.5 63.6404568696413 0.859543130358681 51 65 64.8544848840001 0.145515115999856 52 65.4 65.7332485941135 -0.333248594113471 53 66.3 66.1385904314292 0.161409568570846 54 67.7 67.1904502054334 0.509549794566581 55 69 68.0970975772327 0.902902422767326 56 70 69.9888353955661 0.0111646044338727 57 71.4 71.329479750624 0.07052024937596 58 72.5 72.3027234698917 0.197276530108297 59 73.4 73.3173246785926 0.0826753214073932 60 74.6 74.3535784996001 0.246421500399862 61 75.2 75.4102000489749 -0.210200048974869 62 75.9 75.5608171342242 0.339182865775783 63 76.8 76.736330848968 0.0636691510320162 64 77.9 77.992844020204 -0.0928440202039553 65 79.2 79.1628671025947 0.0371328974053284 66 80.5 80.5901160574392 -0.0901160574392463 67 82.6 81.2685132958353 1.33148670416469 68 84.4 84.0210331656687 0.378966834331351 69 85.9 86.2614008780557 -0.361400878055647 70 87.6 87.250365001704 0.349634998296025 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 71 88.8863167154654 87.480718230571 90.2919152003597 72 90.298242146459 88.0900541420414 92.5064301508767 73 91.5036153215507 88.5083630740932 94.4988675690082 74 92.3156843180334 88.5120429508068 96.1193256852599 75 93.5221149005942 88.8777414878298 98.1664883133585 76 95.0678363912434 89.5465374927368 100.589135289750 77 96.7066384695665 90.2710379304204 103.142239008713 78 98.462359163651 91.0750390828492 105.849679244453 79 99.6390533356885 91.2630741202454 108.015032551132 80 101.151015056405 91.7501534424879 110.551876670322 81 103.004461232828 92.5433108641415 113.465611601514 82 104.439694354084 92.883696477012 115.995692231156

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/1n1u01263897231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/1n1u01263897231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/25j081263897231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/25j081263897231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/34g551263897232.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263897309wy3fw0z9lihkbd5/34g551263897232.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=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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