Ken Soltvedt Sigaretten O10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 16:05:23 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g.htm/, Retrieved Sat, 06 Jun 2009 00:05:58 +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/2009/Jun/06/t1244239554ci881xylo80qw9g.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:

» Textbox « » Textfile « » CSV «

3.42 3.42 3.43 3.47 3.51 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.58 3.6 3.61 3.61 3.61 3.63 3.68 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.78 3.79 3.79 3.8 3.8 3.8 3.8 3.81 3.95 3.99 4 4.06 4.16 4.19 4.2 4.2 4.2 4.2 4.2 4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68

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 0.873418950693836 beta 0.0296759775106365 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.52 3.46502409710897 0.0549759028910324 14 3.52 3.51637916866576 0.00362083133424251 15 3.58 3.58007339645459 -7.33964545860388e-05 16 3.6 3.59803506364187 0.00196493635812889 17 3.61 3.60741244019217 0.00258755980783043 18 3.61 3.60741060078114 0.00258939921886370 19 3.61 3.64964552079433 -0.039645520794326 20 3.63 3.61742053476775 0.0125794652322471 21 3.68 3.62894473810215 0.051055261897853 22 3.69 3.6739557396976 0.0160442603024031 23 3.69 3.69092692300590 -0.000926923005895475 24 3.69 3.69477467449461 -0.00477467449460711 25 3.69 3.70288088133550 -0.0128808813354953 26 3.69 3.6885750275598 0.00142497244019779 27 3.69 3.75299048235024 -0.0629904823502381 28 3.69 3.71561636123817 -0.0256163612381686 29 3.69 3.69930899812387 -0.0093089981238701 30 3.78 3.68673093869279 0.0932690613072071 31 3.79 3.80424694387552 -0.0142469438755199 32 3.79 3.80185326741977 -0.0118532674197676 33 3.8 3.79707125002915 0.00292874997084658 34 3.8 3.79433025124074 0.00566974875926229 35 3.8 3.7987281476632 0.00127185233679983 36 3.8 3.80280392207294 -0.00280392207293678 37 3.81 3.81066134800965 -0.000661348009649565 38 3.95 3.80782061859225 0.142179381407754 39 3.99 3.99278607106964 -0.00278607106963724 40 4 4.01831319290046 -0.0183131929004636 41 4.06 4.01512783117502 0.0448721688249751 42 4.16 4.06869352788346 0.091306472116539 43 4.19 4.17807196660782 0.0119280333921798 44 4.2 4.20555035994741 -0.00555035994741004 45 4.2 4.21472478598400 -0.0147247859840043 46 4.2 4.20170280812858 -0.00170280812857726 47 4.2 4.20408432051875 -0.0040843205187473 48 4.2 4.20816490533 -0.00816490533000191 49 4.23 4.21753393106047 0.0124660689395295 50 4.38 4.25044840952595 0.129551590474050 51 4.43 4.41493866768527 0.0150613323147262 52 4.44 4.46179694593563 -0.0217969459356278 53 4.44 4.47062818506073 -0.0306281850607295 54 4.44 4.46879802914675 -0.0287980291467473 55 4.44 4.4647068575573 -0.0247068575572955 56 4.44 4.45819796749402 -0.0181979674940225 57 4.45 4.45496059279912 -0.00496059279912053 58 4.45 4.45150519670828 -0.00150519670828153 59 4.45 4.45328331929561 -0.00328331929560921 60 4.45 4.45731156450628 -0.00731156450628223 61 4.45 4.47054849457995 -0.0205484945799475 62 4.45 4.48956230108177 -0.0395623010817703 63 4.45 4.48728060425283 -0.0372806042528264 64 4.45 4.47759229284161 -0.0275922928416064 65 4.46 4.47388736617346 -0.0138873661734555 66 4.46 4.48098975504584 -0.0209897550458367 67 4.46 4.47850731393273 -0.0185073139327319 68 4.48 4.47265444591991 0.00734555408009285 69 4.58 4.48847182153645 0.0915281784635482 70 4.67 4.56688434571314 0.103115654286857 71 4.68 4.65940996839529 0.0205900316047112 72 4.68 4.68410351827942 -0.00410351827941913 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4.6994642720259 4.62041017000297 4.77851837404882 74 4.73647951725077 4.62998053074079 4.84297850376076 75 4.77261180698504 4.64312143238524 4.90210218158483 76 4.80085150748046 4.65089424252500 4.95080877243591 77 4.8278078425174 4.65889446600094 4.99672121903386 78 4.85106451220569 4.66431315058774 5.03781587382363 79 4.8725758773511 4.66877061335302 5.07638114134918 80 4.89180771201712 4.67157531882776 5.11204010520648 81 4.9176855681833 4.68115405196285 5.15421708440374 82 4.91924156963804 4.66783082303564 5.17065231624044 83 4.91023177593882 4.64475346653108 5.17571008534656 84 4.91292529328788 0.885039005800385 8.94081158077537

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/1mq5e1244239521.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/1mq5e1244239521.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/2mzq91244239521.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/2mzq91244239521.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/3tl7d1244239521.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244239554ci881xylo80qw9g/3tl7d1244239521.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')

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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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