exponential smoothing eigen reeks

*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 04:49:31 -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/t1263901879s82qpaqipea7xbt.htm/, Retrieved Tue, 19 Jan 2010 12:51:23 +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/t1263901879s82qpaqipea7xbt.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 «

76.3 71 85.9 109 83.4 101.3 81.6 84.8 88 88.4 85.2 139.5 85.3 79.4 131 91.4 88.2 113.2 81.9 89 95.7 93.2 98 140.5 93 82.1 86.3 84.8 85.7 110.8 87.4 100.4 100.4 99.4 108 161.7 109.3 99.9 110.3 97.5 102.4 122.3 104.4 122.7 127.3 128.4 125.3 187.1 131.4 125.6 142.9 116.6 129.7 155.4 138.7 167.7 155.8 157.1 159.9 244.6 154.3 143.2 147.3 155.1 152.2 166.5 161.2 180.1 169.2 164.5 166.2 267.3

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 0.246690113402272 beta 0.0345331971607616 gamma 0.853252708606075 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 85.3 81.6231400418526 3.67685995814739 14 79.4 77.1785710477302 2.22142895226980 15 131 128.445402914129 2.55459708587060 16 91.4 90.1895797124119 1.21042028758814 17 88.2 87.2656512809064 0.934348719093578 18 113.2 112.415499185951 0.784500814048712 19 81.9 88.2360701997203 -6.3360701997203 20 89 89.9336033969772 -0.93360339697719 21 95.7 91.4617599959235 4.23824000407647 22 93.2 92.4150531873506 0.784946812649366 23 98 90.344885342564 7.65511465743604 24 140.5 150.981461409249 -10.4814614092488 25 93 93.4541160966085 -0.454116096608516 26 82.1 86.4078620284123 -4.30786202841229 27 86.3 140.160185743814 -53.8601857438139 28 84.8 87.9587463038027 -3.1587463038027 29 85.7 83.5875034479842 2.11249655201576 30 110.8 107.384340373894 3.41565962610629 31 87.4 80.160875735995 7.23912426400507 32 100.4 88.405457789373 11.9945422106271 33 100.4 96.4100807687469 3.98991923125315 34 99.4 94.8961414054013 4.50385859459875 35 108 98.0143128973651 9.98568710263487 36 161.7 148.916724557558 12.7832754424425 37 109.3 100.021646058106 9.27835394189353 38 99.9 91.9962431539862 7.9037568460138 39 110.3 116.142568305204 -5.84256830520438 40 97.5 107.273099402642 -9.77309940264182 41 102.4 105.009987240767 -2.60998724076696 42 122.3 134.260094240738 -11.9600942407381 43 104.4 100.998357440243 3.40164255975670 44 122.7 112.973639941045 9.7263600589545 45 127.3 115.424055154325 11.8759448456752 46 128.4 115.988053891539 12.4119461084614 47 125.3 125.821040363661 -0.521040363661271 48 187.1 184.866664800708 2.2333351992919 49 131.4 122.584676903301 8.81532309669932 50 125.6 111.840432253498 13.7595677465016 51 142.9 130.876207542756 12.0237924572444 52 116.6 121.904635867697 -5.30463586769743 53 129.7 126.691776520755 3.00822347924517 54 155.4 157.269692224559 -1.86969222455920 55 138.7 131.271785368478 7.42821463152194 56 167.7 152.876807549844 14.8231924501557 57 155.8 158.632476671689 -2.83247667168857 58 157.1 155.499724811334 1.60027518866619 59 159.9 154.252275382001 5.6477246179989 60 244.6 231.737175848192 12.8628241518083 61 154.3 161.44561212402 -7.14561212402018 62 143.2 147.629675817796 -4.42967581779587 63 147.3 163.542011807314 -16.2420118073143 64 155.1 133.372119040691 21.7278809593095 65 152.2 152.322602343346 -0.122602343345761 66 166.5 183.765220364102 -17.2652203641022 67 161.2 156.821930669021 4.37806933097886 68 180.1 185.651291455172 -5.55129145517157 69 169.2 173.796727071584 -4.59672707158441 70 164.5 172.901609962885 -8.40160996288535 71 166.2 171.560705224965 -5.36070522496462 72 267.3 255.888240736133 11.4117592638675 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 166.475390173274 147.757267638598 185.193512707950 74 155.121582977313 135.755966874575 174.487199080051 75 164.751956344182 144.462586520229 185.041326168136 76 162.076288326031 141.095829861594 183.056746790468 77 161.298247363775 139.575673267784 183.020821459766 78 182.366241027696 158.923520360589 205.808961694803 79 172.643077140927 148.918033160368 196.368121121486 80 195.307417356729 169.395943421752 221.218891291705 81 184.411287061899 158.430042640031 210.392531483768 82 181.772756403171 155.173233321444 208.372279484898 83 184.58422612996 156.94118569666 212.227266563260 84 291.100628146095 250.789083433606 331.412172858583

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/1t3op1263901769.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/1t3op1263901769.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/29cft1263901769.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/29cft1263901769.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/326nl1263901769.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263901879s82qpaqipea7xbt/326nl1263901769.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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