Growth of number of distinct PubMed documents tagged in Citeulike per month (2004-2008)

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Nov 2008 12:53:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0.htm/, Retrieved Sun, 16 Nov 2008 20:15:06 +0000

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/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

481 487 371 1147 1638 1193 1646 1930 1472 1952 2040 2601 3289 2964 2925 3565 3614 3046 3153 3797 4716 3898 3267 3739 4422 3719 4260 4573 4199 4647 5708 4715 5018 7280 6355 5868 7071 7009 6440 8446 9328 8166 10332 9238 9597 8929 12394 15581

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.180689939825716 beta 0.54265603293671 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 371 493 -122 4 1147 464.9934240569 682.0065759431 5 1638 649.135188137312 988.864811862688 6 1193 985.683801460212 207.316198539788 7 1646 1201.34231151284 444.657688487159 8 1930 1503.48583284955 426.51416715045 9 1472 1844.17177678432 -372.171776784321 10 1952 2004.05083766043 -52.050837660433 11 2040 2216.66881773606 -176.668817736062 12 2601 2389.44676572398 211.553234276017 13 3289 2653.11585345784 635.884146542158 14 2964 3055.8072895319 -91.8072895318987 15 2925 3318.01027084427 -393.010270844268 16 3565 3487.25326953277 77.7467304672305 17 3614 3749.1805826566 -135.180582656597 18 3046 3959.37928020488 -913.379280204883 19 3153 3939.40619289292 -786.40619289292 20 3797 3865.26678291713 -68.2667829171273 21 4716 3914.19421194436 801.805788055637 22 3898 4198.95405222252 -300.954052222522 23 3267 4254.94699034525 -987.946990345253 24 3739 4089.93655744017 -350.936557440174 25 4422 4005.61729946175 416.382700538254 26 3719 4100.77227092366 -381.772270923657 27 4260 4014.27494839449 245.725051605512 28 4573 4065.25403148093 507.745968519072 29 4199 4213.36341271554 -14.3634127155447 30 4647 4265.72451294913 381.275487050868 31 5708 4426.95859150655 1281.04140849345 32 4715 4876.38061495819 -161.380614958191 33 5018 5049.34771931031 -31.3477193103081 34 7280 5242.73673794556 2037.26326205444 35 6355 6009.66167767979 345.338322320207 36 5868 6504.73408285676 -636.734082856764 37 7071 6759.92252453264 311.077475467362 38 7009 7216.87289943692 -207.872899436920 39 6440 7559.67170777841 -1119.67170777841 40 8446 7627.93104992607 818.068950073926 41 9328 8126.53432916186 1201.46567083814 42 8166 8812.22023459604 -646.220234596038 43 10332 9100.6843844953 1231.31561550470 44 9238 9849.13393124366 -611.133931243656 45 9597 10204.748179059 -607.748179058999 46 8929 10501.3829784522 -1572.38297845219 47 12394 10469.5419141064 1924.45808589364 48 15581 11258.2427506615 4322.75724933855 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 49 12904.1492131450 10999.7937761928 14808.5046500972 50 13768.9769283644 11792.0236047992 15745.9302519296 51 14633.8046435838 12530.6583075543 16736.9509796133 52 15498.6323588033 13209.3216293269 17787.9430882796 53 16363.4600740227 13827.4719936426 18899.4481544027 54 17228.2877892421 14388.5987079858 20067.9768704984 55 18093.1155044615 14898.0453951407 21288.1856137823 56 18957.9432196809 15361.432952229 22554.4534871328 57 19822.7709349003 15783.8593038181 23861.6825659825 58 20687.5986501197 16169.6378305533 25205.5594696861 59 21552.4263653391 16522.3062575807 26582.5464730976 60 22417.2540805585 16844.7361629600 27989.7719981571

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/1yple1226865182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/1yple1226865182.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/21onn1226865182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/21onn1226865182.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/30b261226865182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/16/t1226866506mfqeu7wwjf7jyl0/30b261226865182.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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