forcast

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 02 Jul 2010 15:49:39 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw.htm/, Retrieved Fri, 02 Jul 2010 17:52:08 +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/2010/Jul/02/t1278085924ww7qcejslkw1ujw.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:

thomas talboom

Dataseries X:

» Textbox « » Textfile « » CSV «

68 67 66 64 84 83 68 58 59 59 60 62 58 58 59 62 87 83 68 58 68 63 65 68 62 69 74 72 94 102 92 81 99 95 92 93 85 92 99 107 125 137 125 115 135 128 120 123 119 128 139 155 164 176 162 155 174 171 162 160 156 163 180 195 203 212 203 184 200 198 195 177 176 180 194 204 206 219 213 196 214 209 213 194 197 211 240 251 254 273 271 245 264 264 262 237 237 251 272 282 278 291 293 271 284 290 288 262 263 275 297 301 296 309 310 292 300 314 310 288

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.370054769208693 beta 0.326909085417736 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 58 58.8875534188034 -0.887553418803435 14 58 58.4961736516680 -0.496173651668045 15 59 58.8146015905362 0.185398409463829 16 62 61.2410102910503 0.758989708949656 17 87 86.138164077243 0.861835922756953 18 83 82.0943032303197 0.905696769680318 19 68 67.7179059677209 0.282094032279119 20 58 58.8532009899306 -0.8532009899306 21 68 60.3401593110719 7.65984068892813 22 63 64.6123862454992 -1.61238624549921 23 65 65.8416574721796 -0.841657472179648 24 68 68.170988328808 -0.170988328807979 25 62 64.2937082696555 -2.29370826965550 26 69 64.1590837589823 4.84091624101774 27 74 68.0580926163945 5.94190738360550 28 72 74.8486577497965 -2.84865774979653 29 94 99.911741095756 -5.91174109575591 30 102 94.0056564164047 7.99434358359525 31 92 83.3338957070902 8.6661042929098 32 81 79.3450940781803 1.65490592181966 33 99 89.9148897735373 9.0851102264627 34 95 91.837920742671 3.16207925732904 35 92 98.8614814556668 -6.86148145566678 36 93 102.199347618506 -9.19934761850621 37 85 95.365398756152 -10.3653987561520 38 92 97.4832784492366 -5.48327844923662 39 99 97.7514211462646 1.24857885373540 40 107 96.1959383208125 10.8040616791875 41 125 124.961643801628 0.0383561983715737 42 137 131.317244322475 5.68275567752482 43 125 121.233350885060 3.76664911494028 44 115 111.442212476216 3.55778752378355 45 135 128.054401005713 6.94559899428674 46 128 125.853285384102 2.14671461589765 47 120 126.462753165306 -6.46275316530604 48 123 128.799620719379 -5.79962071937931 49 119 123.224665849066 -4.22466584906618 50 128 132.168749293474 -4.16874929347395 51 139 138.801393225319 0.198606774681167 52 155 144.387126505618 10.6128734943816 53 164 167.787480660072 -3.78748066007182 54 176 177.307350328411 -1.30735032841122 55 162 163.608445481613 -1.60844548161310 56 155 151.225161040959 3.77483895904066 57 174 169.606568527835 4.39343147216474 58 171 162.683992582396 8.3160074176036 59 162 160.145284855324 1.85471514467565 60 160 166.976349408252 -6.97634940825168 61 156 162.814262955529 -6.81426295552896 62 163 171.378190569990 -8.3781905699905 63 180 179.237984300815 0.762015699185383 64 195 191.69446386685 3.30553613315016 65 203 202.537105258370 0.462894741629583 66 212 214.924215633429 -2.92421563342899 67 203 199.973732264040 3.02626773595952 68 184 192.793824593662 -8.79382459366195 69 200 205.490437424686 -5.49043742468552 70 198 194.762222709355 3.23777729064463 71 195 183.040622333976 11.9593776660238 72 177 186.036873460918 -9.03687346091812 73 176 178.954110472808 -2.95411047280848 74 180 186.168020924693 -6.16802092469288 75 194 199.077605215509 -5.0776052155093 76 204 208.743017317973 -4.74301731797345 77 206 211.610510424352 -5.61051042435156 78 219 215.67567418456 3.32432581544012 79 213 203.601124673788 9.39887532621213 80 196 188.919494246069 7.08050575393102 81 214 209.077891389442 4.9221086105577 82 209 208.467296009413 0.532703990587322 83 213 201.677666444361 11.322333555639 84 194 191.573487679117 2.42651232088303 85 197 194.313187068830 2.68681293117049 86 211 204.020941400578 6.97905859942239 87 240 226.504006476405 13.4959935235950 88 251 249.521806031691 1.47819396830926 89 254 261.165987977382 -7.16598797738231 90 273 277.116797650029 -4.11679765002856 91 271 272.047874277667 -1.04787427766666 92 245 256.708756485545 -11.7087564855445 93 264 270.950236334135 -6.9502363341345 94 264 264.140701155495 -0.140701155495435 95 262 264.77684837389 -2.77684837389018 96 237 243.023779628400 -6.02377962839955 97 237 240.950575137248 -3.95057513724763 98 251 248.253250724667 2.74674927533331 99 272 270.110679787957 1.88932021204255 100 282 276.693948391564 5.30605160843623 101 278 280.203487767387 -2.2034877673874 102 291 296.406053680970 -5.40605368097027 103 293 289.131858272017 3.8681417279829 104 271 265.829444838415 5.17055516158536 105 284 288.290044970731 -4.29004497073146 106 290 286.051618633582 3.94838136641818 107 288 286.332053861114 1.66794613888607 108 262 264.50785130725 -2.50785130724972 109 263 265.796512632208 -2.79651263220774 110 275 278.639588482012 -3.63958848201156 111 297 297.715393283297 -0.715393283297374 112 301 305.293829411977 -4.29382941197736 113 296 299.165650483880 -3.16565048388048 114 309 311.523687410122 -2.52368741012225 115 310 310.036017736218 -0.0360177362176728 116 292 284.514654960632 7.48534503936833 117 300 300.557578556411 -0.557578556411499 118 314 304.027043345781 9.97295665421882 119 310 304.966087418331 5.03391258166931 120 288 282.029883757016 5.97011624298364 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 287.572563128397 276.846972692500 298.298153564294 122 302.556262813834 290.607408626486 314.505117001182 123 326.898146665613 313.265007532133 340.531285799093 124 334.650792050579 318.913336491661 350.388247609496 125 333.505392304797 315.296677099104 351.714107510489 126 350.50539330611 329.507798036758 371.502988575462 127 354.890121512827 330.826461795886 378.953781229768 128 337.495890772697 310.120599657954 364.87118188744 129 348.172448144501 317.264412626670 379.080483662331 130 361.019583395977 326.376732396389 395.662434395565 131 356.487964349178 317.923277398746 395.05265129961 132 333.000924792096 290.339494427769 375.662355156422

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/1fnv01278085775.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/1fnv01278085775.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/2pfcl1278085775.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/2pfcl1278085775.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/3pfcl1278085775.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278085924ww7qcejslkw1ujw/3pfcl1278085775.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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