*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 14:51:29 +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/Jun/02/t1275490558fe5o88k86g7s6dl.htm/, Retrieved Wed, 02 Jun 2010 16:56:02 +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/Jun/02/t1275490558fe5o88k86g7s6dl.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 «

182900 191400 189300 192200 187900 193900 189100 193100 194800 200200 211500 202100 200300 199200 204900 207300 200000 197700 202200 200200 208300 215100 210700 208100 209000 211000 210200 205500 211400 211700 209300 207500 203300 207100 206900 228700 226900 226500 227100 228100 226500 225200 217800 221300 215300 231300 227100 237800 230200 233400 231100 237200 243700 239700 248400 241000 254500 242800 268300 253900 262100 264100 261000 269300 260400 263200 279200 272200 269200 289600 283200 284300 283000 289100 289600 289100 287400 279600 289300 295000 299600 293600 294400 290200 301000 307900 298800 310300 293900 305000 311300 317300 296200 306800 291800 301900 314600 321500 329400 311700 309700 306500 307100 301300 292200 310100 316800 284400 284600 301200 287600 314300 298200 299400 301900 265500 287100 274000 290100 263100 245200 258600 259800 269800 274600 274800 271100 257800 etc...

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 0.469466513979295 beta 0.144645237637946 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 189300 199900 -10600 4 192200 202703.850339757 -10503.8503397570 5 187900 204839.564261275 -16939.5642612747 6 193900 202803.626335014 -8903.62633501447 7 189100 203935.681673547 -14835.6816735474 8 193100 201275.402455368 -8175.40245536788 9 194800 201186.741644174 -6386.74164417389 10 200200 201504.098500822 -1304.09850082250 11 211500 204119.029878472 7380.970121528 12 202100 211312.523007717 -9212.52300771713 13 200300 210090.340295885 -9790.34029588458 14 199200 207932.067933169 -8732.06793316864 15 204900 205677.658368631 -777.658368631004 16 207300 207104.769989691 195.230010308791 17 2e+05 209001.877434223 -9001.87743422337 18 197700 205969.968559552 -8269.96855955201 19 202200 202720.085118221 -520.085118221497 20 200200 203073.195490144 -2873.19549014387 21 208300 202126.491851472 6173.50814852817 22 215100 205846.131466817 9253.86853318344 23 210700 211640.291213897 -940.291213896795 24 208100 212584.782816620 -4484.78281661961 25 209000 211560.710212642 -2560.71021264163 26 211000 211266.037434506 -266.037434506172 27 210200 212030.571122817 -1830.57112281691 28 205500 211936.301697029 -6436.30169702874 29 211400 209242.731876676 2157.26812332356 30 211700 210730.046977676 969.95302232419 31 209300 211725.823119757 -2425.82311975677 32 207500 210962.667897779 -3462.66789777894 33 203300 209477.612515452 -6177.61251545162 34 207100 206298.484002521 801.515997479146 35 206900 206450.250445021 449.749554979178 36 228700 206467.415058247 22232.5849417532 37 226900 218220.619500855 8679.38049914513 38 226500 224200.431141404 2299.56885859565 39 227100 227341.289593690 -241.28959368958 40 228100 229272.915051679 -1172.91505167884 41 226500 230687.525472085 -4187.52547208508 42 225200 230402.518742895 -5202.51874289528 43 217800 229287.723926667 -11487.7239266667 44 221300 224442.149265384 -3142.14926538398 45 215300 223301.171359468 -8001.17135946755 46 231300 219335.716983425 11964.2830165752 47 227100 225555.82261816 1544.17738184004 48 237800 226988.896641986 10811.1033580144 49 230200 233506.621915997 -3306.62191599744 50 233400 233172.008136766 227.991863234492 51 231100 234512.259203966 -3412.25920396566 52 237200 233911.821093339 3288.17890666079 53 243700 236680.301695426 7019.69830457433 54 239700 241677.286004391 -1977.28600439106 55 248400 242316.217681299 6083.78231870066 56 241000 247152.676905797 -6152.67690579701 57 254500 245826.724009312 8673.27599068786 58 242800 252050.027843088 -9250.0278430884 59 268300 249230.807433147 19069.1925668532 60 253900 261001.427118797 -7101.4271187972 61 262100 260003.587023991 2096.41297600884 62 264100 263466.184074342 633.815925657982 63 261000 266285.180750871 -5285.18075087119 64 269300 265966.51070273 3333.48929726979 65 260400 269920.381879722 -9520.38187972165 66 263200 267193.299003204 -3993.29900320445 67 279200 266789.827113818 12410.1728861817 68 272200 274929.962374402 -2729.96237440204 69 269200 275776.930027378 -6576.9300273782 70 289600 274371.261548532 15228.7384514681 71 283200 284236.748402727 -1036.74840272655 72 284300 286395.732309285 -2095.73230928456 73 283000 287915.245734581 -4915.24573458085 74 289100 287777.316874837 1322.68312516279 75 289600 290657.704977912 -1057.70497791219 76 289100 292348.755961102 -3248.7559611015 77 287400 292790.571544784 -5390.57154478412 78 279600 291860.823766810 -12260.8237668098 79 289300 286873.137958660 2426.86204134038 80 295000 288945.627530775 6054.37246922497 81 299600 293132.240572845 6467.7594271549 82 293600 297952.125238165 -4352.12523816549 83 294400 297396.900536047 -2996.90053604660 84 290200 297274.400636552 -7074.40063655243 85 301000 294757.256054051 6242.7439459489 86 307900 298915.985281291 8984.01471870928 87 298800 304971.718703352 -6171.71870335226 88 310300 303493.245469428 6806.75453057158 89 293900 308569.950944454 -14669.9509444539 90 305000 302567.883278873 2432.11672112654 91 311300 304759.819252368 6540.18074763153 92 317300 309324.47186188 7975.52813812008 93 296200 315104.558982385 -18904.5589823847 94 306800 306981.610519747 -181.610519746842 95 291800 307636.126941984 -15836.1269419839 96 301900 299866.002563324 2033.997436676 97 314600 300623.424005226 13976.5759947739 98 321500 307936.580874673 13563.4191253268 99 329400 315976.813263021 13423.1867369785 100 311700 324862.727441040 -13162.7274410397 101 309700 320373.615742594 -10673.6157425942 102 306500 316328.255066415 -9828.2550664153 103 307100 312012.364493019 -4912.36449301912 104 301300 309670.740437935 -8370.74043793522 105 292200 305137.100384565 -12937.1003845652 106 310100 297581.199271559 12518.8007284414 107 316800 302826.094191807 13973.9058081926 108 284400 309703.025603326 -25303.0256033264 109 284600 296422.523272784 -11822.5232727844 110 301200 288667.843983904 12532.1560160962 111 287600 293197.880862827 -5597.88086282689 112 314300 288836.342297543 25463.6577024575 113 298200 300786.293532488 -2586.29353248753 114 299400 299392.106848323 7.89315167651512 115 301900 299216.339936497 2683.66006350319 116 265500 300478.992865488 -34978.9928654882 117 287100 281685.00458746 5414.99541253992 118 274000 282222.352367533 -8222.35236753296 119 290100 275799.074180452 14300.9258195483 120 263100 280920.840921366 -17820.8409213655 121 245200 269752.370082469 -24552.3700824693 122 258600 253756.416127538 4843.58387246166 123 259800 251889.787069822 7910.21293017824 124 269800 251999.989339984 17800.0106600162 125 274600 257961.849697714 16638.1503022856 126 274800 264508.087346568 10291.9126534319 127 271100 268773.862532821 2326.13746717875 128 257800 269457.931924182 -11657.9319241816 129 290300 262785.304368821 27514.6956311793 130 262200 276371.329263852 -14171.3292638522 131 270000 269424.841731724 575.158268276486 132 290600 269440.393047023 21159.6069529773 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 280556.520018531 260532.393989006 300580.646048056 134 281738.920076654 259006.735971873 304471.104181435 135 282921.320134776 257159.897689650 308682.742579902 136 284103.720192898 255028.651911064 313178.788474733 137 285286.120251021 252642.955308814 317929.285193228 138 286468.520309143 250026.804547836 322910.23607045 139 287650.920367265 247199.408877287 328102.431857244 140 288833.320425388 244176.265935517 333490.374915258 141 290015.72048351 240970.030102301 339061.410864719 142 291198.120541632 237591.177285395 344805.063797870 143 292380.520599755 234048.503042373 350712.538157136 144 293562.920657877 230349.493589252 356776.347726502

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/1gpt81275490286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/1gpt81275490286.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/2ryat1275490286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/2ryat1275490286.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/3ryat1275490286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275490558fe5o88k86g7s6dl/3ryat1275490286.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=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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