oef 10, exponential smoothing (eigen data) wauters kathleen

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 04:50:41 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0.htm/, Retrieved Tue, 27 May 2008 12:51:47 +0200

User-defined keywords:

Dataseries X:

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209 214 265 290 287 270 263 265 252 281 259 312 275 250 312 331 256 247 291 318 296 291 313 311 273 258 361 391 446 433 449 479 460 466 410 415 382 409 496 471 488 584 610 684 626 580 444 552 473 431 513 467 470 455 406 424 406 373 332 310 301 296 333 374 422 424 341 216 319 383 360 400

Text written by user:

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.912381994071253 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 265 214 51 4 290 260.531481697634 29.4685183023661 5 287 287.418027188672 -0.418027188671942 6 270 287.036626708695 -17.0366267086955 7 263 271.492715259968 -8.49271525996835 8 265 263.744114775999 1.25588522400096 9 252 264.889961840998 -12.8899618409977 10 281 253.129392753006 27.8706072469942 11 259 278.558032968995 -19.5580329689951 12 312 260.713635848632 51.286364151368 13 275 307.506391041722 -32.5063910417215 14 250 277.848145163016 -27.8481451630157 15 312 252.439998947998 59.5600010520023 16 331 306.781471474710 24.2185285252905 17 256 328.878020824086 -72.8780208240856 18 247 262.38542686064 -15.3854268606401 19 291 248.348040421892 42.6519595781081 20 318 287.262920352813 30.7370796471873 21 296 315.30687837324 -19.3068783732404 22 291 297.691630183772 -6.69163018377213 23 313 291.586307293115 21.4136927068852 24 311 311.123774945452 -0.123774945451771 25 273 311.010844913904 -38.0108449139044 26 258 276.330434435023 -18.3304344350232 27 361 259.606076113004 101.393923886996 28 391 352.11606657573 38.8839334242696 29 446 387.593067290699 58.4069327093006 30 433 440.882501023597 -7.8825010235966 31 449 433.690649021419 15.3093509785812 32 479 447.658625195193 31.3413748048066 33 460 476.253931236537 -16.2539312365374 34 466 461.424137043448 4.57586295655165 35 410 465.599072012344 -55.5990720123438 36 415 414.87147982121 0.128520178789643 37 382 414.988739318213 -32.9887393182129 38 409 384.890407557165 24.109592442835 39 496 406.887565586404 89.112434413596 40 471 488.192146193225 -17.1921461932245 41 488 472.506341567086 15.4936584329142 42 584 486.642476543567 97.357523456433 43 610 575.469727932586 34.5302720674139 44 684 606.974526417276 77.0254735827239 45 626 677.251181598964 -51.2511815989643 46 580 630.490526333193 -50.4905263331933 47 444 584.423879235607 -140.423879235607 48 552 456.303660283403 95.696339716597 49 473 543.615277539352 -70.6152775393518 50 431 479.187169806103 -48.187169806103 51 513 435.222063729761 77.7779362702393 52 467 506.185252318748 -39.1852523187485 53 470 470.433333669984 -0.43333366998354 54 455 470.037967832066 -15.0379678320658 55 406 456.317596754666 -50.3175967546663 56 424 410.408727490771 13.5912725092294 57 406 422.809159804707 -16.8091598047072 58 373 407.472785063426 -34.4727850634261 59 332 376.020436686068 -44.0204366860677 60 310 335.856982882546 -25.8569828825459 61 301 312.265537279502 -11.2655372795024 62 296 301.987063912146 -5.98706391214597 63 333 296.52457460135 36.4754253986498 64 374 329.804095961168 44.1959040388325 65 422 370.127643017899 51.8723569821008 66 424 417.455047518404 6.54495248159577 67 341 423.426544314664 -82.4265443146642 68 216 348.222049448448 -132.222049448448 69 319 227.585032312485 91.4149676875148 70 383 310.990402819179 72.0095971808209 71 360 376.690662687284 -16.6906626872842 72 400 361.462402582289 38.5375974177108 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 396.623412560975 298.628073375495 494.618751746456 74 396.623412560975 263.969394519808 529.277430602143 75 396.623412560975 236.651257162433 556.595567959518 76 396.623412560975 213.361052805230 579.885772316721 77 396.623412560975 192.713887271858 600.532937850093 78 396.623412560975 173.973246371901 619.27357875005 79 396.623412560975 156.691967134555 636.554857987396 80 396.623412560975 140.574392830768 652.672432291183 81 396.623412560975 125.412973039947 667.833852082003 82 396.623412560975 111.055374248600 682.19145087335 83 396.623412560975 97.3858706215203 695.86095450043 84 396.623412560975 84.3140971277721 708.932727994179

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/1pum91211885435.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/1pum91211885435.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/2b5q31211885435.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/2b5q31211885435.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/35upt1211885435.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211885503tqqyx73r31a7tu0/35upt1211885435.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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