tijdreeks A-Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 17:07:59 +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/Aug/19/t1282237697ezl2ws6j50ei0vq.htm/, Retrieved Thu, 19 Aug 2010 19:08:17 +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/Aug/19/t1282237697ezl2ws6j50ei0vq.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:

gilian keirsebelik

Dataseries X:

» Textbox « » Textfile « » CSV «

668 667 666 664 684 683 668 658 659 659 660 662 659 655 655 655 674 674 665 644 638 648 641 637 651 649 652 650 661 666 652 624 613 623 615 613 621 612 611 609 631 632 624 596 584 587 581 574 593 582 571 572 594 588 571 546 535 537 527 515 545 538 520 523 541 529 504 473 455 458 450 442 469 455 439 443 461 451 425 393 366 359 351 343 366 355 344 351 367 364 353 313 278 274 261 255 274 262 265 274 291 289 277 238 203 198 190 187 201 181 181 196 207 202 186 154 120 107 99 100

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.410159378916772 beta 0.0621038460609066 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 659 663.780715811966 -4.78071581196593 14 655 657.445024279532 -2.44502427953159 15 655 656.755057715721 -1.75505771572114 16 655 656.178381745534 -1.17838174553435 17 674 674.724885200313 -0.724885200312883 18 674 675.022263229662 -1.02226322966226 19 665 656.004962630036 8.9950373699644 20 644 649.533811019997 -5.53381101999696 21 638 648.045889448822 -10.0458894488220 22 648 643.326402924535 4.67359707546484 23 641 645.721633268688 -4.72163326868827 24 637 645.143050085044 -8.14305008504437 25 651 634.842190015435 16.1578099845648 26 649 638.32601449009 10.6739855099097 27 652 643.611774314797 8.38822568520277 28 650 647.981853783806 2.01814621619417 29 661 668.63460303119 -7.63460303119052 30 666 666.274151416039 -0.274151416038649 31 652 653.843024530955 -1.84302453095540 32 624 634.451480795414 -10.4514807954143 33 613 628.25450405094 -15.2545040509395 34 623 629.917510515415 -6.91751051541473 35 615 621.558300715687 -6.55830071568744 36 613 617.702965915233 -4.70296591523311 37 621 622.72901586869 -1.72901586868954 38 612 614.768479643678 -2.76847964367835 39 611 611.976710575761 -0.976710575761217 40 609 607.294052130446 1.70594786955371 41 631 620.662924378497 10.3370756215032 42 632 629.010759495528 2.98924050447249 43 624 616.071425815865 7.92857418413473 44 596 594.937752048662 1.06224795133801 45 584 590.251078380621 -6.25107838062115 46 587 600.374618770544 -13.3746187705436 47 581 589.26456046195 -8.26456046194949 48 574 585.445994867391 -11.4459948673914 49 593 588.930978973086 4.06902102691436 50 582 582.353628527687 -0.353628527687079 51 571 581.288888234256 -10.2888882342560 52 572 573.811586256488 -1.81158625648811 53 594 590.181590894884 3.81840910511585 54 588 590.708527852677 -2.70852785267698 55 571 577.387330105693 -6.38733010569263 56 546 545.008863701434 0.991136298566403 57 535 534.654562491243 0.345437508756618 58 537 542.125238354085 -5.12523835408547 59 527 536.466258996523 -9.46625899652327 60 515 529.3010542324 -14.3010542324005 61 545 539.716458145953 5.2835418540468 62 538 530.00959587246 7.9904041275397 63 520 525.700561661114 -5.70056166111408 64 523 524.415880544631 -1.41588054463057 65 541 543.589485776745 -2.58948577674505 66 529 536.795585282875 -7.79558528287532 67 504 518.245669553395 -14.2456695533951 68 473 485.823672713266 -12.8236727132661 69 455 467.897863252303 -12.8978632523032 70 458 464.848133213476 -6.84813321347644 71 450 454.016380624446 -4.01638062444562 72 442 444.467956419912 -2.46795641991201 73 469 469.823245445614 -0.823245445613793 74 455 457.587328167737 -2.58732816773681 75 439 438.973892820147 0.0261071798527723 76 443 440.820852774447 2.17914722555275 77 461 459.123841744516 1.87615825548397 78 451 449.551638492467 1.44836150753252 79 425 429.684999153194 -4.6849991531945 80 393 400.962993010947 -7.96299301094672 81 366 384.050730431177 -18.050730431177 82 359 381.388277941086 -22.3882779410861 83 351 364.389423828184 -13.3894238281839 84 343 350.207678811148 -7.20767881114836 85 366 372.766108399427 -6.76610839942651 86 355 355.077827879593 -0.0778278795927463 87 344 337.124806507962 6.87519349203808 88 351 341.315005675159 9.6849943248414 89 367 360.973137276655 6.02686272334518 90 364 351.412045456422 12.5879545435781 91 353 331.341455385795 21.6585446142055 92 313 311.006788087881 1.99321191211931 93 278 291.997389437932 -13.9973894379323 94 274 288.311630089255 -14.3116300892552 95 261 280.011749786204 -19.0117497862039 96 255 267.105356053602 -12.1053560536021 97 274 287.725814278332 -13.7258142783319 98 262 270.761084446498 -8.76108444649827 99 265 252.759654156396 12.2403458436038 100 274 260.356355014748 13.6436449852524 101 291 279.129885792836 11.8701142071636 102 289 275.633735019415 13.3662649805847 103 277 261.050682421303 15.9493175786973 104 238 226.447585577297 11.5524144227035 105 203 201.843249330203 1.15675066979736 106 198 204.489936299126 -6.48993629912613 107 190 197.127298964809 -7.12729896480883 108 187 193.973245567061 -6.97324556706093 109 201 216.677752309969 -15.6777523099687 110 181 202.725972776541 -21.7259727765409 111 181 192.349277495900 -11.3492774958997 112 196 191.052218713309 4.94778128669063 113 207 204.945476551542 2.05452344845781 114 202 197.788349890296 4.21165010970421 115 186 180.223335013539 5.7766649864605 116 154 137.844534096135 16.1554659038653 117 120 108.103825818682 11.8961741813175 118 107 110.026049167775 -3.02604916777503 119 99 103.177436709157 -4.17743670915672 120 100 100.868525698083 -0.868525698082635 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 120.642532975459 103.13276033637 138.152305614547 122 109.652859716508 90.5537577689906 128.751961664026 123 114.960501862893 94.224965754181 135.696037971606 124 128.872846687314 106.455213266732 151.290480107895 125 139.845856114932 115.701766789424 163.989945440441 126 133.881766013898 107.968051420728 159.795480607068 127 116.168489231190 88.4430710211985 143.893907441181 128 78.0511039562588 48.4729102177818 107.629297694736 129 39.2691874286761 7.79807914636272 70.7402957109895 130 27.3047357634337 -6.0985576781182 60.7080292049856 131 20.8896174586161 -14.4843203525997 56.2635552698318 132 22.2237279204456 -15.1585527733534 59.6060086142446

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/12anu1282237674.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/12anu1282237674.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/2v1nf1282237674.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/2v1nf1282237674.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/3v1nf1282237674.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282237697ezl2ws6j50ei0vq/3v1nf1282237674.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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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