Opgave 10 oef 1 willem dierickx

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 13:30:07 -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/Jun/01/t1212348671ngajh0z1j5c3y7w.htm/, Retrieved Sun, 01 Jun 2008 19:31:15 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.274854973274752 beta 0.0174528263411903 gamma 0.87662614165094 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 115 107.371084989080 7.62891501092015 14 126 120.178100844322 5.82189915567754 15 141 136.542725454413 4.45727454558738 16 135 132.481583629579 2.51841637042088 17 125 124.285661006030 0.714338993970415 18 149 149.172962641139 -0.172962641138525 19 170 170.015932902319 -0.0159329023193209 20 170 169.789341636774 0.210658363226145 21 158 157.342395202648 0.657604797352178 22 133 132.031002084669 0.968997915330988 23 114 112.617969885674 1.38203011432574 24 140 137.811799692617 2.18820030738303 25 145 141.869270296047 3.13072970395265 26 150 154.230670503883 -4.23067050388335 27 178 169.578736890564 8.42126310943615 28 163 163.535279134548 -0.53527913454775 29 172 150.880280045629 21.1197199543707 30 178 186.563274816568 -8.56327481656808 31 199 209.729942557624 -10.7299425576245 32 199 206.262536204416 -7.26253620441608 33 184 189.192943072255 -5.19294307225505 34 162 157.373126462438 4.62687353756198 35 146 135.202159118603 10.7978408813968 36 166 168.589898544461 -2.58989854446054 37 171 172.425057807298 -1.4250578072984 38 180 179.798110195103 0.201889804897291 39 193 208.778128013111 -15.7781280131105 40 181 187.887029385977 -6.88702938597666 41 183 186.514735444686 -3.51473544468621 42 218 197.083571560435 20.9164284395648 43 230 229.718791673841 0.281208326158975 44 242 231.307868523757 10.6921314762426 45 209 217.760016067638 -8.760016067638 46 191 186.859841715794 4.14015828420614 47 172 164.881790829373 7.11820917062684 48 194 191.760520633402 2.23947936659772 49 196 198.225633501461 -2.22563350146129 50 196 207.499397891270 -11.4993978912703 51 236 225.085803036303 10.9141969636969 52 235 214.993585475695 20.0064145243045 53 229 223.514682064813 5.48531793518654 54 243 257.580294276997 -14.580294276997 55 264 269.438427422852 -5.43842742285165 56 272 277.013533669516 -5.01353366951633 57 237 242.283067701004 -5.28306770100352 58 211 217.26966644941 -6.2696664494101 59 180 191.255685703346 -11.2556857033463 60 201 211.817969221856 -10.8179692218559 61 204 211.761924088343 -7.76192408834271 62 188 213.438092509385 -25.438092509385 63 235 242.602402461502 -7.60240246150227 64 227 232.273607722294 -5.27360772229409 65 234 224.192995903838 9.80700409616168 66 264 245.921776059523 18.0782239404773 67 302 272.687295813742 29.3127041862583 68 293 290.264489889345 2.73551011065513 69 259 254.877026675448 4.12297332455199 70 229 229.645523391416 -0.645523391416248 71 203 199.350846341409 3.64915365859133 72 229 226.549285493568 2.45071450643229 73 242 232.477640270737 9.52235972926283 74 233 225.829212707355 7.17078729264486 75 267 284.583524923987 -17.5835249239866 76 269 271.656501420331 -2.65650142033064 77 270 274.320820653381 -4.32082065338085 78 315 301.240966124434 13.7590338755660 79 364 337.925346125484 26.0746538745155 80 347 336.450473308564 10.5495266914356 81 312 298.365793573789 13.6342064262112 82 274 267.705069940284 6.29493005971631 83 237 237.161751900662 -0.161751900661926 84 278 266.805564118881 11.1944358811188 85 284 281.262372712095 2.73762728790541 86 277 269.324012372139 7.67598762786082 87 317 319.086032989223 -2.08603298922259 88 313 320.134667969163 -7.1346679691627 89 318 320.883864334419 -2.8838643344194 90 374 366.808235997134 7.1917640028663 91 413 416.186680240357 -3.18668024035730 92 405 393.841002336437 11.1589976635631 93 355 351.895368484845 3.10463151515455 94 306 308.227400182515 -2.22740018251483 95 271 266.548321197281 4.45167880271862 96 306 309.229239358864 -3.22923935886399 97 315 314.829579615657 0.170420384342776 98 301 304.046984776360 -3.04698477636032 99 356 348.440752227457 7.55924777254279 100 348 348.516511754091 -0.5165117540908 101 355 354.183314443022 0.81668555697837 102 422 413.321177120566 8.67882287943371 103 465 460.901371478958 4.09862852104231 104 467 447.956278613358 19.0437213866424 105 404 396.788042935545 7.21195706445536 106 347 344.778789964379 2.22121003562074 107 305 303.740976896175 1.25902310382537 108 336 345.057657654639 -9.05765765463929 109 340 352.101440452606 -12.1014404526057 110 318 334.349057334057 -16.3490573340572 111 362 386.496757849826 -24.4967578498258 112 348 371.824983369092 -23.8249833690921 113 363 371.88300074848 -8.88300074847996 114 435 435.460725333532 -0.460725333531684 115 491 478.485397302471 12.5146026975285 116 505 476.532772464755 28.4672275352454 117 404 417.38054896059 -13.3805489605897 118 359 354.672832099537 4.3271679004626 119 310 312.158635349119 -2.15863534911881 120 337 346.306881338648 -9.30688133864777 121 360 351.043415799218 8.95658420078223 122 342 335.3044472583 6.69555274170017 123 406 390.89400421288 15.1059957871199 124 396 386.459019026098 9.5409809739022 125 420 406.896340795887 13.1036592041131 126 472 491.070479548327 -19.0704795483272 127 548 543.142014933589 4.85798506641106 128 559 549.377711199274 9.62228880072553 129 463 449.029752197355 13.9702478026455 130 407 399.45541788503 7.5445821149699 131 362 347.975060661832 14.0249393381676 132 405 386.08532467554 18.9146753244597 133 417 413.28687274385 3.7131272561499 134 391 391.752860004379 -0.752860004379386 135 419 459.317214052471 -40.3172140524709 136 461 434.693358199415 26.3066418005853 137 472 464.279874552552 7.72012544744837 138 535 533.158503024146 1.84149697585428 139 622 615.387134392081 6.61286560791859 140 606 626.140064584157 -20.1400645841572 141 508 509.020761738341 -1.02076173834143 142 461 445.270715734584 15.7292842654155 143 390 394.727036901138 -4.72703690113809 144 432 433.867514911904 -1.86751491190398 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 145 446.397513472092 426.688822667634 466.10620427655 146 418.986547994825 398.484502103232 439.488593886419 147 463.749707173368 442.006591734538 485.492822612197 148 494.965042338409 471.988876595052 517.941208081766 149 506.122949107584 482.136276962898 530.109621252269 150 573.550385932582 547.468799011193 599.631972853971 151 664.139122101699 635.212683081081 693.065561122317 152 655.087901982859 625.606479534423 684.569324431296 153 547.726606144639 520.214971584962 575.238240704316 154 490.510674033967 463.69427880187 517.327069266064 155 417.874494194049 392.190619526104 443.558368861994 156 462.91197975764 442.309981214744 483.513978300535

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/1ssw21212348599.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/1ssw21212348599.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/24e1r1212348600.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/24e1r1212348600.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/3vcdt1212348600.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212348671ngajh0z1j5c3y7w/3vcdt1212348600.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

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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