Tijdsreeks 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 20:45:19 +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/t12822507590s3cwrgfwvxl1pa.htm/, Retrieved Thu, 19 Aug 2010 22:46:03 +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/t12822507590s3cwrgfwvxl1pa.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:

Van Boxel Dieter

Dataseries X:

» Textbox « » Textfile « » CSV «

356 355 354 352 372 371 356 346 347 347 348 350 353 350 343 346 373 363 349 350 353 356 355 346 349 348 342 342 379 375 363 361 363 373 367 360 358 367 357 346 386 383 367 354 363 370 361 354 363 366 353 351 389 385 364 348 347 352 342 338 343 354 329 320 353 345 324 310 314 313 310 301 294 296 274 269 292 287 271 256 260 265 263 256 246 245 220 224 240 238 222 203 209 214 216 214 206 196 169 177 193 183 164 142 141 137 140 146 136 124 105 114 135 123 100 74 64 57 62 64

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.658681111002325 beta 0.0625489335806356 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 353 355.748664529915 -2.74866452991461 14 350 350.827694757025 -0.82769475702463 15 343 342.596263962347 0.403736037653118 16 346 344.98425388273 1.01574611727017 17 373 371.775545153595 1.22445484640519 18 363 362.296422884791 0.703577115208532 19 349 354.503195530486 -5.50319553048615 20 350 340.853287046443 9.1467129535572 21 353 348.563172646151 4.43682735384903 22 356 352.395208637345 3.60479136265491 23 355 356.327714924480 -1.32771492448035 24 346 358.039904232956 -12.0399042329558 25 349 352.595297336999 -3.59529733699878 26 348 347.658702350461 0.341297649539058 27 342 340.552110173856 1.44788982614432 28 342 343.814308810741 -1.81430881074141 29 379 368.673688627559 10.3263113724408 30 375 365.247952635750 9.75204736425047 31 363 361.905038865206 1.09496113479446 32 361 358.48209066464 2.51790933536017 33 363 360.825618854876 2.17438114512356 34 373 363.397705572466 9.60229442753405 35 367 370.358463117726 -3.35846311772599 36 360 367.754464817046 -7.75446481704563 37 358 368.869159432285 -10.8691594322851 38 367 361.039621107342 5.96037889265807 39 357 358.797995448988 -1.79799544898844 40 346 359.461093954553 -13.4610939545531 41 386 380.965287357280 5.03471264272036 42 383 373.812563238337 9.18743676166332 43 367 367.074157386902 -0.0741573869016179 44 354 363.249877859877 -9.24987785987696 45 363 357.123169616077 5.87683038392254 46 370 364.220052362909 5.7799476370912 47 361 363.632646526404 -2.63264652640419 48 354 359.429490602323 -5.42949060232343 49 363 360.531485299738 2.46851470026229 50 366 367.299957423934 -1.29995742393447 51 353 357.397378361618 -4.39737836161828 52 351 352.029755257315 -1.02975525731483 53 389 388.209652123687 0.790347876313376 54 385 379.67822862389 5.32177137611029 55 364 367.07274066793 -3.07274066792979 56 348 357.858278913217 -9.8582789132165 57 347 356.185568294151 -9.18556829415104 58 352 352.399206459288 -0.399206459287768 59 342 343.686892149996 -1.68689214999563 60 338 338.007596854715 -0.00759685471535931 61 343 344.455535686608 -1.45553568660756 62 354 346.270295870293 7.7297041297071 63 329 340.547432945162 -11.5474329451620 64 320 330.614313400402 -10.6143134004017 65 353 359.702072631114 -6.70207263111399 66 345 346.073301658595 -1.07330165859537 67 324 324.417926586511 -0.417926586511101 68 310 312.773118377198 -2.7731183771981 69 314 314.425795249205 -0.425795249205464 70 313 318.198099858792 -5.19809985879226 71 310 304.477438354091 5.52256164590949 72 301 303.009182051353 -2.00918205135287 73 294 306.45117348886 -12.4511734888599 74 296 302.512060348188 -6.51206034818756 75 274 278.595657051527 -4.5956570515267 76 269 271.61333597285 -2.61333597284994 77 292 305.68945192654 -13.6894519265402 78 287 287.474495763584 -0.474495763584343 79 271 264.556969111037 6.44303088896265 80 256 255.029877027782 0.970122972217894 81 260 258.505967270611 1.49403272938935 82 265 260.549670407435 4.45032959256486 83 263 255.876646589917 7.1233534100827 84 256 251.991262678782 4.00873732121761 85 246 255.180219583985 -9.18021958398452 86 245 254.904640710207 -9.90464071020656 87 220 228.749827035597 -8.74982703559684 88 224 218.878798887788 5.12120111221154 89 240 253.758644722309 -13.7586447223085 90 238 239.495399990311 -1.49539999031083 91 222 217.711217730945 4.28878226905451 92 203 204.253113520854 -1.25311352085350 93 209 205.707980872657 3.29201912734322 94 214 209.283461026448 4.71653897355239 95 216 205.047542970864 10.9524570291362 96 214 202.128403441365 11.871596558635 97 206 205.82594878197 0.174051218029859 98 196 211.681098570010 -15.6810985700105 99 169 182.094117811691 -13.0941178116913 100 177 173.895564266526 3.10443573347391 101 193 200.719399464561 -7.71939946456064 102 183 194.585026907671 -11.5850269076714 103 164 167.6788163532 -3.67881635320 104 142 146.302355948336 -4.30235594833587 105 141 146.395760586422 -5.39576058642174 106 137 143.472721131887 -6.47272113188671 107 140 132.271831385403 7.7281686145974 108 146 125.686539586649 20.3134604133506 109 136 129.443697044552 6.55630295544839 110 124 132.845709923259 -8.84570992325857 111 105 107.680329139749 -2.68032913974920 112 114 111.335332996309 2.66466700369078 113 135 133.6223222603 1.37767773969989 114 123 131.982609556056 -8.98260955605616 115 100 109.418318830872 -9.41831883087198 116 74 83.741282029476 -9.741282029476 117 64 79.3476377788613 -15.3476377788613 118 57 68.5605511026289 -11.5605511026289 119 62 57.7044714676871 4.29552853231285 120 64 51.8613739100283 12.1386260899717 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 43.9091547761073 30.1163524637596 57.7019570884551 122 35.8363485003482 19.0010295385318 52.6716674621646 123 17.0669638494532 -2.62843301416942 36.7623607130758 124 22.8873602278348 0.430082670032359 45.3446377856372 125 41.445688374019 16.2795250173210 66.6118517307169 126 33.7713820176706 5.92225480600992 61.6205092293313 127 15.7541508572672 -14.7694380674662 46.2777397820005 128 -4.66231768248794 -37.8636490074922 28.5390136425163 129 -4.98464670685161 -40.8752651139402 30.905971700237 130 -4.16913856730358 -42.7665424306451 34.4282652960379 131 -1.32143817223447 -42.6475017189214 40.0046253744524 132 -6.81681291113506 -50.8966740717622 37.2630482494921

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/1th1g1282250717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/1th1g1282250717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/2th1g1282250717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/2th1g1282250717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/3mrij1282250717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507590s3cwrgfwvxl1pa/3mrij1282250717.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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