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: Tue, 03 Aug 2010 16:11:26 +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/03/t1280852115u744kx1qt87wzyk.htm/, Retrieved Tue, 03 Aug 2010 18:15:15 +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/03/t1280852115u744kx1qt87wzyk.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:

Lisa Bruggeman

Dataseries X:

» Textbox « » Textfile « » CSV «

95 94 93 91 111 110 95 85 86 86 87 89 93 96 99 92 109 110 97 88 93 93 89 89 91 97 99 85 101 105 88 80 87 84 87 87 85 96 102 93 111 117 101 88 98 89 93 93 95 105 109 94 113 125 106 95 109 100 94 94 94 103 103 80 106 117 99 95 116 118 100 100 105 121 131 108 136 149 131 137 164 169 154 160 166 186 197 166 191 207 187 191 222 230 210 224 234 251 258 227 254 281 261 264 286 293 276 292 299 319 329 293 318 346 327 329 353 355 332 346

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 0.222642629632828 beta 0.178363459675705 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 93 93 0 4 91 92 -1 5 111 90.7376460606746 20.2623539393254 6 110 95.0138431269703 14.9861568730297 7 95 98.7104537206517 -3.71045372065174 8 85 98.0970547897341 -13.0970547897341 9 86 94.8736971146655 -8.87369711466548 10 86 92.2382527640152 -6.23825276401523 11 87 89.9418414863921 -2.94184148639215 12 89 88.2625275056377 0.737472494362294 13 93 87.4316716634167 5.56832833658333 14 96 87.897495880329 8.10250411967098 15 99 89.2492967079217 9.75070329207828 16 92 91.3552701315703 0.644729868429721 17 109 91.4594687542844 17.5405312457156 18 110 96.0219504938628 13.9780495061372 19 97 100.346358583759 -3.34635858375943 20 88 100.680726617627 -12.6807266176270 21 93 98.4332981446338 -5.43329814463382 22 93 97.5836928196699 -4.58369281966986 23 89 96.7412214133082 -7.74122141330822 24 89 94.8883354967752 -5.88833549677517 25 91 93.2141474586223 -2.21414745862225 26 97 92.2700636116147 4.72993638838527 27 99 93.0598608214413 5.9401391785587 28 85 94.354991469398 -9.35499146939802 29 101 91.873275045903 9.12672495409697 30 105 93.8688107681946 11.1311892318054 31 88 96.7526597911115 -8.75265979111145 32 80 94.8619367967451 -14.8619367967451 33 87 91.0208413299216 -4.02084132992162 34 84 89.4337629906549 -5.43376299065487 35 87 87.3163262124592 -0.316326212459174 36 87 86.3256872873539 0.674312712646142 37 85 85.5823846585122 -0.582384658512183 38 96 84.5361603647688 11.4638396352312 39 102 86.6271832109523 15.3728167890477 40 93 90.1989856981938 2.80101430180625 41 111 91.0830009668437 19.9169990331563 42 117 96.5686942015898 20.4313057984102 43 101 102.980247958975 -1.98024795897503 44 88 104.323396213692 -16.3233962136915 45 98 101.824924781487 -3.82492478148735 46 89 101.957253122791 -12.9572531227913 47 93 99.5417863759923 -6.54178637599232 48 93 98.2948931113027 -5.29489311130268 49 95 97.1153443018028 -2.11534430180281 50 105 96.5596955076205 8.44030449237947 51 109 98.6893596640524 10.3106403359476 52 94 101.644889342503 -7.6448893425027 53 113 100.299164108647 12.7008358913533 54 125 103.987631470080 21.0123685299201 55 106 110.361028988510 -4.36102898850956 56 95 110.912044387976 -15.9120443879758 57 109 108.259423221442 0.740576778557809 58 100 109.343794695509 -9.34379469550936 59 94 107.811900861538 -13.8119008615384 60 94 104.736727448728 -10.7367274487280 61 94 101.919849222321 -7.91984922232103 62 103 99.4156205864104 3.58437941358956 63 103 99.6150640668451 3.38493593315488 64 80 99.9045231654639 -19.9045231654639 65 106 94.2183211639325 11.7816788360675 66 117 96.054684396057 20.945315603943 67 99 100.763029729739 -1.76302972973896 68 95 100.345517124125 -5.34551712412465 69 116 98.9181126184146 17.0818873815854 70 118 103.162348547639 14.8376514523606 71 100 107.496144460001 -7.49614446000074 72 100 106.559803606599 -6.55980360659943 73 105 105.571433750488 -0.571433750487699 74 121 105.893637923720 15.1063620762798 75 131 110.306281209411 20.6937187905894 76 108 116.784682962256 -8.78468296225641 77 136 116.35108456581 19.6489154341899 78 149 123.028301452203 25.9716985477967 79 131 132.144609561883 -1.14460956188259 80 137 135.1782175833 1.82178241670010 81 164 138.944616281093 25.0553837189073 82 169 148.878787170978 20.1212128290218 83 154 158.513440992926 -4.51344099292609 84 160 162.484136054812 -2.48413605481167 85 166 166.807992608255 -0.807992608254693 86 186 171.472943701585 14.5270562984147 87 197 180.129018840633 16.8709811593669 88 166 189.976920332023 -23.9769203320228 89 191 189.778182711607 1.22181728839314 90 207 195.238278263155 11.7617217368449 91 187 203.512079231596 -16.5120792315956 92 191 204.835210510672 -13.8352105106725 93 222 206.204912551706 15.7950874482942 94 230 214.798825656409 15.2011743435912 95 210 223.864166927757 -13.8641669277569 96 224 225.907759960778 -1.90775996077838 97 234 230.537599235267 3.46240076473342 98 251 236.500561684282 14.4994383157181 99 258 245.496630882329 12.5033691176709 100 227 254.544815148427 -27.5448151484268 101 254 253.582725672716 0.417274327284417 102 281 258.862759837943 22.1372401620573 103 261 269.857683111974 -8.85768311197404 104 264 273.600064965789 -9.60006496578859 105 286 276.795929818553 9.20407018144738 106 293 284.543902449876 8.45609755012367 107 276 292.461147196273 -16.4611471962726 108 292 294.177057334920 -2.17705733491965 109 299 298.986761004164 0.0132389958356498 110 319 304.284643746027 14.7153562539728 111 329 313.440210604850 15.5597893951496 112 293 323.401683894197 -30.401683894197 113 318 321.922883224305 -3.92288322430511 114 346 326.183609534473 19.8163904655268 115 327 336.516644983285 -9.516644983285 116 329 339.940977848495 -10.9409778484946 117 353 342.61371293944 10.3862870605601 118 355 350.447259434631 4.55274056536859 119 332 357.162805088589 -25.1628050885895 120 346 356.263155571568 -10.2631555715683 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 358.273239854298 334.134989736376 382.411489972221 122 362.568340081813 337.613199701773 387.523480461853 123 366.863440309328 340.864931236798 392.861949381857 124 371.158540536842 343.882486442201 398.434594631484 125 375.453640764357 346.665124464909 404.242157063805 126 379.748740991872 349.2176619798 410.279820003944 127 384.043841219386 351.548839263316 416.538843175457 128 388.338941446901 353.669769974652 423.00811291915 129 392.634041674416 355.59266803114 429.675415317691 130 396.929141901931 357.329917604624 436.528366199237 131 401.224242129445 358.893464417798 443.555019841092 132 405.51934235696 360.294464557766 450.744220156153

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/1f38x1280851881.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/1f38x1280851881.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/2f38x1280851881.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/2f38x1280851881.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/3qdpi1280851881.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280852115u744kx1qt87wzyk/3qdpi1280851881.ps (open in new window)

Parameters (Session):

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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