tijdreeks 1 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: Mon, 16 Aug 2010 12:21:29 +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/16/t12819612633xjg3ggggkk2809.htm/, Retrieved Mon, 16 Aug 2010 14:21:07 +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/16/t12819612633xjg3ggggkk2809.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:

Magali De Reu

Dataseries X:

» Textbox « » Textfile « » CSV «

333 332 331 329 349 348 333 323 324 324 325 327 329 333 329 333 355 358 338 326 320 322 322 324 326 330 331 333 364 363 341 327 313 321 312 312 312 314 312 319 356 351 329 313 298 303 278 275 276 276 273 287 320 313 281 266 258 259 237 231 237 236 229 243 271 262 227 208 212 222 200 193 204 203 190 209 240 234 210 195 202 204 180 169 178 181 163 174 194 187 160 143 151 154 141 127 134 138 120 129 151 152 124 99 104 109 96 87 94 89 63 76 100 104 80 55 60 71 62 61

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 0.999950136832542 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 332 333 -1 3 331 332.000049863167 -1.00004986316748 4 329 331.000049865654 -2.00004986565381 5 349 329.000099728821 19.9999002711786 6 348 348.999002741624 -0.999002741623599 7 333 348.000049813441 -15.0000498134410 8 323 333.000747949996 -10.0007479499957 9 324 323.00049866897 0.999501331030274 10 324 323.999950161698 4.98383022318194e-05 11 325 323.999999997515 1.00000000248508 12 327 324.999950136832 2.00004986316759 13 329 326.999900271179 2.00009972882128 14 333 328.999900268692 4.00009973130773 15 329 332.999800542357 -3.99980054235721 16 333 329.000199442724 3.99980055727576 17 355 332.999800557275 22.0001994427250 18 358 354.998903000371 3.00109699962894 19 338 357.999850355798 -19.9998503557977 20 326 338.000997255887 -12.0009972558875 21 320 326.000598407736 -6.00059840773582 22 322 320.000299208843 1.99970079115678 23 322 321.999900288585 9.97114154301926e-05 24 324 321.999999995028 2.00000000497192 25 326 323.999900273665 2.00009972633512 26 330 325.999900268692 4.00009973130761 27 331 329.999800542357 1.00019945764279 28 333 330.999950126887 2.00004987311303 29 364 332.999900271178 31.0000997288218 30 363 363.998454236836 -0.998454236835983 31 341 363.000049786091 -22.0000497860908 32 327 341.001096992167 -14.0010969921666 33 313 327.000698139044 -14.0006981390439 34 321 313.000698119156 7.99930188084414 35 312 320.999601129471 -8.99960112947082 36 312 312.000448748618 -0.000448748618168793 37 312 312.000000022376 -2.23760707740439e-08 38 314 312.000000000001 1.99999999999886 39 312 313.999900273665 -1.99990027366505 40 319 312.000099721362 6.99990027863777 41 356 318.9996509628 37.0003490371998 42 351 355.9981550454 -4.99815504539998 43 329 351.000249223842 -22.000249223842 44 313 329.001097002111 -16.0010970021112 45 298 313.000797865379 -15.0007978653793 46 303 298.000747987296 4.99925201270406 47 278 302.99975072146 -24.9997507214597 48 275 278.001246566757 -3.00124656675661 49 276 275.00014965166 0.999850348339862 50 276 275.999950144295 4.98557053560944e-05 51 273 275.999999997514 -2.99999999751401 52 287 273.000149589502 13.9998504104978 53 320 286.999301923115 33.0006980768854 54 313 319.998354480666 -6.99835448066557 55 281 313.000348960121 -32.0003489601214 56 266 281.001595638759 -15.0015956387589 57 258 266.000748027075 -8.00074802707547 58 259 258.000398942639 0.999601057361303 59 237 258.999950156725 -21.9999501567251 60 231 237.001096987199 -6.00109698719874 61 237 231.000299233704 5.999700766296 62 236 236.999700835916 -0.999700835916002 63 229 236.00004984825 -7.00004984825017 64 243 229.000349044658 13.9996509553422 65 271 242.99930193306 28.0006980669399 66 262 270.998603796503 -8.99860379650335 67 227 262.000448698888 -35.000448698888 68 208 227.001745233235 -19.0017452332346 69 212 208.000947487205 3.99905251279543 70 222 211.999800594575 10.0001994054251 71 200 221.999501358382 -21.9995013583824 72 193 200.001096964820 -7.00109696482025 73 204 193.000349096870 10.9996509031297 74 203 203.999451522565 -0.99945152256504 75 190 203.000049835819 -13.0000498358186 76 209 190.000648223662 18.9993517763381 77 240 208.999052632141 31.0009473678592 78 234 239.99845419457 -5.99845419457006 79 210 234.000299101926 -24.000299101926 80 195 210.001196730933 -15.0011967309332 81 202 195.000748007185 6.99925199281535 82 204 201.999650995126 2.00034900487418 83 180 203.999900256263 -23.9999002562626 84 169 180.001196711045 -11.0011967110455 85 178 169.000548554514 8.99945144548616 86 181 177.999551258846 3.00044874115446 87 163 180.999850388122 -17.999850388122 88 174 163.000897529554 10.9991024704459 89 194 173.999451549912 20.0005484500884 90 187 193.999002709303 -6.9990027093034 91 160 187.000348992444 -27.0003489924441 92 143 160.001346322923 -17.0013463229232 93 151 143.000847740979 7.99915225902132 94 154 150.999601136931 3.00039886306860 95 141 153.999850390609 -12.9998503906090 96 127 141.000648213717 -14.0006482137169 97 134 127.000698116666 6.9993018833336 98 138 133.999650992638 4.00034900736190 99 120 137.999800529928 -17.9998005299275 100 129 120.000897527068 8.99910247293197 101 151 128.999551276246 22.0004487237536 102 152 150.998902987941 1.00109701205884 103 124 151.999950082132 -27.9999500821320 104 99 124.001396166200 -25.0013961661998 105 104 99.0012466488037 4.99875335119629 106 109 103.999750746325 5.00024925367542 107 96 108.999750671734 -12.9997506717341 108 87 96.0006482087447 -9.00064820874466 109 94 87.0004488008289 6.99955119917114 110 89 93.9996509802064 -4.99965098020643 111 63 89.000249298434 -26.0002492984341 112 76 63.0012964547847 12.9987035452153 113 100 75.9993518434684 24.0006481565316 114 104 99.9988032516619 4.00119674833812 115 80 103.999800487657 -23.9998004876565 116 55 80.0011967060707 -25.0011967060707 117 60 55.001246638858 4.998753361142 118 71 59.9997507463241 11.0002492536759 119 62 70.9994514927294 -8.9994514927294 120 61 62.0004487411568 -1.00044874115681 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 61.0000498855431 32.9685201719337 89.0315795991525 122 61.0000498855431 21.358468730212 100.641631040874 123 61.0000498855431 12.4496301664054 109.550469604681 124 61.0000498855431 4.93908705654619 117.06101271454 125 61.0000498855431 -1.67785572499808 123.677955496084 126 61.0000498855431 -7.66004150773751 129.660141278824 127 61.0000498855431 -13.1612368383493 135.161336609436 128 61.0000498855431 -18.2816298831974 140.281729654284 129 61.0000498855431 -23.0908119566503 145.090911727737 130 61.0000498855431 -27.6394522778411 149.639552048927 131 61.0000498855431 -31.9658021364888 153.965901907575 132 61.0000498855431 -36.0995790560345 158.099678827121

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/1tyya1281961286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/1tyya1281961286.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/2tyya1281961286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/2tyya1281961286.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/3m8fv1281961286.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819612633xjg3ggggkk2809/3m8fv1281961286.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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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