Tijdreeks B - Stap 27

*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 20:46:50 +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/t1282250779pa2mtv2cq1hsyh3.htm/, Retrieved Thu, 19 Aug 2010 22:46:19 +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/t1282250779pa2mtv2cq1hsyh3.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:

Gregory Goris

Dataseries X:

» Textbox « » Textfile « » CSV «

225 224 223 221 219 218 219 221 222 222 223 225 226 229 235 229 231 229 226 232 234 230 232 231 237 241 256 255 264 259 253 258 265 258 257 255 255 255 275 276 278 268 253 257 255 253 245 248 246 243 260 262 262 251 236 238 239 243 233 238 232 224 238 236 231 209 179 179 165 174 163 166 164 152 163 167 157 138 111 110 91 100 88 89

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999924474600477 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 224 225 -1 3 223 224.000075525400 -1.00007552539952 4 221 223.000075531104 -2.00007553110362 5 219 221.000151056504 -2.00015105650357 6 218 219.000151062208 -1.00015106220764 7 219 218.000075536809 0.999924463191434 8 221 218.999924480305 2.00007551969458 9 222 220.999848943497 1.00015105650269 10 222 221.999924463192 7.55368081399865e-05 11 223 221.999999994295 1.00000000570495 12 225 222.9999244746 2.00007552539995 13 226 224.999848943497 1.00015105650314 14 229 225.999924463192 3.00007553680814 15 235 228.999773418096 6.00022658190352 16 229 234.99954683049 -5.99954683049017 17 231 229.000453118171 1.99954688182868 18 229 230.999848983423 -1.99984898342288 19 226 229.000151039393 -3.00015103939347 20 232 226.000226587606 5.99977341239412 21 234 231.999546864716 2.00045313528403 22 230 233.999848914978 -3.99984891497772 23 232 230.000302090187 1.99969790981265 24 231 231.999848972016 -0.999848972016423 25 237 231.000075513993 5.99992448600693 26 241 236.999546853306 4.00045314669393 27 256 240.999697864178 15.0003021358222 28 255 255.998867096188 -0.998867096188235 29 264 255.000075439837 8.9999245601635 30 259 263.999320277102 -4.9993202771019 31 253 259.000377575661 -6.00037757566128 32 258 253.000453180914 4.99954681908631 33 265 257.999622407229 7.00037759277097 34 258 264.999471293685 -6.99947129368547 35 257 258.000528637866 -1.00052863786590 36 255 257.000075565325 -2.00007556532512 37 255 255.000151056506 -0.000151056506155101 38 255 255.000000011409 -1.14086162739113e-08 39 275 255.000000000001 19.9999999999991 40 276 274.998489492010 1.00151050799047 41 278 275.999924360519 2.00007563948122 42 268 277.999848943488 -9.99984894348825 43 253 268.000755242587 -15.0007552425866 44 257 253.001132938033 3.99886706196716 45 255 256.999697983968 -1.99969798396751 46 253 255.000151027989 -2.00015102798918 47 245 253.000151062206 -8.0001510622055 48 248 245.000604214605 2.99939578539477 49 246 247.999773469435 -1.99977346943498 50 243 246.00015103369 -3.00015103369023 51 260 243.000226587605 16.9997734123945 52 262 259.998716085321 2.00128391467877 53 262 261.999848852233 0.000151147767212478 54 251 261.999999988584 -10.9999999885845 55 236 251.000830779394 -15.0008307793939 56 238 236.001132943738 1.99886705626221 57 239 237.999849034767 1.00015096523302 58 243 238.999924463199 4.00007553680123 59 233 242.999697892697 -9.99969789269696 60 238 233.000755231178 4.99924476882154 61 232 237.999622430042 -5.99962243004151 62 224 232.000453123881 -8.00045312388102 63 238 224.000604237419 13.9993957625815 64 236 237.998942690042 -1.99894269004196 65 231 236.000150970945 -5.0001509709453 66 209 231.000377638400 -22.0003776383998 67 179 209.001661587311 -30.0016615873108 68 179 179.002265887478 -0.00226588747773349 69 165 179.000000171132 -14.0000001711321 70 174 165.001057355606 8.99894264439376 71 163 173.999320351262 -10.9993203512615 72 166 163.000830728064 2.99916927193598 73 164 165.999773486542 -1.99977348654249 74 152 164.000151033692 -12.0001510336915 75 163 152.000906316201 10.9990936837988 76 167 162.999169289055 4.00083071094485 77 157 166.999697835662 -9.99969783566212 78 138 157.000755231174 -19.0007552311741 79 111 138.00143503963 -27.0014350396301 80 110 111.002039294169 -1.00203929416907 81 91 110.000075679418 -19.0000756794180 82 100 91.0014349883067 8.99856501169334 83 88 99.9993203797824 -11.9993203797824 84 89 88.0009062534657 0.999093746534314 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 88.9999245430456 71.8050580448059 106.194791041285 86 88.9999245430456 64.68362940433 113.316219681761 87 88.9999245430456 59.2190416707404 118.780807415351 88 88.9999245430456 54.6121395019179 123.387709584173 89 88.9999245430456 50.5533572656456 127.446491820446 90 88.9999245430456 46.8839262668978 131.115922819193 91 88.9999245430456 43.5095290053354 134.490320080756 92 88.9999245430456 40.3687117105636 137.631137375528 93 88.9999245430456 37.4187880982270 140.581060987864 94 88.9999245430456 34.6286783524364 143.371170733655 95 88.9999245430456 31.9749196092389 146.024929476852 96 88.9999245430456 29.4392834863753 148.560565599716

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/1645x1282250805.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/1645x1282250805.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/2yv5i1282250805.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/2yv5i1282250805.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/3yv5i1282250805.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282250779pa2mtv2cq1hsyh3/3yv5i1282250805.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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