Opgave 10 oefening 2 - Renske van der Eijk - Tripel smoothing model

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 09:45:45 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/03/t12440439877sptib91c179i87.htm/, Retrieved Wed, 03 Jun 2009 17:46:30 +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/2009/Jun/03/t12440439877sptib91c179i87.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565 1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722 832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753 2258 1208 1241 1265 1828 809 997 1164 1205 1538 1513 1378 2083 1357 1536 1526 1376

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.209519063877484 beta 0 gamma 0.465190252066663 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 530 488.836959000463 41.163040999537 14 883 820.160720694814 62.8392793051855 15 894 844.409000513037 49.5909994869633 16 1045 1013.82641473477 31.1735852652289 17 1199 1185.10440405179 13.8955959482057 18 1287 1283.33563537775 3.6643646222476 19 1565 1489.44447771464 75.5555222853648 20 1577 1437.15912845219 139.840871547813 21 1076 1294.77226900069 -218.772269000687 22 918 1069.44046705832 -151.440467058321 23 1008 1075.02870997955 -67.028709979546 24 1063 1022.26333615748 40.7366638425229 25 544 581.785735147963 -37.7857351479632 26 635 942.48289047864 -307.482890478641 27 804 883.952871712233 -79.9528717122333 28 980 1018.44134462843 -38.4413446284339 29 1018 1165.74639585476 -147.746395854757 30 1064 1222.54495453123 -158.544954531232 31 1404 1404.70509513422 -0.705095134221892 32 1286 1364.16298139455 -78.162981394548 33 1104 1076.99276264309 27.0072373569128 34 999 938.473765457125 60.5262345428753 35 996 1017.39665210894 -21.3966521089432 36 1015 1013.92604839961 1.07395160039459 37 615 550.708641012437 64.291358987563 38 722 827.219571156814 -105.219571156814 39 832 898.346982730057 -66.3469827300567 40 977 1059.47969247122 -82.4796924712214 41 1270 1160.55657930228 109.443420697716 42 1437 1272.22597311833 164.774026881674 43 1520 1620.1494184966 -100.149418496598 44 1708 1518.23450979679 189.765490203213 45 1151 1281.53135550461 -130.531355504612 46 934 1100.90437589662 -166.904375896615 47 1159 1104.40174385509 54.5982561449059 48 1209 1124.92990250048 84.0700974995202 49 699 645.402034526066 53.5979654739335 50 830 878.698732627998 -48.6987326279976 51 996 988.610251462677 7.38974853732338 52 1124 1182.62029356514 -58.6202935651388 53 1458 1385.96274438518 72.0372556148216 54 1270 1522.12793662550 -252.127936625497 55 1753 1699.69788130466 53.3021186953367 56 2258 1735.53144398777 522.468556012228 57 1208 1395.37652222639 -187.376522226388 58 1241 1165.2299345522 75.7700654477992 59 1265 1319.89166166391 -54.8916616639074 60 1828 1329.0833845422 498.9166154578 61 809 810.754172821664 -1.75417282166381 62 997 1029.56191649395 -32.5619164939549 63 1164 1190.09698892522 -26.0969889252178 64 1205 1382.97132720244 -177.971327202437 65 1538 1651.98726775624 -113.987267756240 66 1513 1624.62899778875 -111.628997788746 67 1378 1997.13485081984 -619.134850819837 68 2083 2066.52737864586 16.4726213541367 69 1357 1345.65953698183 11.3404630181678 70 1536 1248.58565571582 287.414344284179 71 1526 1405.93532530904 120.064674690959 72 1376 1664.04549005685 -288.045490056852 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 803.455573633234 611.871659473103 995.039487793364 74 1009.6704681992 799.380063535085 1219.96087286331 75 1179.18690328686 948.331756757436 1410.04204981628 76 1320.32929492619 1069.02341755962 1571.63517229275 77 1659.46068342254 1367.26960623858 1951.65176060649 78 1655.52595773419 1356.93713340172 1954.11478206667 79 1859.95079848722 1531.42321262129 2188.47838435315 80 2348.55859754072 1953.36582818472 2743.75136689671 81 1525.53338140676 1228.24392812832 1822.82283468519 82 1520.9503547358 1217.54329498931 1824.35741448229 83 1557.53273024024 1243.04119120697 1872.02426927352 84 1640.16808882558 1368.97303082830 1911.36314682286

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/1wv8y1244043944.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/1wv8y1244043944.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/2fxcz1244043944.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/2fxcz1244043944.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/3k1lp1244043944.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440439877sptib91c179i87/3k1lp1244043944.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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