*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 08:24:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn.htm/, Retrieved Fri, 20 May 2011 10:24:56 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

19097,1 19304,6 19601,7 16006,9 17681,2 19790,4 17014,2 17424,5 18908,9 15692,1 15160 15794,3 16032,1 16065 16236,8 12521 14762,1 15446,9 13635 14212,6 15021,7 14134,3 13721,4 14384,5 15638,6 19711,6 20359,8 16141,4 20056,9 20605,5 19325,8 20547,7 19211,2 19009,5 18746,8 16471,5 18957,2 20515,2 18374,4 16192,9 18147,5 19301,4 18344,7 17183,6 19630 17167,2 17428,5 16016,5 18466,5 18406,6 18174,1 14851,9 16260,7 18329,6 18003,8 15903,8 19554,2 16554,2 16198,9 16571,8 17535,2 16198,1 17487,5 13768 14915,8 17160,9 15607,4 16181,5 17413,2 15116,3 14544,5 15050,6 15535,4 15919,3 15853,1 12336,4 14355,5 16040,8 13867,7 14656,6

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.380888896422215 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 19304.6 19097.1 207.5 3 19601.7 19176.1344460076 425.565553992394 4 16006.9 19338.2276402231 -3331.32764022308 5 17681.2 18069.3619317177 -388.161931717685 6 19790.4 17921.5153619126 1868.88463808738 7 17014.2 18633.3527692542 -1619.15276925415 8 17424.5 18016.635457834 -592.135457833963 9 18908.9 17791.0976367671 1117.80236323288 10 15692.1 18216.856145317 -2524.75614531704 11 15160 17255.204563392 -2095.20456339202 12 15794.3 16457.1644094628 -662.864409462847 13 16032.1 16204.686716065 -172.586716064978 14 16065 16138.9503522459 -73.9503522458544 15 16236.8 16110.7834841889 126.016515811103 16 12521 16158.7817758272 -3637.78177582716 17 14762.1 14773.1910898075 -11.0910898075053 18 15446.9 14768.9666168506 677.933383149395 19 13635 15027.1839150062 -1392.18391500616 20 14212.6 14496.9165200027 -284.3165200027 21 15021.7 14388.6235144643 633.076485535734 22 14134.3 14629.7553183908 -495.455318390828 23 13721.4 14441.0418889424 -719.641888942428 24 14384.5 14166.9382840439 217.561715956053 25 15638.6 14249.8051259382 1388.79487406183 26 19711.6 14778.7816728764 4932.81832712359 27 20359.8 16657.6374017458 3702.16259825421 28 16141.4 18067.7500281704 -1926.35002817044 29 20056.9 17334.0246918177 2722.87530818231 30 20605.5 18371.1376630465 2234.36233695345 31 19325.8 19222.1814677761 103.618532223889 32 20547.7 19261.6486161638 1286.05138383625 33 19211.2 19751.4913084954 -540.291308495402 34 19009.5 19545.7003482561 -536.200348256076 35 18746.8 19341.4675893476 -594.667589347613 36 16471.5 19114.9653075029 -2643.46530750294 37 18957.2 18108.0987237977 849.101276202269 38 20515.2 18431.5119718411 2083.68802815889 39 18374.4 19225.1656053747 -850.765605374727 40 16192.9 18901.1184328296 -2708.21843282957 41 18147.5 17869.5881026788 277.911897321188 42 19301.4 17975.4416585521 1325.95834144792 43 18344.7 18480.484467928 -135.78446792801 44 17183.6 18428.7656717876 -1245.16567178763 45 19630 17954.4958931976 1675.50410680239 46 17167.2 18592.6768033885 -1425.47680338846 47 17428.5 18049.7285168704 -621.228516870364 48 16016.5 17813.1094726536 -1796.6094726536 49 18466.5 17128.8008733129 1337.69912668713 50 18406.6 17638.3156174217 768.284382578306 51 18174.1 17930.9466080404 243.153391959633 52 14851.9 18023.5610351652 -3171.66103516519 53 16260.7 16815.5105636558 -554.810563655778 54 18329.6 16604.1893803415 1725.41061965846 55 18003.8 17261.3791271384 742.420872861578 56 15903.8 17544.1589940835 -1640.35899408349 57 19554.2 16919.3644670908 2634.83553290923 58 16554.2 17922.9440654746 -1368.74406547461 59 16198.9 17401.6046488915 -1202.70464889153 60 16571.8 16943.5078024534 -371.707802453366 61 17535.2 16801.9284277854 733.271572214628 62 16198.1 17081.223427704 -883.123427703986 63 17487.5 16744.8515199212 742.648480078791 64 13768 17027.7180799281 -3259.71807992805 65 14915.8 15786.1276578167 -870.327657816715 66 17160.9 15454.6295167052 1706.27048329483 67 15607.4 16104.5289980851 -497.128998085142 68 16181.5 15915.178082625 266.321917374989 69 17413.2 16016.617143827 1396.58285617298 70 15116.3 16548.5600466769 -1432.26004667693 71 14544.5 16003.0280981085 -1458.52809810852 72 15050.6 15447.4909404192 -396.890940419175 73 15535.4 15296.3195881229 239.080411877059 74 15919.3 15387.382662359 531.91733764104 75 15853.1 15589.9840700809 263.115929919104 76 12336.4 15690.2020062589 -3353.80200625889 77 14355.5 14412.7760612763 -57.2760612763268 78 16040.8 14390.9602455054 1649.83975449462 79 13867.7 15019.3658888683 -1151.66588886833 80 14656.6 14580.7091394102 75.8908605898378 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 14609.6151255488 11438.6444359379 17780.5858151596 82 14609.6151255488 11216.4151868967 18002.8150642008 83 14609.6151255488 11007.87158485 18211.3586662476 84 14609.6151255488 10810.7590816504 18408.4711694471 85 14609.6151255488 10623.3815709813 18595.8486801163 86 14609.6151255488 10444.4250145386 18774.8052365589 87 14609.6151255488 10272.8468160637 18946.3834350339 88 14609.6151255488 10107.8032592608 19111.4269918368 89 14609.6151255488 9948.60012999804 19270.6301210995 90 14609.6151255488 9794.65806467627 19424.5721864212 91 14609.6151255488 9645.48758817192 19573.7426629256 92 14609.6151255488 9500.67072218712 19718.5595289104

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/1s9w31305879839.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/1s9w31305879839.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/2vv311305879839.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/2vv311305879839.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/3hq2z1305879839.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058798932afrdy4hgsk9lnn/3hq2z1305879839.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

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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