single exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 07 May 2008 09:00:15 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/07/t1210172595zhxlh4bquas335w.htm/, Retrieved Wed, 07 May 2008 17:03:20 +0200

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 0.639263220109391 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 53152 56421 -3269 3 53536 54331.2485334624 -795.2485334624 4 52408 53822.875395174 -1414.87539517396 5 41454 52918.3975940015 -11464.3975940015 6 38271 45589.6298714458 -7318.62987144575 7 35306 40911.0989730366 -5605.09897303657 8 26414 37327.9653545014 -10913.9653545014 9 31917 30351.0687178205 1565.93128217950 10 38030 31352.1109917366 6677.8890082634 11 27534 35621.0398226922 -8087.03982269217 12 18387 30451.2927044851 -12064.2927044851 13 50556 22739.0341018737 27816.9658981263 14 43901 40521.397295583 3379.60270441696 15 48572 42681.853003099 5890.14699690097 16 43899 46447.2073392556 -2548.20733925560 17 37532 44818.2321100567 -7286.23211005668 18 40357 40160.4119089174 196.588091082594 19 35489 40286.083445058 -4797.08344505802 20 29027 37219.4844348368 -8192.48443483678 21 34485 31982.3304543270 2502.66954567304 22 42598 33582.1950469636 9015.80495303639 23 30306 39345.6675531198 -9039.66755311985 24 26451 33566.9405643941 -7115.94056439408 25 47460 29017.9814850925 18442.0185149075 26 50104 40807.2856262493 9296.71437375073 27 61465 46750.3331932504 14714.6668067496 28 53726 56156.8784789699 -2430.87847896993 29 39477 54602.907274809 -15125.907274809 30 43895 44933.4710832385 -1038.47108323854 31 31481 44269.614714577 -12788.614714577 32 29896 36094.3236913982 -6198.32369139817 33 33842 32131.9633291546 1710.03667084535 34 39120 33225.1268778644 5894.87312213561 35 33702 36993.5024520571 -3291.5024520571 36 25094 34889.3659955571 -9795.36599555712 37 51442 28627.5487870872 22814.4512129128 38 45594 43211.9883344824 2382.01166551755 39 52518 44734.7207821193 7783.27921788067 40 48564 49710.2849179522 -1146.28491795223 41 41745 48977.5071301393 -7232.50713013926 42 49585 44354.0313326623 5230.96866733769 43 32747 47697.9972072359 -14950.9972072359 44 33379 38140.3745886918 -4761.37458869178 45 35645 35096.6029369777 548.397063022348 46 37034 35447.1730093839 1586.82699061614 47 35681 36461.5731411616 -780.573141161629 48 20972 35962.5814414117 -14990.5814414117 49 58552 26379.6540778628 32172.3459221372 50 54955 46946.2515305214 8008.74846947855 51 65540 52065.9498661665 13474.0501338335 52 51570 60679.4145426363 -9109.41454263626 53 51145 54856.1008687993 -3711.10086879929 54 46641 52483.7305772599 -5842.7305772599 55 35704 48748.6878142091 -13044.6878142091 56 33253 40409.6986767761 -7156.69867677608 57 35193 35834.6844353076 -641.684435307587 58 41668 35424.4791768988 6243.52082310121 59 34865 39415.7324030945 -4550.7324030945 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 36506.6165532362 16667.5094810545 56345.7236254179 61 36506.6165532362 12960.2000500247 60053.0330564476 62 36506.6165532362 9761.94809644034 63251.285010032 63 36506.6165532362 6907.27785141464 66105.9552550577 64 36506.6165532362 4304.68474307345 68708.5483633989 65 36506.6165532362 1897.25404787369 71115.9790585986 66 36506.6165532362 -353.274029195163 73366.5071356675 67 36506.6165532362 -2474.08501138462 75487.318117857 68 36506.6165532362 -4485.31747275546 77498.5505792278 69 36506.6165532362 -6402.38268832702 79415.6157947993 70 36506.6165532362 -8237.38613576887 81250.6192422412 71 36506.6165532362 -10000.0425114065 83013.2756178788

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/1oujt1210172412.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/1oujt1210172412.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/2d7lu1210172412.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/2d7lu1210172412.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/3yoot1210172412.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210172595zhxlh4bquas335w/3yoot1210172412.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=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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