Exponential Smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 30 Apr 2008 10:21:01 -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/Apr/30/t1209572547r4akop6btrwqpql.htm/, Retrieved Wed, 30 Apr 2008 18:22:31 +0200

User-defined keywords:

berekening 1 met gebruikt: multiplicatief & triple

Dataseries X:

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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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0839511832014079 beta 0.000901008505166857 gamma 0.332107274688902 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50556 50171.6294214468 384.3705785532 14 43901 43678.138856552 222.861143448012 15 48572 48307.8467109056 264.153289094429 16 43899 43551.2092739331 347.790726066887 17 37532 37142.4550482428 389.544951757176 18 40357 39697.3815437588 659.618456241224 19 35489 34940.8176738392 548.182326160771 20 29027 28659.9527614384 367.047238561579 21 34485 33559.6925869967 925.307413003276 22 42598 40772.1108339023 1825.88916609770 23 30306 28904.2925460086 1401.70745399144 24 26451 25309.2463842449 1141.75361575508 25 47460 54449.3897326998 -6989.38973269978 26 50104 46809.7794505801 3294.22054941986 27 61465 52043.0275898611 9421.97241013893 28 53726 47627.5389202883 6098.46107971165 29 39477 41041.7339863003 -1564.7339863003 30 43895 43749.2787984640 145.721201535962 31 31481 38438.2903889479 -6957.29038894793 32 29896 30971.5037701096 -1075.50377010957 33 33842 36271.5255148524 -2429.52551485235 34 39120 43930.9885469839 -4810.9885469839 35 33702 30768.6486141644 2933.35138583565 36 25094 27013.4599955897 -1919.45999558971 37 51442 54522.4051628419 -3080.40516284193 38 45594 50130.2407638437 -4536.24076384374 39 52518 56751.5887668554 -4233.58876685536 40 48564 50076.2193714957 -1512.21937149567 41 41745 40525.3620548161 1219.63794518391 42 49585 44000.1868936988 5584.81310630123 43 32747 36834.6941442789 -4087.6941442789 44 33379 31285.9309563146 2093.06904368541 45 35645 36578.0412183693 -933.041218369319 46 37034 43854.0936960822 -6820.09369608221 47 35681 32565.7011990652 3115.29880093484 48 20972 27183.8757485128 -6211.87574851281 49 58552 54378.9940953938 4173.00590460616 50 54955 50014.668335736 4940.33166426398 51 65540 57806.134809596 7733.86519040394 52 51570 52615.2593318077 -1045.25933180771 53 51145 43395.163493654 7749.83650634602 54 46641 49061.9837464375 -2420.98374643749 55 35704 37643.9982540233 -1939.99825402327 56 33253 33932.7830177759 -679.783017775873 57 35193 38294.4481858341 -3101.44818583415 58 41668 43838.7008424369 -2170.70084243691 59 34865 35489.3063727399 -624.306372739928 60 21210 26494.3984978382 -5284.39849783824 61 56126 58498.6109940148 -2372.61099401478 62 49231 53611.4973649141 -4380.49736491407 63 59723 61643.2913694242 -1920.29136942422 64 48103 52871.902105855 -4768.90210585498 65 47472 45944.6386698931 1527.36133010690 66 50497 47977.0667621269 2519.93323787311 67 40059 37100.5365391226 2958.4634608774 68 34149 34141.4228103923 7.57718960772036 69 36860 37865.8761038096 -1005.87610380958 70 46356 43975.2500522298 2380.74994777018 71 36577 36262.3319912097 314.668008790264 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 25590.6361774667 22807.5905037272 28373.6818512062 73 60475.1376839279 57351.6808801278 63598.594487728 74 54889.0591977937 51776.4855913448 58001.6328042426 75 64545.9798684929 61242.4490181343 67849.5107188514 76 54477.3370214964 51276.5859635601 57678.0880794326 77 49539.7032918179 46362.0467745057 52717.35980913 78 51872.1908571548 48600.5760437782 55143.8056705314 79 40249.4687111308 37129.7760041134 43369.1614181481 80 35922.3433038529 32823.0558642189 39021.6307434868 81 39507.1285516215 36279.4967452504 42734.7603579926 82 47109.8316636883 43640.7268589657 50578.9364684108 83 38140.7408002406 36399.6990594129 39881.7825410684

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/1jnej1209572459.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/1jnej1209572459.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/22dfn1209572459.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/22dfn1209572459.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/31y1h1209572459.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/30/t1209572547r4akop6btrwqpql/31y1h1209572459.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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