exponential smoothing 2

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 11:06:25 -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/t12101800587ad4h8gohcmfbs3.htm/, Retrieved Wed, 07 May 2008 19:07:42 +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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.633488893561455 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 53536 53152 384 4 52408 53395.2597351276 -987.259735127598 5 41454 52769.8416578638 -11315.8416578638 6 38271 45601.3816463071 -7330.38164630705 7 35306 40957.6662878048 -5651.66628780481 8 26414 37377.3984643648 -10963.3984643648 9 31917 30432.207301501 1484.79269849903 10 38030 31372.8069852413 6657.19301475875 11 27534 35590.0648223858 -8056.06482238582 12 18387 30486.6372315933 -12099.6372315933 13 50556 22821.6514292563 27734.3485707437 14 43901 40391.0532189844 3509.94678101556 15 48572 42614.5655217496 5957.43447825042 16 43899 46388.5340978413 -2489.5340978413 17 37532 44811.4418967163 -7279.4418967163 18 40357 40199.9963038206 157.003696179410 19 35489 40299.4564015983 -4810.45640159834 20 29027 37252.0856982242 -8225.08569822419 21 34485 32041.585259808 2443.414740192 22 42598 33589.461360084 9008.53863991602 23 30306 39296.27053569 -8990.27053569 24 26451 33601.0340012176 -7150.03400121759 25 47460 29071.5668728595 18388.4331271405 26 50104 40720.4350289005 9383.56497109947 27 61465 46664.8192201044 14800.1807798956 28 53726 56040.56936687 -2314.56936686996 29 39477 54574.3153795803 -15097.3153795803 30 43895 45010.3337640216 -1115.33376402163 31 31481 44303.7822118998 -12822.7822118998 32 29896 36180.6920961039 -6284.6920961039 33 33842 32199.4094537686 1642.59054623138 34 39120 33239.9723214752 5880.02767852476 35 33702 36964.9045496546 -3262.90454965462 36 25094 34897.8907566973 -9803.89075669728 37 51442 28687.2348486397 22754.7651513603 38 45594 43102.1258476257 2491.87415237429 39 52518 44680.7004473077 7837.29955269231 40 48564 49645.5426694524 -1081.54266945243 41 41745 48960.3974004415 -7215.3974004415 42 49585 44389.5232846296 5195.47671537039 43 32747 47680.8000805739 -14933.8000805739 44 33379 38220.4035908632 -4841.40359086318 45 35645 35153.4281868028 491.571813197195 46 37034 35464.8334708511 1569.16652914890 47 35681 36458.8830392153 -777.883039215303 48 20972 35966.1027733826 -14994.1027733826 49 58552 26467.5051975257 32084.4948024743 50 54955 46792.6763104234 8162.3236895766 51 65540 51963.4177134237 13576.5822865763 52 51570 60564.031804493 -8994.03180449299 53 51145 54866.4125480082 -3721.41254800819 54 46641 52508.9390304848 -5867.93903048476 55 35704 48791.6648265769 -13087.6648265769 56 33253 40500.7745162855 -7247.77451628553 57 35193 35909.3898571809 -716.389857180897 58 41668 35455.5648391967 6212.43516080327 59 34865 39391.0735155363 -4526.07351553627 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 36523.8562120014 16529.6298764116 56518.0825475912 61 36523.8562120014 12855.3182197022 60192.3942043006 62 36523.8562120014 9679.29820433379 63368.414219669 63 36523.8562120014 6841.18620808917 66206.5262159136 64 36523.8562120014 4251.70873936997 68796.0036846328 65 36523.8562120014 1855.10794458639 71192.6044794164 66 36523.8562120014 -386.206242070803 73433.9186660736 67 36523.8562120014 -2499.00009424085 75546.7125182436 68 36523.8562120014 -4503.13390708667 77550.8463310895 69 36523.8562120014 -6413.82563233982 79461.5380563426 70 36523.8562120014 -8243.04144798828 81290.753871991 71 36523.8562120014 -10000.3926270085 83048.1050510113

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/1k6ql1210179982.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/1k6ql1210179982.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/2ad9t1210179982.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/2ad9t1210179982.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/39ltt1210179982.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101800587ad4h8gohcmfbs3/39ltt1210179982.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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