*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 12:41:13 +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/18/t1305722239z6svyk8dgz8ginu.htm/, Retrieved Wed, 18 May 2011 14:37:22 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4734 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6923 9858 11331 4016 3957 4510 4276 4968 4677 3523 1821

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 0.0409527574646179 beta 0.213826354573099 gamma 0.447049703127968 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2541 2393.50833868648 147.491661313524 14 2475 2352.71674743204 122.283252567958 15 3031 2909.94895616264 121.051043837358 16 3266 3143.69713027014 122.302869729856 17 3776 3628.34529602076 147.654703979244 18 3230 3064.23475525313 165.765244746867 19 3028 2423.0330404558 604.966959544204 20 1759 2419.06012184961 -660.060121849606 21 3595 3191.03786233196 403.962137668041 22 4474 4729.88256768319 -255.882567683188 23 6838 6291.64062789902 546.359372100982 24 8357 7810.17732415066 546.822675849338 25 3113 2867.70568146713 245.294318532867 26 3006 2817.92641705209 188.073582947914 27 4047 3481.96781679856 565.032183201442 28 3523 3789.84617732456 -266.846177324564 29 3937 4369.59721924909 -432.597219249086 30 3986 3695.31439670542 290.685603294582 31 3260 3166.98600695915 93.0139930408532 32 1573 2497.69029989874 -924.690299898737 33 3528 3918.88531217404 -390.885312174042 34 5211 5318.31789454648 -107.317894546477 35 7614 7503.12819436748 110.871805632515 36 9254 9194.53184143441 59.4681585655926 37 5375 3377.04932592901 1997.95067407099 38 3088 3363.09759626089 -275.097596260895 39 3718 4291.02816634234 -573.028166342339 40 4514 4173.03737217756 340.96262782244 41 4520 4772.1122244441 -252.112224444103 42 4539 4360.09627193035 178.903728069648 43 3663 3649.62685814045 13.3731418595548 44 1643 2377.99734193208 -734.997341932077 45 4734 4262.99823563221 471.001764367787 46 5428 6048.21133711549 -620.21133711549 47 8314 8632.15450989888 -318.154509898883 48 10651 10513.2537071004 137.74629289957 49 3633 4803.64341602592 -1170.64341602592 50 4292 3549.8333992673 742.166600732702 51 4154 4456.01782046898 -302.017820468982 52 4121 4752.11165747155 -631.111657471546 53 4647 5057.35921811475 -410.359218114747 54 4753 4776.88814941631 -23.888149416307 55 3965 3903.78098141118 61.2190185888244 56 1723 2186.57995221726 -463.579952217257 57 5048 4735.44973133142 312.550268668577 58 6923 6088.11011265394 834.88988734606 59 9858 9004.22351387919 853.77648612081 60 11331 11240.7296594008 90.2703405991979 61 4016 4557.17612771076 -541.176127710756 62 3957 4116.08279119259 -159.082791192587 63 4510 4545.77811521034 -35.7781152103371 64 4276 4706.3851694402 -430.3851694402 65 4968 5124.26571975536 -156.265719755356 66 4677 5005.43847633557 -328.438476335567 67 3523 4106.88558389211 -583.88558389211 68 1821 2054.40221049811 -233.402210498113 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 69 5042.57595991266 4565.4878373487 5519.66408247662 70 6632.94338187883 6151.26010410767 7114.62665964998 71 9545.87286176303 9050.39895455502 10041.346768971 72 11387.0243968679 10871.9598855871 11902.0889081488 73 4340.41692158648 3855.5556244054 4825.27821876755 74 4065.3169760509 3577.31155043569 4553.32240166612 75 4539.17960197821 4041.77124748213 5036.5879564743 76 4513.74816647788 4008.98805098465 5018.5082819711 77 5052.22992703902 4529.57938677134 5574.8804673067 78 4851.8789216231 4321.17377201501 5382.58407123118 79 3847.02437529266 3326.93249642272 4367.1162541626 80 1959.24378072299 1830.56627001336 2087.92129143262

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/17pwn1305722470.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/17pwn1305722470.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/262121305722470.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/262121305722470.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/3z1351305722470.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722239z6svyk8dgz8ginu/3z1351305722470.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=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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