Ws9forcasting4

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Dec 2009 09:26:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6.htm/, Retrieved Fri, 04 Dec 2009 17:28:42 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

ShwWs9forcasting4

Dataseries X:

» Textbox « » Textfile « » CSV «

58608 46865 51378 46235 47206 45382 41227 33795 31295 42625 33625 21538 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

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.199376799003901 beta 0 gamma 0.684151704720979 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 56421 57234.381038922 -813.381038922009 14 53152 54201.1357606105 -1049.13576061049 15 53536 54461.1980064574 -925.198006457373 16 52408 53057.4198218257 -649.419821825708 17 41454 42097.387400011 -643.387400011001 18 38271 38905.0556552769 -634.05565527692 19 35306 39515.6186778861 -4209.61867788613 20 26414 31391.1847454938 -4977.18474549379 21 31917 27746.5052679411 4170.49473205891 22 38030 38378.6830845338 -348.683084533761 23 27534 30028.7838410811 -2494.7838410811 24 18387 19041.5831630339 -654.583163033851 25 50556 49491.9561710655 1064.04382893450 26 43901 47033.0895712692 -3132.08957126924 27 48572 46834.9487503428 1737.05124965725 28 43899 46207.4166924274 -2308.41669242737 29 37532 36294.3735774642 1237.62642253582 30 40357 33827.798117882 6529.201882118 31 35489 33949.1238106013 1539.87618939874 32 29027 26905.0162816868 2121.98371831315 33 34485 29589.1074065604 4895.89259343959 34 42598 37817.4939242395 4780.50607576048 35 30306 29132.3782028329 1173.62179716713 36 26451 19482.3312014727 6968.66879852731 37 47460 56370.3845567696 -8910.3845567696 38 50104 49197.7801417312 906.219858268814 39 61465 52820.0757512737 8644.92424872626 40 53726 50952.4212021446 2773.5787978554 41 39477 42841.3859745836 -3364.38597458358 42 43895 42261.9970477072 1633.00295229285 43 31481 38295.1509791512 -6814.15097915116 44 29896 29526.4138223395 369.586177660527 45 33842 33446.4831296276 395.51687037239 46 39120 40711.7028193735 -1591.70281937352 47 33702 29050.3941651947 4651.6058348053 48 25094 23021.0513582380 2072.94864176204 49 51442 48708.4559282571 2733.54407174286 50 45594 49230.1589700954 -3636.15897009538 51 52518 55820.2128373136 -3302.21283731356 52 48564 48791.8887243184 -227.888724318414 53 41745 37645.4239278865 4099.57607211349 54 49585 41142.8600356399 8442.13996436012 55 32747 33903.1120178406 -1156.11201784058 56 33379 30150.2574978125 3228.74250218748 57 35645 34789.0996927706 855.900307229422 58 37034 41279.1139050477 -4245.11390504766 59 35681 32249.7573672378 3431.24263276219 60 20972 24441.1266246407 -3469.12662464072 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 48503.7594744825 43039.8199015168 53967.6990474481 62 45106.4897985651 39474.8359902228 50738.1436069073 63 52347.0844162315 46406.5790083298 58287.5898241332 64 47743.8478680854 41725.4341188792 53762.2616172915 65 39119.6034260896 33150.8106960551 45088.396156124 66 43795.6820918943 37480.9271901814 50110.4369936071 67 30688.7985670687 24697.6680381675 36679.92909597 68 29600.4552754024 23472.9665380691 35727.9440127356 69 32030.244022973 25588.5680250853 38471.9200208608 70 35152.0426999979 28322.2455426080 41981.8398573878 71 31430.7634576107 24709.7357751162 38151.7911401052 72 20288.1785769024 17574.9405207773 23001.4166330275

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/1o89d1259943999.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/1o89d1259943999.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/26n0q1259943999.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/26n0q1259943999.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/37uis1259943999.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599441177rshu7589pavlx6/37uis1259943999.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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