shw-ws9

*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 06:41:32 -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/t1259934144hzokm2ccp9ks52o.htm/, Retrieved Fri, 04 Dec 2009 14:42:28 +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/t1259934144hzokm2ccp9ks52o.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:

Workshop 9 - Populaire technieken 2

Dataseries X:

» Textbox « » Textfile « » CSV «

1178 2141 2238 2685 4341 5376 4478 6404 4617 3024 1897 2075 1351 2211 2453 3042 4765 4992 4601 6266 4812 3159 1916 2237 1595 2453 2226 3597 4706 4974 5756 5493 5004 3225 2006 2291 1588 2105 2191 3591 4668 4885 5822 5599 5340 3082 2010 2301 1514 1979 2480 3499 4676 5585 5610 5796 6199 3030 1930 2552

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 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1351 1325.67314843956 25.3268515604386 14 2211 2175.17007602979 35.8299239702087 15 2453 2417.38047870524 35.619521294755 16 3042 2993.08120691172 48.9187930882804 17 4765 4690.8914041574 74.1085958426038 18 4992 4915.3982232269 76.6017767730964 19 4601 4548.80447484791 52.1955251520876 20 6266 6501.21656954778 -235.216569547776 21 4812 4681.78202297392 130.217977026077 22 3159 3052.28190202208 106.718097977923 23 1916 1901.18721872033 14.8127812796731 24 2237 2083.46592721638 153.534072783622 25 1595 1390.04234789620 204.957652103798 26 2453 2274.74185435041 178.258145649585 27 2226 2523.54908394488 -297.549083944876 28 3597 3129.2797341701 467.720265829899 29 4706 4901.38919535208 -195.389195352082 30 4974 5134.54663409665 -160.546634096650 31 5756 4732.06973178163 1023.93026821837 32 5493 6444.07821864397 -951.078218643966 33 5004 4948.43277147129 55.5672285287146 34 3225 3248.35478283920 -23.3547828391957 35 2006 1970.06811023505 35.9318897649521 36 2291 2299.97839372023 -8.97839372023054 37 1588 1639.79902715819 -51.7990271581941 38 2105 2521.73692872997 -416.736928729972 39 2191 2288.23071382301 -97.2307138230103 40 3591 3697.32506853949 -106.325068539491 41 4668 4836.95217044497 -168.952170444973 42 4885 5112.08949621537 -227.089496215372 43 5822 5915.43073937987 -93.4307393798745 44 5599 5644.79574515114 -45.795745151142 45 5340 5141.96481026847 198.035189731531 46 3082 3313.71234637878 -231.712346378783 47 2010 2061.05425348902 -51.054253489016 48 2301 2353.73254583912 -52.7325458391233 49 1514 1631.38388665256 -117.383886652562 50 1979 2162.37760879342 -183.377608793421 51 2480 2250.58642769829 229.413572301713 52 3499 3688.43999092501 -189.439990925013 53 4676 4794.37808067904 -118.378080679036 54 5585 5016.95527768273 568.044722317265 55 5610 5978.91262488975 -368.912624889754 56 5796 5749.56423925193 46.4357607480651 57 6199 5483.27832142343 715.721678576568 58 3030 3164.5091085043 -134.509108504300 59 1930 2063.69050781928 -133.690507819285 60 2552 2362.32709862512 189.672901374883 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 1554.26226134105 974.562714429145 2133.96180825295 62 2031.51177562162 1451.81222870972 2611.21132253352 63 2545.66037139168 1965.96082447978 3125.35991830359 64 3591.43542773787 3011.73588082597 4171.13497464977 65 4799.25767707737 4219.55813016547 5378.95722398928 66 5731.89591297263 5152.19636606073 6311.59545988453 67 5757.2307559684 5177.5312090565 6336.9303028803 68 5947.78025575339 5368.08070884149 6527.47980266529 69 6360.98016267635 5781.28061576445 6940.67970958825 70 3109.00201585648 2529.30246894458 3688.70156276838 71 1980.21231609032 1400.51276917842 2559.91186300222 72 2618.25109443243 2570.32721290493 2666.17497595992

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/1u9nr1259934089.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/1u9nr1259934089.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/2xz401259934089.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/2xz401259934089.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/3gl281259934089.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934144hzokm2ccp9ks52o/3gl281259934089.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

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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