W8 Smoothing Model

*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: Sun, 28 Nov 2010 14:41:54 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0.htm/, Retrieved Sun, 28 Nov 2010 15:51:28 +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/2010/Nov/28/t12909558880s4jxk0srnzpif0.htm/}, year = {2010}, } @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 = {2010}, 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:

Dataseries X:

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10057 10900 11771 11992 11993 14504 11727 11477 13578 11555 11846 11397 10066 10269 14279 13870 13695 14420 11424 9704 12464 14301 13464 9893 11572 12380 16692 16052 16459 14761 13654 13480 18068 16560 14530 10650 11651 13735 13360 17818 20613 16231 13862 12004 17734 15034 12609 12320 10833 11350 13648 14890 16325 18045 15616 11926 16855 15083 12520 12355

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.680282906594522 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 10900 10057 843 3 11771 10630.4784902592 1140.52150974082 4 11992 11406.3557779392 585.644222060762 5 11993 11804.7595315530 188.240468446978 6 14504 11932.8163045668 2571.18369543315 7 11727 13681.9486222846 -1954.94862228456 8 11477 12352.0304912739 -875.030491273861 9 13578 11756.7622053112 1821.23779468875 10 11555 12995.7191458819 -1440.71914588191 11 11846 12015.6225377350 -169.622537734987 12 11397 11900.2312247407 -503.231224740692 13 10066 11557.8916244850 -1491.89162448497 14 10269 10542.9832538563 -273.983253856313 15 14279 10356.5971295647 3922.40287043528 16 13870 13024.9407550991 845.059244900873 17 13695 13599.8201144649 95.1798855351353 18 14420 13664.5693636460 755.43063635396 19 11424 14178.4759126755 -2754.47591267546 20 9704 12304.653032656 -2600.653032656 21 12464 10535.4732285569 1928.52677144308 22 14301 11847.4170260796 2453.58297392043 23 13464 13516.547583149 -52.5475831489912 24 9893 13480.8003605499 -3587.80036054988 25 11572 11040.0811029941 531.918897005868 26 12380 11401.9364363218 978.063563678164 27 16692 12067.2963602550 4624.70363974499 28 16052 15213.403194439 838.596805561003 29 16459 15783.8862667869 675.113733213082 30 14761 16243.154599499 -1482.15459949899 31 13654 15234.8701605294 -1580.87016052938 32 13480 14159.4312127759 -679.431212775904 33 18068 13697.2257725177 4370.77422748233 34 16560 16670.5887680578 -110.588768057776 35 14530 16595.3571194867 -2065.35711948673 36 10650 15190.3299750866 -4540.32997508661 37 11651 12101.6211027365 -450.621102736457 38 13735 11795.0712691941 1939.92873080593 39 13360 13114.7716247730 245.228375227049 40 17818 13281.5962966519 4536.40370334814 41 20613 16367.6341934517 4245.36580654831 42 16231 19255.6839838874 -3024.68398388737 43 13862 17198.0431717986 -3336.04317179857 44 12004 14928.5900263626 -2924.59002636263 45 17734 12939.0414226313 4794.95857736869 46 15034 16200.9697806440 -1166.96978064402 47 12609 15407.1001863595 -2798.10018635953 48 12320 13503.6004586402 -1183.60045864020 49 10833 12698.4172983898 -1865.41729838983 50 11350 11429.4057966295 -79.4057966294968 51 13648 11375.3873904979 2272.61260950207 52 14890 12921.4069020534 1968.59309794664 53 16325 14260.6071366264 2064.39286337358 54 18045 15664.9783140752 2380.02168592481 55 15616 17284.0663843341 -1668.06638433411 56 11926 16149.3093360067 -4223.30933600669 57 16855 13276.2641854603 3578.73581453972 58 15083 15710.8169873093 -627.816987309274 59 12520 15283.7238223731 -2763.72382237311 60 12355 13403.6097474646 -1048.60974746461 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 12690.2584605760 8101.32154325347 17279.1953778986 62 12690.2584605760 7140.1392428101 18240.3776783420 63 12690.2584605760 6322.4248704401 19058.0920507120 64 12690.2584605760 5598.37676867562 19782.1401524765 65 12690.2584605760 4941.69296545624 20438.8239556958 66 12690.2584605760 4336.4719818342 21044.0449393179 67 12690.2584605760 3772.23010041376 21608.2868207383 68 12690.2584605760 3241.62304942235 22138.8938717297 69 12690.2584605760 2739.26894027423 22641.2479808778 70 12690.2584605760 2261.08429703820 23119.4326241139 71 12690.2584605760 1803.88371809845 23576.6332030536 72 12690.2584605760 1365.12551063224 24015.3914105198

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/1dse31290955310.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/1dse31290955310.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/26jdo1290955310.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/26jdo1290955310.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/36jdo1290955310.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909558880s4jxk0srnzpif0/36jdo1290955310.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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