nen trippel veu de wim

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 13:19:24 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh.htm/, Retrieved Thu, 04 Jun 2009 21:19:48 +0200

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/Jun/04/t1244143184y6erz6doumgj2lh.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

9.370 9.330 9.310 9.260 9.350 9.380 9.430 9.270 9.290 9.270 9.290 9.310 9.330 9.350 9.340 9.470 9.630 9.620 9.630 9.500 9.550 9.580 9.610 9.570 9.610 9.650 9.620 9.650 9.960 10.030 10.030 9.720 9.750 9.770 9.780 9.820 9.840 9.900 9.940 10.120 10.520 10.570 10.570 10.120 10.050 10.140 10.170 10.200 10.200 10.350 10.430 10.570 10.820 10.900 10.830 10.650 10.570 10.610 10.630 10.710 10.720 10.770 10.790 10.920 10.900 11.000 10.990 10.910 10.880 10.870 11.000 10.990 11.030 11.040 10.990

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.00102339612864802 gamma 0.434544625204061 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 9.33 9.23815170940171 0.0918482905982856 14 9.35 9.3499628783039 3.71216960992626e-05 15 9.34 9.3374629162941 0.00253708370589933 16 9.47 9.4641321794024 0.00586782059758839 17 9.63 9.6216381845073 0.00836181549270698 18 9.62 9.61373007529023 0.00626992470976795 19 9.63 9.63206982524024 -0.00206982524023935 20 9.5 9.48873437365577 0.0112656263442297 21 9.55 9.53582923618749 0.0141707638125137 22 9.58 9.53792707182565 0.0420729281743508 23 9.61 9.5975534624308 0.0124465375692004 24 9.57 9.62631620016916 -0.0563162001691584 25 9.61 9.58959189972126 0.0204081002787362 26 9.65 9.63002945195874 0.0199705480412575 27 9.62 9.6375498897403 -0.0175498897402981 28 9.65 9.74419859591775 -0.0941985959177458 29 9.96 9.80160219343936 0.158397806560641 30 10.03 9.94384763047471 0.086152369525287 31 10.03 10.0422691318095 -0.0122691318094930 32 9.72 9.88892324229416 -0.168923242294163 33 9.75 9.7558337002353 -0.00583370023529284 34 9.77 9.73791106338239 0.0320889366176083 35 9.78 9.78752723640923 -0.00752723640923314 36 9.82 9.79626953306463 0.0237304669353708 37 9.84 9.83962715206596 0.000372847934039910 38 9.9 9.86004420030375 0.0399557996962461 39 9.94 9.88758509091448 0.0524149090855186 40 10.12 10.0643053987962 0.0556946012038093 41 10.52 10.2718623964354 0.248137603564553 42 10.57 10.5041996728316 0.0658003271683594 43 10.57 10.5826003459651 -0.0126003459650637 44 10.12 10.4292541174865 -0.309254117486452 45 10.05 10.1560209613532 -0.106020961353176 46 10.14 10.0379957932451 0.102004206754891 47 10.17 10.1576835172887 0.0123164827112578 48 10.2 10.1864461219295 0.0135538780705353 49 10.2 10.2197933262491 -0.0197933262491468 50 10.35 10.2201897365024 0.129810263497648 51 10.43 10.3378225838235 0.0921774161765239 52 10.57 10.5545835845010 0.0154164154989918 53 10.82 10.7220993616009 0.0979006383990537 54 10.9 10.8042828860686 0.095717113931391 55 10.83 10.9127141759258 -0.0827141759257852 56 10.65 10.6892961932250 -0.0392961932250255 57 10.57 10.6863393109863 -0.116339310986339 58 10.61 10.5583035831192 0.0516964168807963 59 10.63 10.6279398223654 0.00206017763456323 60 10.71 10.6466919307433 0.0633080692567489 61 10.72 10.7300900533096 -0.0100900533095771 62 10.77 10.7404963938547 0.0295036061452549 63 10.79 10.7580265877311 0.0319734122689432 64 10.92 10.9147259758641 0.00527402413594125 65 10.9 11.0722313732799 -0.172231373279940 66 11 10.8841384456926 0.115861554307372 67 10.99 11.0125903512921 -0.0225903512920986 68 10.91 10.8492338990807 0.0607661009192899 69 10.88 10.9463794202065 -0.0663794202064736 70 10.87 10.8683948210981 0.00160517890184941 71 11 10.8879797971654 0.112020202834643 72 10.99 11.0168444382073 -0.0268444382072666 73 11.03 11.0101502990465 0.0198497009535341 74 11.04 11.0505872798202 -0.0105872798202391 75 10.99 11.0280764448391 -0.0380764448390583 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 11.1147041442195 10.9546379547138 11.2747703337251 77 11.2669082884390 11.0404246507895 11.4933919260884 78 11.2511957659918 10.9736691673235 11.5287223646600 79 11.2638165768779 10.9431925552773 11.5844405984785 80 11.1231040544308 10.7644522141064 11.4817558947551 81 11.1594748653169 10.7663906444957 11.5525590861381 82 11.1479290095364 10.723132583978 11.5727254350948 83 11.1659664870892 10.7116080473503 11.6203249268281 84 11.1827539646420 10.700587993102 11.6649199361821 85 11.2028747755282 10.6943677904406 11.7113817606158 86 11.223412253081 10.6898134948879 11.7570110112741 87 11.2114497306338 10.6538397232214 11.7690597380463

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/1iadv1244143162.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/1iadv1244143162.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/2egwl1244143162.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/2egwl1244143162.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/3ikx01244143162.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244143184y6erz6doumgj2lh/3ikx01244143162.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

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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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