*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 01:59:07 +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/20/t1305856500av3rvfhfxhdgoei.htm/, Retrieved Fri, 20 May 2011 03:55:00 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

90 51 47 59 54 79 59 80 46 62 55 77 72 72 71 50 66 78 59 52 71 98 70 84 90 98 98 78 59 0 58 55 62 80 91 86 61 49 61 56 73 85 82 32 39 30 51 48 57 59 32 56 54 74 62 78 72 48 59 61 80 69 58 63 27 23 34 45 51 51 73 37 35 66 54 30 66 61 37 55 64 53 63 70 72 52 53 50 60 73 66 78

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 0.439852181310189 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 51 90 -39 3 47 72.8457649289026 -25.8457649289026 4 59 61.4774488472944 -2.47744884729442 5 54 60.3877375677276 -6.38773756772756 6 79 57.5780772649255 21.4219227350745 7 59 67.0005567078064 -8.00055670780638 8 80 63.4814943881819 16.5185056118181 9 46 70.7471951135247 -24.7471951135247 10 62 59.862087361532 2.137912638468 11 55 60.8024528990128 -5.80245289901277 12 77 58.2502313344324 18.7497686655676 13 72 66.4973579810437 5.50264201895628 14 72 68.9177070760507 3.08229292394925 15 71 70.2734603420868 0.726539657913207 16 50 70.5930303954283 -20.5930303954283 17 66 61.5351410562121 4.46485894378788 18 78 63.4990190018795 14.5009809981205 19 59 69.8773071250404 -10.8773071250404 20 52 65.0928998593105 -13.0928998593105 21 71 59.3339592965169 11.6660407034831 22 98 64.4652927471974 33.5347072528026 23 70 79.2156068819412 -9.21560688194124 24 84 75.1621020928222 8.8378979071778 25 90 79.0494707654911 10.9505292345089 26 98 83.8660849357908 14.1339150642092 27 98 90.0829183072362 7.91708169276382 28 78 93.5652639594093 -15.5652639594093 29 59 86.7188486541942 -27.7188486541942 30 0 74.5266526102399 -74.5266526102399 31 58 41.7459418938792 16.2540581061208 32 55 48.895324806999 6.10467519300101 33 62 51.5804795068307 10.4195204931693 34 80 56.1635283239574 23.8364716760426 35 91 66.6480523854033 24.3519476145967 36 86 77.3593096628351 8.6406903371649 37 61 81.159936155663 -20.159936155663 38 49 72.2925442625205 -23.2925442625205 39 61 62.0472678603867 -1.04726786038671 40 56 61.5866248075796 -5.58662480757956 41 73 59.1293356998041 13.8706643001959 42 85 65.2303776484666 19.7696223515334 43 82 73.9260891634672 8.07391083653276 44 32 77.4774164566201 -45.4774164566201 45 39 57.4740756278239 -18.4740756278239 46 30 49.3482131652361 -19.3482131652361 47 51 40.8378594000525 10.1621405999475 48 48 45.3076991097202 2.69230089027975 49 57 46.4919135290532 10.5080864709468 50 59 51.1139182846952 7.88608171530479 51 32 54.5826285291624 -22.5826285291624 52 56 44.6496101108926 11.3503898891074 53 54 49.6421038623376 4.35789613766238 54 74 51.5589339844117 22.4410660155883 55 62 61.4296858222941 0.570314177705853 56 78 61.6805397573902 16.3194602426098 57 72 68.858689942907 3.14131005709298 58 48 70.240402023691 -22.240402023691 59 59 60.457912680355 -1.45791268035497 60 61 59.816646607741 1.18335339225894 61 80 60.337147178587 19.662852821413 62 69 68.9858958828667 0.0141041171333001 63 58 68.9920996095532 -10.9920996095532 64 63 64.1572006191124 -1.15720061911237 65 27 63.6482034025823 -36.6482034025823 66 23 47.528411194857 -24.528411194857 67 34 36.7395360267259 -2.73953602672587 68 45 35.5345451295927 9.46545487040735 69 51 39.6979461014345 11.3020538985655 70 51 44.6691791620039 6.33082083799615 71 73 47.4538045170805 25.5461954829195 72 37 58.6903543244191 -21.6903543244191 73 35 49.1498046614325 -14.1498046614325 74 66 42.9259822159883 23.0740177840117 75 54 53.075139269876 0.924860730124045 76 30 53.4819412794292 -23.4819412794292 77 66 43.1533581862745 22.8466418137255 78 61 53.2025034236542 7.79749657634578 79 37 56.6322493015186 -19.6322493015186 80 55 47.9969616222202 7.00303837777977 81 64 51.0772633284856 12.9227366715144 82 53 56.7613572419484 -3.7613572419484 83 63 55.1069160543905 7.89308394560948 84 70 58.5787062451313 11.4212937548687 85 72 63.6023872165947 8.39761278340527 86 52 67.2960955171739 -15.2960955171739 87 53 60.5680745384159 -7.56807453841594 88 50 57.2392404443756 -7.23924044437558 89 60 54.055044743888 5.94495525611196 90 73 56.6699462810804 16.3300537189196 91 66 63.8527560302597 2.14724396974027 92 78 64.7972259741551 13.2027740258449 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 93 70.6044949287685 35.3862506134328 105.822739244104 94 70.6044949287685 32.129954177741 109.079035679796 95 70.6044949287685 29.128527919544 112.080461937993 96 70.6044949287685 26.3301073813604 114.878882476177 97 70.6044949287685 23.6983445213232 117.510645336214 98 70.6044949287685 21.2065951819808 120.002394675556 99 70.6044949287685 18.8346383253212 122.374351532216 100 70.6044949287685 16.5666969898323 124.642292867705 101 70.6044949287685 14.3901803866779 126.818809470859 102 70.6044949287685 12.2948498193623 128.914140038175 103 70.6044949287685 10.2722459558295 130.936743901708 104 70.6044949287685 8.31528382860682 132.89370602893

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/1nocv1305856743.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/1nocv1305856743.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/2t4h21305856743.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/2t4h21305856743.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/3ydhb1305856743.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856500av3rvfhfxhdgoei/3ydhb1305856743.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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