*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, 06 Dec 2009 08:52:59 -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/06/t1260114884l797xirkc1d9tb9.htm/, Retrieved Sun, 06 Dec 2009 16:54:49 +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/06/t1260114884l797xirkc1d9tb9.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:

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62 64 62 64 64 69 69 65 56 58 53 62 55 60 59 58 53 57 57 53 54 53 57 57 55 49 50 49 54 58 58 52 56 52 59 53 52 53 51 50 56 52 46 48 46 48 48 49 53 48 51 48 50 55 52 53 52 55 53 53 56 54 52 55 54 59 56 56 51 53 52 51 46 49 46 55 57 53 52 53 50 54 53 50 51 52 47 51 49 53 52 45 53 51 48 48 48 48 40 43 40 39 39 36 41 39 40 39 46 40 37 37 44 41 40 36 38 43 42 45 46

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 0.423371990682941 beta 0.0195569935214878 gamma 0.730774983925955 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 55 58.9023392751817 -3.90233927518170 14 60 62.8634077747937 -2.86340777479365 15 59 60.546313553452 -1.54631355345199 16 58 58.475457358636 -0.47545735863595 17 53 52.6409854174408 0.359014582559205 18 57 56.1241628758627 0.875837124137291 19 57 61.2947882409337 -4.29478824093374 20 53 55.6947116162030 -2.69471161620295 21 54 46.554605496123 7.44539450387703 22 53 51.1657213287351 1.83427867126492 23 57 47.4515283774653 9.54847162253474 24 57 60.6274256909451 -3.62742569094512 25 55 51.2492026821145 3.7507973178855 26 49 58.6305811592515 -9.63058115925155 27 50 54.0261322304602 -4.0261322304602 28 49 51.4089408524789 -2.40894085247891 29 54 45.7257468904879 8.27425310951212 30 58 52.5544652279684 5.44553477203164 31 58 57.4309098105022 0.569090189497842 32 52 54.6943984799615 -2.69439847996153 33 56 49.7645607960945 6.23543920390546 34 52 51.6194578680072 0.380542131992812 35 59 50.3566340598945 8.64336594010547 36 53 57.555527799128 -4.55552779912804 37 52 51.0814827200731 0.91851727992691 38 53 51.3707331095737 1.62926689042625 39 51 54.0787039994874 -3.07870399948737 40 50 52.7136347268283 -2.71363472682827 41 56 51.3380282213526 4.66197177864736 42 52 55.5220162897591 -3.5220162897591 43 46 54.5521144379234 -8.55211443792344 44 48 47.0063366698534 0.993663330146553 45 46 47.249880566214 -1.24988056621404 46 48 43.8421149534354 4.15788504656458 47 48 47.1188014458565 0.88119855414353 48 49 45.6174371822074 3.38256281779258 49 53 45.0174338622736 7.98256613772642 50 48 48.5925208556935 -0.5925208556935 51 51 48.3359086650429 2.66409133495714 52 48 49.5868036537874 -1.58680365378743 53 50 51.7158859689251 -1.71588596892507 54 55 49.8087595693327 5.19124043066726 55 52 50.2720246748589 1.72797532514111 56 53 51.3386324166819 1.66136758331808 57 52 51.0562815592371 0.943718440762858 58 55 50.9875632933225 4.01243670667746 59 53 53.1057351936292 -0.105735193629229 60 53 52.3621708859726 0.637829114027426 61 56 52.4967445865758 3.50325541342418 62 54 50.5598916583423 3.44010834165772 63 52 53.6694461616626 -1.66944616166263 64 55 51.3529095740268 3.64709042597318 65 54 56.1215125883556 -2.12151258835559 66 59 57.2550060558415 1.74499394415845 67 56 54.740933005483 1.25906699451698 68 56 55.764588620256 0.235411379743958 69 51 54.6501131039374 -3.65011310393743 70 53 53.9979510761349 -0.997951076134868 71 52 52.3255943171342 -0.325594317134190 72 51 51.8514706285443 -0.851470628544305 73 46 52.5242473405578 -6.52424734055778 74 49 46.5600251488706 2.43997485112942 75 46 47.0591717230597 -1.05917172305969 76 55 47.0552876934929 7.9447123065071 77 57 51.1087416372215 5.89125836277847 78 53 57.2586583767913 -4.25865837679129 79 52 52.1779199812679 -0.177919981267898 80 53 52.1355367781645 0.8644632218355 81 50 49.7694773413206 0.230522658679448 82 54 51.8315330125222 2.16846698747776 83 53 51.8456996817621 1.15430031823792 84 50 51.8421779770833 -1.84217797708325 85 51 49.6141042896784 1.38589571032156 86 52 50.9394342440312 1.06056575596885 87 47 49.3879241678224 -2.38792416782242 88 51 52.7086080942778 -1.70860809427776 89 49 51.7175238785488 -2.71752387854877 90 53 49.8816189863834 3.11838101361658 91 52 49.7127336984029 2.28726630159712 92 45 51.1621189657747 -6.16211896577473 93 53 45.752511049142 7.24748895085803 94 51 51.5505192219968 -0.550519221996836 95 48 50.0404845254472 -2.04048452544724 96 48 47.5014491799112 0.498550820088795 97 48 47.6145105029583 0.385489497041654 98 48 48.3219208580364 -0.321920858036364 99 40 44.9262089909116 -4.92620899091164 100 43 46.9442843611873 -3.94428436118725 101 40 44.5513370720774 -4.55133707207737 102 39 44.0083697566031 -5.00836975660307 103 39 40.2145498272243 -1.21454982722427 104 36 37.0151467322396 -1.01514673223964 105 41 38.5153669693893 2.48463303061067 106 39 38.9201937746157 0.0798062253843028 107 40 37.2793976429623 2.7206023570377 108 39 37.7825650532049 1.21743494679509 109 46 38.0220027391725 7.97799726082753 110 40 41.5297337835317 -1.52973378353173 111 37 36.2868820656346 0.713117934365442 112 37 40.5493501836833 -3.54935018368331 113 44 38.0524330466864 5.94756695331359 114 41 41.7288759229973 -0.728875922997325 115 40 41.4643457946619 -1.46434579466186 116 36 38.2481997700295 -2.24819977002948 117 38 40.8968713160479 -2.89687131604788 118 43 38.0964923106784 4.90350768932164 119 42 39.6663427236364 2.33365727636360 120 45 39.4302618704117 5.56973812958829 121 46 44.4262479507252 1.57375204927482 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 122 41.2495753911415 35.0356598989813 47.4634908833018 123 37.5874894903192 30.7270154223533 44.4479635582851 124 39.8137142224284 32.0687297611420 47.5586986837148 125 42.9685072469998 34.2176522859268 51.7193622080729 126 41.3718965473154 32.1550643280524 50.5887287665783 127 41.1597321952546 31.3233004842789 50.9961639062304 128 38.2167786122307 28.2214641605535 48.212093063908 129 41.7879389438208 30.4944730619125 53.0814048257292 130 43.6901237194493 31.3802880272407 55.9999594116578 131 42.1128691228340 29.5472617001239 54.678476545544 132 42.1848186594751 28.9909225032004 55.3787148157497 133 43.0901751614808 6.84186215887056 79.3384881640911

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/1pk4d1260114777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/1pk4d1260114777.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/2b7de1260114777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/2b7de1260114777.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/3gpku1260114777.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260114884l797xirkc1d9tb9/3gpku1260114777.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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