*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 25 Jan 2010 10:33:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg.htm/, Retrieved Mon, 25 Jan 2010 18:34:53 +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/Jan/25/t1264440888bk6c38b14te71yg.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

0.96 1 1.05 1.03 1.07 1.12 1.1 1.06 1.11 1.08 1.07 1.02 1 1.04 1.02 1.07 1.12 1.08 1.02 1.01 1.04 0.98 0.95 0.94 0.94 0.96 0.97 1.03 1.01 0.99 1 1 1.02 1.01 0.99 0.98 1.01 1.03 1.03 1 0.96 0.97 0.98 1.02 1.04 1.01 1.01 1 1.01 1.02 1.03 1.06 1.12 1.12 1.13 1.13 1.13 1.17 1.14 1.08 1.07 1.12 1.14 1.21 1.2 1.23 1.29 1.31 1.37 1.35 1.26 1.26 1.28 1.28 1.27 1.35 1.37 1.37 1.4 1.4 1.28 1.23 1.23 1.25 1.21 1.22 1.29 1.32 1.36 1.36 1.37 1.32 1.33 1.36 1.42 1.39 1.42 1.4 1.42 1.44 1.49 1.54 1.55 1.47 1.47 1.35 1.2 1.12

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 1 beta 0.236026842400955 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.05 1.04 0.01 4 1.03 1.09236026842401 -0.0623602684240097 5 1.07 1.05764157117661 0.0123584288233853 6 1.12 1.10055849210884 0.0194415078911647 7 1.1 1.1551472098279 -0.0551472098279002 8 1.06 1.12213098802500 -0.0621309880249981 9 1.11 1.06746640710621 0.042533592893794 10 1.08 1.12750547673290 -0.047505476732896 11 1.07 1.08629290906288 -0.0162929090628785 12 1.02 1.07244734518324 -0.0524473451832415 13 1 1.01006836390733 -0.0100683639073280 14 1.04 0.987691959766138 0.0523080402338625 15 1.02 1.04003806133472 -0.0200380613347182 16 1.07 1.01530854099005 0.0546914590099521 17 1.12 1.07821719336647 0.0417828066335317 18 1.08 1.13807905728283 -0.0580790572828305 19 1.02 1.08437084078274 -0.0643708407827399 20 1.01 1.00917759449010 0.000822405509904867 21 1.04 0.999371704265771 0.040628295734229 22 0.98 1.03896107262005 -0.0589610726200533 23 0.95 0.965044676824969 -0.0150446768249687 24 0.94 0.931493729259029 0.00850627074097143 25 0.94 0.923501437482628 0.0164985625173724 26 0.96 0.927395541097758 0.0326044589022422 27 0.97 0.955091068580646 0.0149089314193542 28 1.03 0.968609976587128 0.0613900234128717 29 1.01 1.04309966996819 -0.0330996699681891 30 0.99 1.01528725938108 -0.0252872593810838 31 1 0.989318787396393 0.0106812126036074 32 1 1.00183984028024 -0.00183984028023532 33 1.02 1.00140558858837 0.0185944114116308 34 1.01 1.02579436880016 -0.0157943688001607 35 0.99 1.01206647380454 -0.0220664738045426 36 0.98 0.986858193669533 -0.00685819366953311 37 1.01 0.975239475873139 0.0347605241268610 38 1.03 1.01344389262300 0.0165561073769958 39 1.03 1.03735157836965 -0.00735157836964762 40 1 1.03561640854040 -0.0356164085403967 41 0.96 0.997209980094944 -0.0372099800949444 42 0.97 0.948427425987332 0.0215725740126678 43 0.98 0.963519132514003 0.0164808674859969 44 1.02 0.977409059626752 0.0425909403732485 45 1.04 1.02746166479794 0.0125383352020634 46 1.01 1.05042104846464 -0.0404210484646446 47 1.01 1.01088059602900 -0.00088059602899837 48 1 1.01067275172884 -0.0106727517288432 49 1.01 0.998153695838555 0.0118463041614451 50 1.02 1.01094974160390 0.00905025839609785 51 1.03 1.02308584551605 0.00691415448395416 52 1.06 1.03471777156677 0.0252822284332341 53 1.12 1.07068505611272 0.0493149438872782 54 1.12 1.14232470660162 -0.0223247066016163 55 1.13 1.13705547659491 -0.00705547659490935 56 1.13 1.14539019473258 -0.0153901947325787 57 1.13 1.14175769566591 -0.0117576956659124 58 1.17 1.13898256388398 0.0310174361160243 59 1.14 1.18630351138981 -0.0463035113898143 60 1.08 1.1453746398044 -0.0653746398043995 61 1.07 1.06994446999827 5.55300017324178e-05 62 1.12 1.05995757656924 0.060042423430765 63 1.14 1.1241292001817 0.0158707998183003 64 1.21 1.14787513494919 0.0621248650508095 65 1.2 1.23253827068172 -0.0325382706817186 66 1.23 1.21485836539552 0.0151416346044750 67 1.29 1.24843219760001 0.0415678023999917 68 1.31 1.31824331474603 -0.00824331474602524 69 1.37 1.33629767119560 0.0337023288043965 70 1.35 1.40425232544486 -0.0542523254448641 71 1.26 1.37144732037720 -0.111447320377204 72 1.26 1.25514276125452 0.00485723874547528 73 1.28 1.25628919997841 0.0237108000215931 74 1.28 1.28188558523830 -0.00188558523830396 75 1.27 1.28144053650843 -0.0114405365084294 76 1.35 1.26874026280097 0.0812597371990282 77 1.37 1.36791974198639 0.00208025801361011 78 1.37 1.38841073871672 -0.0184107387167216 79 1.4 1.38406531019114 0.0159346898088550 80 1.4 1.41782632471137 -0.0178263247113675 81 1.28 1.41361883357813 -0.133618833578129 82 1.23 1.26208120220338 -0.0320812022033847 83 1.23 1.20450917734689 0.0254908226531068 84 1.25 1.21052569572791 0.0394743042720913 85 1.21 1.23984269112123 -0.0298426911212251 86 1.22 1.19279901496714 0.0272009850328647 87 1.29 1.20921917757464 0.0807808224253621 88 1.32 1.29828562001825 0.0217143799817516 89 1.36 1.33341079656004 0.0265892034399642 90 1.36 1.37968656228993 -0.0196865622899272 91 1.37 1.37504000515491 -0.00504000515490599 92 1.32 1.38385042865251 -0.063850428652509 93 1.33 1.31878001359171 0.0112199864082903 94 1.36 1.33142823155544 0.0285717684445599 95 1.42 1.36817193584322 0.051828064156779 96 1.39 1.4404047501739 -0.0504047501738996 97 1.42 1.39850787614834 0.021492123851655 98 1.4 1.43358059427754 -0.0335805942775413 99 1.42 1.40565467264427 0.0143453273557343 100 1.44 1.42904055496325 0.0109594450367523 101 1.49 1.45162727816974 0.0383727218302607 102 1.54 1.51068427053767 0.0293157294623341 103 1.55 1.56760356959534 -0.0176035695953412 104 1.47 1.57344865464877 -0.103448654648767 105 1.47 1.46903199534139 0.000968004658608024 106 1.35 1.46926047042439 -0.119260470424392 107 1.2 1.32111179816687 -0.121111798166871 108 1.12 1.14252616286804 -0.0225261628680422 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 1.05720938377489 0.974382940229404 1.14003582732037 110 0.994418767549778 0.862733516921612 1.12610401817794 111 0.931628151324666 0.752165888191685 1.11109041445765 112 0.868837535099555 0.640316938306172 1.09735813189294 113 0.806046918874444 0.526493291668566 1.08560054608032 114 0.743256302649333 0.410454930498806 1.07605767479986 115 0.680465686424221 0.292128746301707 1.06880262654674 116 0.61767507019911 0.171512481897177 1.06383765850104 117 0.554884453973999 0.0486359683901463 1.06113293955785 118 0.492093837748887 -0.076456378478047 1.06064405397582 119 0.429303221523776 -0.203714045451235 1.06232048849879 120 0.366512605298665 -0.333084716270954 1.06610992686828

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/16bgv1264440808.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/16bgv1264440808.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/29kxm1264440808.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/29kxm1264440808.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/3d25j1264440808.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264440888bk6c38b14te71yg/3d25j1264440808.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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