Exponential Smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 15 Aug 2010 13:34:13 +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/Aug/15/t1281879218q17g9ugb8huqey9.htm/, Retrieved Sun, 15 Aug 2010 15:33:43 +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/2010/Aug/15/t1281879218q17g9ugb8huqey9.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:

Sebastien Delforge

Dataseries X:

» Textbox « » Textfile « » CSV «

75 74 73 71 91 90 75 65 66 66 67 69 75 79 75 77 100 100 94 83 83 83 84 88 89 98 94 84 111 98 98 83 79 78 80 94 98 104 94 90 115 104 114 99 96 98 104 111 117 125 117 118 151 145 155 133 124 125 131 133 136 141 130 137 177 183 191 166 156 153 164 164 168 173 164 165 205 207 215 190 169 175 188 188 196 201 194 197 237 236 244 222 195 199 207 204 212 222 214 217 258 256 251 223 198 206 214 212 227 238 228 235 275 278 278 251 225 232 238 239

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.582467316896955 beta 0.00891834531619204 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 75 71.579117470209 3.42088252979096 14 79 77.0417429649607 1.95825703503931 15 75 73.8751102584585 1.12488974154145 16 77 76.2055124857065 0.794487514293508 17 100 99.1724884770231 0.827511522976863 18 100 99.1691129035015 0.830887096498472 19 94 86.8250668746314 7.17493312536855 20 83 79.6402467437201 3.3597532562799 21 83 83.547765386508 -0.547765386508033 22 83 83.8698614938643 -0.869861493864306 23 84 84.9372723263794 -0.937272326379414 24 88 87.0332329349251 0.966767065074876 25 89 96.6679258409937 -7.66792584099373 26 98 95.4910926668568 2.50890733314324 27 94 91.0408971193895 2.95910288061047 28 84 94.4670000951766 -10.4670000951766 29 111 114.002231882253 -3.00223188225321 30 98 111.515075359236 -13.5150753592364 31 98 92.8116759230373 5.18832407696266 32 83 82.4776995108891 0.52230048911089 33 79 82.995508253576 -3.99550825357606 34 78 81.0633203144457 -3.06332031444572 35 80 80.6627344700765 -0.662734470076529 36 94 83.466386435808 10.5336135641920 37 98 94.8970385619155 3.10296143808446 38 104 104.739779441506 -0.739779441506158 39 94 98.069994250363 -4.06999425036301 40 90 91.3143922810225 -1.31439228102251 41 115 121.363623452776 -6.36362345277631 42 104 111.628450526258 -7.62845052625785 43 114 103.665377149401 10.3346228505994 44 99 92.4345999625616 6.56540003743835 45 96 94.1401802610363 1.85981973896368 46 98 96.0049210741856 1.99507892581435 47 104 100.000535770001 3.99946422999894 48 111 111.851768129400 -0.851768129399588 49 117 113.786473135019 3.21352686498066 50 125 123.102946923099 1.89705307690106 51 117 114.913541072180 2.08645892781986 52 118 111.996820121169 6.00317987883086 53 151 152.048150724256 -1.04815072425623 54 145 142.462568811754 2.53743118824551 55 155 148.943630074048 6.05636992595183 56 133 127.007557026211 5.9924429737887 57 124 124.972449397232 -0.972449397231827 58 125 125.350525044817 -0.350525044816536 59 131 129.655480030022 1.34451996997751 60 133 139.703546686813 -6.7035466868129 61 136 140.687307443733 -4.68730744373258 62 141 145.939995819250 -4.93999581924956 63 130 132.380154852621 -2.38015485262147 64 137 127.994001089578 9.00599891042238 65 177 171.037958376327 5.96204162367269 66 183 165.714584288692 17.2854157113084 67 191 183.413672571252 7.58632742874761 68 166 156.742893254485 9.25710674551544 69 156 151.742566895054 4.25743310494568 70 153 155.612386256077 -2.61238625607706 71 164 160.407196445408 3.59280355459228 72 164 169.611598706644 -5.61159870664358 73 168 173.346368825837 -5.346368825837 74 173 179.921105711391 -6.92110571139114 75 164 163.774430456826 0.225569543173833 76 165 165.823052935499 -0.823052935498822 77 205 209.226785901903 -4.22678590190284 78 207 201.388714160593 5.61128583940683 79 215 208.430003350338 6.5699966496615 80 190 178.215724439122 11.7842755608785 81 169 171.021462214153 -2.02146221415273 82 175 168.109714185753 6.89028581424708 83 188 182.010331040053 5.98966895994653 84 188 189.033257888467 -1.03325788846652 85 196 196.448183339317 -0.448183339317040 86 201 206.546299973469 -5.54629997346905 87 194 192.483184874036 1.51681512596366 88 197 195.010481749747 1.98951825025298 89 237 246.507635701937 -9.50763570193737 90 236 239.313466768335 -3.31346676833502 91 244 241.981439352066 2.01856064793424 92 222 206.79960194735 15.2003980526502 93 195 193.048149520651 1.95185047934939 94 199 196.295422792557 2.70457720744298 95 207 208.467525120273 -1.46752512027308 96 204 208.164704095828 -4.16470409582845 97 212 214.661651522177 -2.66165152217744 98 222 221.897401194890 0.10259880510975 99 214 213.138230107485 0.861769892514872 100 217 215.551677157162 1.44832284283794 101 258 266.180957549843 -8.18095754984313 102 256 262.297655250605 -6.29765525060452 103 251 265.966797634245 -14.9667976342448 104 223 224.309114938151 -1.30911493815077 105 198 195.072815610504 2.92718438949615 106 206 199.080799111661 6.91920088833854 107 214 212.012744660210 1.98725533978958 108 212 212.431008420139 -0.431008420138539 109 227 221.979080405085 5.02091959491511 110 238 235.329919906229 2.67008009377139 111 228 227.702735963454 0.297264036545982 112 235 230.059536786222 4.94046321377769 113 275 281.870930309566 -6.87093030956606 114 278 279.503066021618 -1.50306602161754 115 278 282.328962909445 -4.32896290944456 116 251 249.357458106118 1.64254189388222 117 225 220.257362897708 4.74263710229155 118 232 227.35953405341 4.6404659465901 119 238 237.625245816383 0.374754183617227 120 239 235.824067154534 3.17593284546595 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 251.1088672358 240.52074376064 261.69699071096 122 261.464424671384 249.070684296064 273.858165046704 123 250.203866503083 236.587899360919 263.819833645247 124 254.614317446025 239.510934443462 269.717700448589 125 302.133271215603 283.957250309501 320.309292121705 126 306.290578728036 286.870341332535 325.710816123537 127 308.955498146876 288.403364221524 329.507632072229 128 277.805810956971 257.919400928858 297.692220985084 129 245.87418933481 226.758238921605 264.990139748015 130 250.464546900181 230.061061653823 270.868032146540 131 256.615329917521 234.853633299169 278.377026535872 132 255.597555892736 234.521485435768 276.673626349703

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/1s2gy1281879251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/1s2gy1281879251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/2lbg01281879251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/2lbg01281879251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/3lbg01281879251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/15/t1281879218q17g9ugb8huqey9/3lbg01281879251.ps (open in new window)

Parameters (Session):

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=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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by