*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 12:29:27 +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/Jun/02/t127548180920p72znewyigipt.htm/, Retrieved Wed, 02 Jun 2010 14:30:10 +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/Jun/02/t127548180920p72znewyigipt.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 «

306 303 344 254 309 310 379 294 356 318 405 545 268 243 273 273 236 222 302 285 309 322 362 471 198 253 173 186 185 105 228 214 189 270 277 378 185 182 258 179 197 168 250 211 260 234 305 347 203 217 227 242 185 175 252 319 202 254 336 431 150 280 187 279 193 227 225 205 259 254 275 394 159 230 188 195 189 220 274

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.215289717700249 beta 0.032381255659449 gamma 0.187381168803615 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 268 293.967403205295 -25.9674032052949 14 243 261.279066016922 -18.2790660169215 15 273 287.52216433785 -14.5221643378497 16 273 282.154029536538 -9.15402953653762 17 236 240.052393908794 -4.05239390879376 18 222 225.321974382947 -3.32197438294742 19 302 331.62591223883 -29.6259122388303 20 285 251.252910722602 33.7470892773981 21 309 313.420014435399 -4.42001443539868 22 322 276.642808039274 45.3571919607256 23 362 362.153841458186 -0.153841458186321 24 471 490.446318134576 -19.4463181345757 25 198 237.556905757886 -39.5569057578857 26 253 207.144754599583 45.8552454004175 27 173 242.749178750529 -69.749178750529 28 186 225.533027265585 -39.5330272655852 29 185 185.187465645161 -0.18746564516124 30 105 173.356597197516 -68.356597197516 31 228 228.919913889412 -0.919913889411617 32 214 180.486255372186 33.5137446278141 33 189 220.432903705423 -31.4329037054227 34 270 191.480284597071 78.5197154029286 35 277 254.895825490684 22.1041745093161 36 378 346.342019413936 31.6579805860641 37 185 167.750604816957 17.2493951830433 38 182 163.144611053542 18.8553889464584 39 258 172.065508197891 85.9344918021087 40 179 192.634343570042 -13.6343435700416 41 197 166.783008331636 30.2169916683642 42 168 152.746752281694 15.2532477183061 43 250 242.962670714408 7.03732928559191 44 211 200.513201229313 10.486798770687 45 260 229.484165491913 30.5158345080868 46 234 231.534012801734 2.46598719826557 47 305 275.103369497467 29.8966305025329 48 347 379.766922808021 -32.7669228080214 49 203 178.917805007184 24.0821949928156 50 217 177.136699081127 39.8633009188732 51 227 202.584847139445 24.4151528605552 52 242 196.242570849108 45.7574291508921 53 185 189.642691850002 -4.64269185000157 54 175 165.731390742943 9.26860925705742 55 252 260.478030455908 -8.47803045590757 56 319 214.338386057477 104.661613942523 57 202 273.969829179295 -71.9698291792946 58 254 250.969535770226 3.03046422977351 59 336 304.68157241278 31.3184275872205 60 431 411.224970251101 19.775029748899 61 150 207.729195404114 -57.7291954041145 62 280 191.141876445533 88.8581235544666 63 187 227.712173791822 -40.712173791822 64 279 210.739884928704 68.2601150712957 65 193 201.106681466562 -8.10668146656226 66 227 178.04668372773 48.9533162722699 67 225 290.934832372585 -65.9348323725854 68 205 246.610130541036 -41.6101305410363 69 259 247.458533606376 11.5414663936241 70 254 254.071138930979 -0.0711389309789752 71 275 312.311437781 -37.3114377809997 72 394 398.862204264107 -4.86220426410745 73 159 188.910702268935 -29.9107022689349 74 230 198.495777349578 31.504222650422 75 188 203.293034542196 -15.2930345421961 76 195 206.610537141597 -11.6105371415968 77 189 172.665527834917 16.3344721650835 78 220 163.926313913599 56.0736860864014 79 274 251.899514837094 22.1004851629063 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 80 231.040701285538 203.79212270492 258.289279866156 81 249.081469270314 216.3841820279 281.778756512728 82 251.865806467589 214.621021325775 289.110591609402 83 304.523245620927 258.040081787761 351.006409454093 84 406.817217799833 343.993209779305 469.641225820362 85 189.373513740147 150.07934087527 228.667686605025 86 216.730358229146 169.517939860746 263.942776597546 87 208.114207807038 158.498575390571 257.729840223504 88 216.359196790053 161.365443341128 271.352950238978 89 187.825570647375 135.064044334421 240.587096960329 90 181.062987484556 126.105756282967 236.020218686145 91 250.825740951645 167.49845593819 334.153025965099

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/1r9zx1275481763.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/1r9zx1275481763.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/22jzi1275481763.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/22jzi1275481763.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/32jzi1275481763.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t127548180920p72znewyigipt/32jzi1275481763.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=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