*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: Fri, 04 Dec 2009 08:54:01 -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/04/t12599420750cwz9m4lwwcefql.htm/, Retrieved Fri, 04 Dec 2009 16:54:39 +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/04/t12599420750cwz9m4lwwcefql.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:

» Textbox « » Textfile « » CSV «

1258 1199 1158 1427 934 709 1186 986 1033 1257 1105 1179 1092 1092 1087 2028 2039 2010 754 760 715 855 971 815 915 843 761 1858 2968 4061 3661 3269 2857 2568 2274 1987 683 381 71 1772 3485 5181 4479 3782 3067 2489 1903 1330 736 483 242 1334 2423 3523 2986 2462 1908 1575 1237 904

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0918611009738237 beta 0 gamma 0.573855305728291 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1092 831.122281907311 260.877718092689 14 1092 884.385368902543 207.614631097457 15 1087 926.685512139121 160.314487860879 16 2028 1820.45916588127 207.540834118727 17 2039 1905.54726232992 133.452737670082 18 2010 1945.49246058456 64.5075394154394 19 754 1256.35942724446 -502.359427244458 20 760 1028.43268285001 -268.432682850010 21 715 1071.31431656251 -356.314316562514 22 855 1253.75893393566 -398.758933935659 23 971 1018.24150647733 -47.2415064773303 24 815 1009.71354350964 -194.713543509635 25 915 1048.28006942312 -133.280069423118 26 843 1034.69041122445 -191.690411224455 27 761 1014.27205040528 -253.272050405278 28 1858 1864.40755848404 -6.4075584840416 29 2968 1890.61702402758 1077.38297597242 30 4061 1981.20565836747 2079.79434163253 31 3661 1076.39106091919 2584.60893908081 32 3269 1222.16913104713 2046.83086895287 33 2857 1429.60795014985 1427.39204985015 34 2568 1892.25294110882 675.747058891177 35 2274 1912.41895570618 361.581044293823 36 1987 1772.07795251764 214.922047482356 37 683 1956.19662333999 -1273.19662333999 38 381 1765.2482088613 -1384.2482088613 39 71 1561.79859879052 -1490.79859879052 40 1772 3071.85565013228 -1299.85565013228 41 3485 3829.64255993234 -344.642559932339 42 5181 4404.72405087655 776.275949123447 43 4479 2988.20475036706 1490.79524963294 44 3782 2518.14827136534 1263.85172863466 45 3067 2244.13752371150 822.862476288496 46 2489 2247.78703064133 241.212969358671 47 1903 2064.61354447124 -161.613544471244 48 1330 1808.93008153061 -478.930081530609 49 736 1159.81561172641 -423.815611726414 50 483 942.078553689241 -459.078553689241 51 242 697.289305379152 -455.289305379152 52 1334 2394.35176643172 -1060.35176643172 53 2423 3683.39617061049 -1260.39617061049 54 3523 4735.9693980243 -1212.9693980243 55 2986 3536.81343804411 -550.813438044111 56 2462 2814.69982590468 -352.699825904685 57 1908 2249.49004861305 -341.490048613054 58 1575 1917.43744973985 -342.437449739849 59 1237 1561.28894104293 -324.288941042926 60 904 1212.35135642901 -308.351356429009 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 728.991369435192 -360.137355609836 1818.12009448022 62 561.081187886313 -535.149132818095 1657.31150859072 63 378.292057814204 -719.456226602321 1476.04034223073 64 1646.10196258095 220.087720173083 3072.11620498881 65 2837.25490505638 903.143132617573 4771.36667749518 66 3986.15390996687 1496.22854469116 6476.07927524258 67 3240.54471663342 1127.63318319338 5353.45625007346 68 2662.48403200613 823.446377126066 4501.5216868862 69 2119.55097013216 515.580849167985 3723.52109109634 70 1803.01609395140 322.150893732776 3283.88129417002 71 1466.04944222245 102.622129655648 2829.47675478924 72 1126.79135778182 487.520457495803 1766.06225806784

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/1a4641259942039.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/1a4641259942039.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/2l7ri1259942039.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/2l7ri1259942039.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/36ub91259942039.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599420750cwz9m4lwwcefql/36ub91259942039.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

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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