Exponential smoothing triple multiplicative

*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: Sat, 18 Dec 2010 13:02:21 +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/Dec/18/t1292677201bm7q0w831oeztug.htm/, Retrieved Sat, 18 Dec 2010 14:00:01 +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/Dec/18/t1292677201bm7q0w831oeztug.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:

Dataseries X:

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37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.445417135362361 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 80 47.875 32.125 14 42 62.1840254735159 -20.1840254735159 15 54 53.1937146670215 0.806285332978497 16 66 53.5528479703215 12.4471520296785 17 81 59.0970227708007 21.9029772291993 18 63 68.8529841441377 -5.85298414413768 19 137 66.2459647133345 70.7540352866655 20 72 97.7610244260485 -25.7610244260485 21 107 86.2866227221982 20.7133772778018 22 58 95.5127158929565 -37.5127158929565 23 36 78.8039094402537 -42.8039094402537 24 52 59.738314715066 -7.73831471506595 25 79 56.2915367421489 22.7084632578511 26 77 66.4062753949424 10.5937246050576 27 54 71.1249018613449 -17.1249018613449 28 84 63.4971771309031 20.5028228690969 29 48 72.6294857600981 -24.6294857600981 30 96 61.6590907673872 34.3409092326128 31 83 76.9551201835164 6.04487981648356 32 66 79.6476132349843 -13.6476132349843 33 61 73.5687324433242 -12.5687324433242 34 53 67.9704036432827 -14.9704036432827 35 30 61.3023293372735 -31.3023293372735 36 74 47.3597354736959 26.6402645263041 37 69 59.2257657842978 9.77423421570218 38 59 63.5793771890167 -4.57937718901666 39 42 61.5396441197411 -19.5396441197411 40 65 52.836351809926 12.1636481900740 41 70 58.2542491423043 11.7457508576957 42 100 63.4860078420191 36.5139921579809 43 63 79.7499656296707 -16.7499656296707 44 105 72.2892439214848 32.7107560785152 45 82 86.859175189514 -4.85917518951398 46 81 84.6948152963768 -3.6948152963768 47 75 83.0490812513716 -8.04908125137162 48 102 79.4638825380868 22.5361174619132 49 121 89.5018554201619 31.4981445798381 50 98 103.531668748143 -5.53166874814286 51 76 101.067768700572 -25.0677687005716 52 77 89.9021549760367 -12.9021549760367 53 63 84.1553140666092 -21.1553140666092 54 37 74.732374677369 -37.7323746773691 55 35 57.925728438156 -22.9257284381560 56 23 47.7142161511371 -24.7142161511371 57 40 36.7060807903714 3.29391920962857 58 29 38.1732488488392 -9.17324884883924 59 37 34.0873266246232 2.91267337537681 60 51 35.3846812557297 15.6153187442703 61 20 42.3400117985728 -22.3400117985728 62 28 32.3893877392911 -4.38938773929114 63 13 30.4342792264614 -17.4342792264614 64 22 22.6687525163034 -0.668752516303439 65 25 22.3708786862252 2.62912131377481 66 13 23.5419343703269 -10.5419343703269 67 16 18.8463761619179 -2.84637616191787 68 13 17.5785514457127 -4.5785514457127 69 16 15.5391861766541 0.46081382334585 70 17 15.7444405497842 1.25555945021576 71 9 16.3036882433765 -7.30368824337648 72 17 13.0505003484320 3.94949965156803 73 25 14.8096751693480 10.1903248306520 74 14 19.3486204638290 -5.34862046382898 75 8 16.9662532586898 -8.96625325868977 76 7 12.9725304172707 -5.97253041727074 77 10 10.3122630279454 -0.312263027945436 78 7 10.1731757245584 -3.1731757245584 79 10 8.75978888332421 1.24021111667579 80 3 9.3122001661585 -6.3122001661585 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 6.50063805031436 NA NA 82 6.50063805031436 NA NA 83 6.50063805031436 NA NA 84 6.50063805031436 NA NA 85 6.50063805031436 NA NA 86 6.50063805031436 NA NA 87 6.50063805031436 NA NA 88 6.50063805031436 NA NA 89 6.50063805031436 NA NA 90 6.50063805031436 NA NA 91 6.50063805031436 NA NA 92 6.50063805031436 NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/1lxzs1292677337.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/1lxzs1292677337.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/2e7zd1292677337.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/2e7zd1292677337.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/3e7zd1292677337.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677201bm7q0w831oeztug/3e7zd1292677337.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

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