*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Jun 2010 14:15:29 +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/05/t1275747391eydbtrbylcywrg7.htm/, Retrieved Sat, 05 Jun 2010 16:16:31 +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/05/t1275747391eydbtrbylcywrg7.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 «

1664.81 2397.53 2840.71 3547.29 3752.96 3714.74 4349.61 3566.34 5021.82 6423.48 7600.60 19756.21 2499.81 5198.24 7225.14 4806.03 5900.88 4951.34 6179.12 4752.15 5496.43 5835.10 12600.08 28541.72 4717.02 5702.63 9957.58 5304.78 6492.43 6630.80 7349.62 8176.62 8573.17 9690.50 15151.84 34061.01 5921.10 5814.58 12421.25 6369.77 7609.12 7224.75 8121.22 7979.25 8093.06 8476.70 17914.66 30114.41 4826.64 6470.23 9638.77 8821.17 8722.37 10209.48 11276.55 12552.22 11637.39 13606.89 21822.11 45060.69 7615.03 9849.69 14558.40 11587.33 9332.56 13082.09 16732.78 19888.61 23933.38 25391.35 36024.80 80721.71 10243.24 11266.88 21826.84 17357.33 15997.79 18601.53 26155.15 28586.52 30505.41 30821.33 46634.38 104660.67

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 0.0218820013470966 beta 1 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2499.81 1442.11065705128 1057.69934294872 14 5198.24 4216.98507326975 981.254926730251 15 7225.14 6396.58272096476 828.557279035236 16 4806.03 4218.88411335655 587.145886643452 17 5900.88 5374.17461841729 526.705381582714 18 4951.34 4104.69918213418 846.64081786582 19 6179.12 5827.90910234919 351.210897650813 20 4752.15 5169.9615550515 -417.811555051501 21 5496.43 6576.9007877307 -1080.47078773070 22 5835.1 7956.12559695512 -2121.02559695512 23 12600.08 9134.81661613924 3465.26338386076 24 28541.72 21490.9862163605 7050.73378363948 25 4717.02 5715.70909868618 -998.689098686176 26 5702.63 8590.06100855337 -2887.43100855337 27 9957.58 10670.2402046897 -712.660204689728 28 5304.78 8323.55537984434 -3018.77537984434 29 6492.43 9362.785924832 -2870.355924832 30 6630.8 8279.53885680331 -1648.73885680331 31 7349.62 9356.58031188177 -2006.96031188177 32 8176.62 7736.25940935995 440.360590640047 33 8573.17 8374.01962039411 199.150379605891 34 9690.5 8651.6617631101 1038.83823688991 35 15151.84 15320.8929183157 -169.052918315658 36 34061.01 30982.3696152979 3078.64038470207 37 5921.1 7037.79247075986 -1116.69247075986 38 5814.58 7850.47035009641 -2035.89035009641 39 12421.25 11883.4194163748 537.830583625248 40 6369.77 7142.76230407558 -772.992304075576 41 7609.12 8259.76627715667 -650.64627715667 42 7224.75 8352.00768933597 -1127.25768933597 43 8121.22 9033.51954392351 -912.299543923514 44 7979.25 9798.31620205185 -1819.06620205185 45 8093.06 10068.6583729870 -1975.59837298696 46 8476.7 10990.3934007887 -2513.69340078874 47 17914.66 16193.0584062714 1721.60159372864 48 30114.41 34906.5354178772 -4792.12541787723 49 4826.64 6347.97321754052 -1521.33321754052 50 6470.23 5905.6320364054 564.597963594599 51 9638.77 12222.7109280304 -2583.94092803038 52 8821.17 5773.11630715854 3048.05369284146 53 8722.37 6818.52595789346 1903.84404210654 54 10209.48 6281.50458368025 3927.97541631975 55 11276.55 7175.53015812463 4101.01984187537 56 12552.22 7164.44562171028 5387.77437828972 57 11637.39 7598.42318225773 4038.96681774227 58 13606.89 8416.10145367728 5190.78854632272 59 21822.11 18389.2166432832 3432.89335671677 60 45060.69 31265.6354398877 13795.0545601123 61 7615.03 7216.43227988702 398.597720112984 62 9849.69 9801.81541571563 47.8745842843691 63 14558.4 13962.0634179994 596.336582000629 64 11587.33 14094.5243893338 -2507.19438933385 65 9332.56 14781.3515428740 -5448.79154287396 66 13082.09 16784.5382363052 -3702.4482363052 67 16732.78 18235.1429173245 -1502.3629173245 68 19888.61 19791.7198746731 96.890125326856 69 23933.38 19106.5311617616 4826.84883823835 70 25391.35 21401.2096825952 3990.14031740477 71 36024.8 29935.4930251932 6089.30697480676 72 80721.71 53370.4531563743 27351.2568436257 73 10243.24 17176.2054264752 -6932.96542647522 74 11266.88 19759.3155481584 -8492.43554815835 75 21826.84 24583.4708185425 -2756.63081854247 76 17357.33 21847.8988074668 -4490.56880746677 77 15997.79 19811.6525941686 -3813.86259416864 78 18601.53 23792.0760980126 -5190.54609801263 79 26155.15 27562.8301822428 -1407.68018224283 80 28586.52 30888.5779340407 -2302.05793404075 81 30505.41 34927.7001630747 -4422.29016307467 82 30821.33 36149.5466525105 -5328.21665251051 83 46634.38 46277.2113898907 357.168610109307 84 104660.67 90002.0590601568 14658.6109398432 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 19336.9378138813 9416.57292639255 29257.3027013701 86 20038.9983093786 10109.1377888585 29968.8588298986 87 30337.6994041606 20386.5068382857 40288.8919700354 88 25705.1931316368 15716.1894121775 35694.1968510962 89 24266.1118055363 14218.3130088962 34313.9106021764 90 26903.8900161447 16772.0256880793 37035.75434421 91 34522.3510863972 24277.1725692074 44767.5296035869 92 37068.9357914634 26677.6158490267 47460.2557339002 93 39199.8090558353 28626.4244566946 49773.193654976 94 39844.3043641751 29050.3837010006 50638.2250273495 95 55978.1141085073 44923.2256161348 67033.0026008798 96 114004.404108507 102646.753999570 125362.054217444

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/1j0cd1275747324.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/1j0cd1275747324.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/2urby1275747324.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/2urby1275747324.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/3urby1275747324.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275747391eydbtrbylcywrg7/3urby1275747324.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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