*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 15 Jan 2011 15:33:55 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2.htm/, Retrieved Sat, 15 Jan 2011 16:32:12 +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/2011/Jan/15/t1295105532khhb5u9s5qmuzn2.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

1,35 1,91 1,31 1,19 1,3 1,14 1,1 1,02 1,11 1,18 1,24 1,36 1,29 1,73 1,41 1,15 1,31 1,15 1,08 1,1 1,14 1,24 1,33 1,49 1,38 1,96 1,36 1,24 1,35 1,23 1,09 1,08 1,33 1,35 1,38 1,5 1,47 2,09 1,52 1,29 1,52 1,27 1,35 1,29 1,41 1,39 1,45 1,53 1,45 2,11 1,53 1,38 1,54 1,35 1,29 1,33 1,47 1,47 1,54 1,59 1,5 2 1,51 1,4 1,62 1,44 1,29 1,28 1,4 1,39 1,46 1,49

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 0.253682747786366 beta 0.000800115960723572 gamma 0.477115909808832 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.29 1.29367788461538 -0.00367788461538465 14 1.73 1.73173450683460 -0.00173450683460397 15 1.41 1.40820044507331 0.00179955492668693 16 1.15 1.14639661240958 0.00360338759042489 17 1.31 1.30255111237233 0.00744888762766527 18 1.15 1.13676599462704 0.0132340053729614 19 1.08 1.10620114762802 -0.0262011476280224 20 1.1 1.03104363112894 0.0689563688710586 21 1.14 1.14337326468262 -0.00337326468261945 22 1.24 1.21152010002621 0.0284798999737896 23 1.33 1.28150331443076 0.0484966855692428 24 1.49 1.41449095231828 0.0755090476817237 25 1.38 1.36428686639987 0.0157131336001277 26 1.96 1.80800172959252 0.151998270407481 27 1.36 1.52480370987104 -0.164803709871041 28 1.24 1.22142227579602 0.0185777242039793 29 1.35 1.38279231521622 -0.0327923152162248 30 1.23 1.20889799792844 0.02110200207156 31 1.09 1.16632799579539 -0.0763279957953855 32 1.08 1.11236859355169 -0.0323685935516942 33 1.33 1.17324889983714 0.156751100162864 34 1.35 1.29340148657753 0.0565985134224749 35 1.38 1.37769388213319 0.00230611786680979 36 1.5 1.50862135208323 -0.00862135208323411 37 1.47 1.41580466431340 0.0541953356865976 38 2.09 1.91783994656133 0.172160053438669 39 1.52 1.52698367819881 -0.00698367819880663 40 1.29 1.32900277942220 -0.0390027794221977 41 1.52 1.45752800113321 0.0624719988667861 42 1.27 1.32706481055688 -0.0570648105568776 43 1.35 1.23003004726162 0.119969952738380 44 1.29 1.24161861656809 0.0483813834319089 45 1.41 1.39043941036186 0.0195605896381372 46 1.39 1.44021287072182 -0.0502128707218179 47 1.45 1.47814100934692 -0.0281410093469177 48 1.53 1.59751171241841 -0.0675117124184088 49 1.45 1.51216955442677 -0.0621695544267717 50 2.11 2.02671255198124 0.0832874480187589 51 1.53 1.54952595070233 -0.0195259507023304 52 1.38 1.33696397591979 0.0430360240802086 53 1.54 1.52245283931432 0.0175471606856790 54 1.35 1.33803791664287 0.0119620833571257 55 1.29 1.32157617716061 -0.03157617716061 56 1.33 1.26922168414342 0.0607783158565791 57 1.47 1.41092020085845 0.0590797991415499 58 1.47 1.44587744060575 0.0241225593942467 59 1.54 1.51054098840056 0.0294590115994395 60 1.59 1.63053484926045 -0.0405348492604511 61 1.5 1.55397410606957 -0.0539741060695722 62 2 2.12242773165260 -0.122427731652603 63 1.51 1.55644048390593 -0.0464404839059258 64 1.4 1.35931787464009 0.0406821253599117 65 1.62 1.53512310709864 0.084876892901357 66 1.44 1.36580309161081 0.0741969083891871 67 1.29 1.34964203821004 -0.0596420382100389 68 1.28 1.32306347764545 -0.0430634776454544 69 1.4 1.43780342253298 -0.0378034225329817 70 1.39 1.43570493454025 -0.0457049345402489 71 1.46 1.48450992384668 -0.0245099238466782 72 1.49 1.56583370910222 -0.0758337091022239 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.47546995564724 1.35057403958556 1.60036587170891 74 2.03318903034457 1.90433070146691 2.16204735922222 75 1.52529006770324 1.39258152860566 1.65799860680082 76 1.37095359371359 1.23449754430929 1.50740964311789 77 1.55214946226665 1.41204035686905 1.69225856766426 78 1.35745161222035 1.21377669574706 1.50112652869363 79 1.27475256904171 1.12759273984494 1.42191239823849 80 1.26916139741412 1.11859193232407 1.41973086250416 81 1.39666148572462 1.24275265435434 1.55057031709490 82 1.40130986044772 1.24412744958904 1.55849227130640 83 1.46923615173132 1.30884191607564 1.62963038738701 84 1.53848692444765 1.37493897642088 1.70203487247443

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/18gkv1295105631.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/18gkv1295105631.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/2o4py1295105631.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/2o4py1295105631.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/3iaqr1295105631.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295105532khhb5u9s5qmuzn2/3iaqr1295105631.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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