exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 13:19:29 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/25/t1211743263coelcalfoyczxbq.htm/, Retrieved Sun, 25 May 2008 21:21:07 +0200

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Dataseries X:

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16.100 15.800 16.900 17.800 17.600 18.300 18.000 15.700 14.500 14.000 15.500 15.800 15.800 15.900 18.000 19.900 20.600 20.600 20.800 20.000 18.500 17.700 17.000 16.600 16.700 17.300 19.100 20.200 20.700 21.500 21.000 16.800 16.800 16.500 17.200 17.300 17.600 18.400 19.900 20.500 21.200 21.300 20.800 18.800 18.100 18.100 18.800 18.700 18.700 19.000 20.100 20.500 21.600 21.800 21.500 21.200 20.400 20.400 20.600 19.300 18.600 19.400 23.500 24.600 25.900 26.600 24.100 21.800 21.300 21.100 21.200 21.600

Text written by user:

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.713479405306526 beta 0.000573542998306538 gamma 0.982697728764368 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 15.8 15.0846527777778 0.715347222222215 14 15.9 15.5124415237590 0.387558476240956 15 18 17.6565183434285 0.343481656571484 16 19.9 19.5942878165249 0.305712183475109 17 20.6 20.4094013159086 0.190598684091420 18 20.6 20.5632950326430 0.0367049673569539 19 20.8 20.8324037719621 -0.0324037719621089 20 20 20.0271915890666 -0.0271915890665824 21 18.5 18.5173537308898 -0.0173537308898339 22 17.7 17.7603612139083 -0.0603612139082514 23 17 17.1143257097058 -0.114325709705835 24 16.6 16.7047408657827 -0.104740865782674 25 16.7 17.8075338245395 -1.10753382453946 26 17.3 16.8423594747473 0.457640525252714 27 19.1 19.0239748809975 0.0760251190025336 28 20.2 20.7601225807557 -0.560122580755731 29 20.7 20.924552229563 -0.224552229562999 30 21.5 20.7382267773663 0.7617732226337 31 21 21.5048082725798 -0.50480827257983 32 16.8 20.3634294147106 -3.56342941471062 33 16.8 16.3312982546762 0.468701745323813 34 16.5 15.9071554680422 0.592844531957795 35 17.2 15.7104101773316 1.48958982266844 36 17.3 16.4469768915516 0.853023108448372 37 17.6 17.9502492360665 -0.350249236066507 38 18.4 17.9658711811545 0.434128818845494 39 19.9 20.0230469528414 -0.123046952841381 40 20.5 21.4377479392110 -0.937747939210954 41 21.2 21.4267822367241 -0.226782236724112 42 21.3 21.5161260207658 -0.216126020765831 43 20.8 21.2275211295833 -0.427521129583308 44 18.8 19.2792689617513 -0.479268961751266 45 18.1 18.5833632120164 -0.483363212016389 46 18.1 17.514947066381 0.585052933618996 47 18.8 17.5651812080911 1.23481879190890 48 18.7 17.9406842219233 0.759315778076687 49 18.7 19.0382067377487 -0.338206737748724 50 19 19.2831831899690 -0.283183189968977 51 20.1 20.6713084119903 -0.571308411990277 52 20.5 21.5362278338246 -1.03622783382458 53 21.6 21.6545737103083 -0.0545737103082864 54 21.8 21.8692488202708 -0.0692488202708432 55 21.5 21.6254405117158 -0.125440511715766 56 21.2 19.8777937713175 1.32220622868251 57 20.4 20.4664352726871 -0.0664352726871158 58 20.4 19.9968704325988 0.403129567401241 59 20.6 20.1007368729603 0.499263127039665 60 19.3 19.8177317103542 -0.517731710354184 61 18.6 19.6947424407981 -1.0947424407981 62 19.4 19.4147864498598 -0.0147864498597698 63 23.5 20.9127392053708 2.5872607946292 64 24.6 23.9010784853506 0.698921514649442 65 25.9 25.5352752947619 0.364724705238064 66 26.6 26.0466107930178 0.553389206982214 67 24.1 26.2331067494480 -2.13310674944795 68 21.8 23.4617002593213 -1.66170025932128 69 21.3 21.5302394334239 -0.230239433423886 70 21.1 21.0757925748480 0.0242074251520243 71 21.2 20.9359952050286 0.264004794971402 72 21.6 20.1983152076934 1.40168479230663 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 21.2826359753601 19.5433571416870 23.0219148090332 74 22.0885907922456 19.9515861218212 24.2255954626701 75 24.3304988373269 21.8586058350457 26.8023918396081 76 24.9409002313303 22.1740446090904 27.7077558535703 77 25.9817535651759 22.9481921213736 29.0153150089782 78 26.2852573506205 23.0063442647242 29.5641704365167 79 25.3195477048674 21.8121527995197 28.8269426102151 80 24.2027169621496 20.4806019668758 27.9248319574234 81 23.8604889587413 19.9351564777996 27.7858214396831 82 23.6426475747132 19.5238971357005 27.7613980137259 83 23.5537784241359 19.2500879926620 27.8574688556099 84 22.9486387773772 18.4674364217207 27.4298411330338

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/1edgo1211743163.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/1edgo1211743163.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/2puaa1211743163.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/2puaa1211743163.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/3zcbi1211743163.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211743263coelcalfoyczxbq/3zcbi1211743163.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=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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