ws 9 theorie 2

*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 12:32:15 -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/t1259955185606htjzu5ua42i1.htm/, Retrieved Fri, 04 Dec 2009 20:33:09 +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/t1259955185606htjzu5ua42i1.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:

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100.01 103.84 104.48 95.43 104.80 108.64 105.65 108.42 115.35 113.64 115.24 100.33 101.29 104.48 99.26 100.11 103.52 101.18 96.39 97.56 96.39 85.10 79.77 79.13 80.84 82.75 92.55 96.60 96.92 95.32 98.52 100.22 104.91 103.10 97.13 103.42 111.72 118.11 111.62 100.22 102.03 105.76 107.68 110.77 105.44 112.26 114.07 117.90 124.72 126.42 134.73 135.79 143.36 140.37 144.74 151.98 150.92 163.38 154.43 146.66 157.95 162.10 180.42 179.57 171.58 185.43 190.64 203.00 202.36 193.41 186.17 192.24 209.60 206.41 209.82 230.37 235.80 232.07 244.64 242.19 217.48 209.39 211.73 221.00 203.11 214.71 224.19 238.04 238.36 246.24 259.87 249.97 266.48 282.98 306.31 301.73 314.62 332.62 355.51 370.32 408.13 433.58 440.51 386.29 342.84 254.97 203.42 170.09 174.03 167.85 177.01 188.19 211.20 240.91 230.26 251.25 241.66

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 0.920153543184328 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 101.29 102.550463407594 -1.26046340759406 14 104.48 104.602730522094 -0.122730522094429 15 99.26 99.6753984574467 -0.415398457446727 16 100.11 101.289862238172 -1.17986223817176 17 103.52 105.559180439175 -2.0391804391746 18 101.18 102.963286964500 -1.78328696450015 19 96.39 94.8978731140655 1.49212688593451 20 97.56 97.8852964365457 -0.325296436545713 21 96.39 103.119535295576 -6.72953529557613 22 85.1 94.6332701866511 -9.53327018665112 23 79.77 86.0655769472826 -6.29557694728264 24 79.13 69.3506367448069 9.77936325519308 25 80.84 78.7549356119757 2.08506438802434 26 82.75 83.1372271531058 -0.387227153105812 27 92.55 78.7840533402804 13.7659466597196 28 96.6 93.1695274464866 3.43047255351337 29 96.92 101.377299851777 -4.45729985177677 30 95.32 96.564852267570 -1.24485226756993 31 98.52 89.5592530805919 8.96074691940808 32 100.22 99.3075764402621 0.912423559737888 33 104.91 105.290777026023 -0.380777026023466 34 103.1 102.191592970719 0.908407029281022 35 97.13 103.729976358562 -6.59997635856163 36 103.42 85.9232096367148 17.4967903632852 37 111.72 101.977383578408 9.74261642159215 38 118.11 114.357394470627 3.7526055293734 39 111.62 113.850245539943 -2.230245539943 40 100.22 113.035460127926 -12.8154601279261 41 102.03 105.902646682722 -3.87264668272198 42 105.76 101.906100937249 3.85389906275057 43 107.68 99.8913280485863 7.78867195141372 44 110.77 108.064869657110 2.70513034289016 45 105.44 116.205272156857 -10.7652721568571 46 112.26 103.629579518495 8.63042048150494 47 114.07 111.71903784818 2.35096215181997 48 117.9 102.259219751822 15.6407802481777 49 124.72 115.932235382006 8.78776461799356 50 126.42 127.359399204059 -0.939399204058844 51 134.73 121.795170688827 12.9348293111733 52 135.79 134.183278729583 1.60672127041653 53 143.36 143.222880571604 0.137119428395977 54 140.37 143.942195012112 -3.57219501211239 55 144.74 133.894603119323 10.8453968806771 56 151.98 144.951847490197 7.02815250980285 57 150.92 157.886378739035 -6.9663787390354 58 163.38 150.177182940924 13.2028170590756 59 154.43 162.202177118590 -7.7721771185904 60 146.66 140.773339567004 5.88666043299571 61 157.95 144.755250911963 13.1947490880372 62 162.1 160.333704216974 1.76629578302607 63 180.42 157.465026378038 22.9549736219623 64 179.57 178.292686484971 1.27731351502882 65 171.58 189.580964914839 -18.0009649148392 66 185.43 173.545805315572 11.8841946844279 67 190.64 177.291228069076 13.3487719309241 68 203 190.815585017929 12.1844149820714 69 202.36 209.395850986913 -7.03585098691346 70 193.41 203.538037353040 -10.1280373530402 71 186.17 192.212178995332 -6.04217899533177 72 192.24 170.861457906277 21.3785420937233 73 209.6 189.562102051625 20.0378979483749 74 206.41 211.583459744775 -5.17345974477499 75 209.82 203.195042896616 6.62495710338416 76 230.37 207.069720475956 23.3002795240444 77 235.8 239.475619716213 -3.67561971621279 78 232.07 240.352155936019 -8.28215593601874 79 244.64 223.98075029129 20.65924970871 80 242.19 244.617380800953 -2.42738080095259 81 217.48 249.497595313175 -32.0175953131751 82 209.39 220.472571918630 -11.0825719186305 83 211.73 208.508698783079 3.22130121692123 84 221 195.932941862973 25.0670581370273 85 203.11 217.721859797283 -14.6118597972831 86 214.71 205.777093583481 8.93290641651939 87 224.19 211.225945582753 12.9640544172466 88 238.04 222.074437893810 15.9655621061904 89 238.36 245.841137318728 -7.48113731872832 90 246.24 242.889907364607 3.35009263539334 91 259.87 239.06069226031 20.8093077396901 92 249.97 258.024929564917 -8.05492956491722 93 266.48 255.205291429979 11.2747085700207 94 282.98 268.294449726952 14.6855502730481 95 306.31 281.265227373421 25.0447726265787 96 301.73 284.538305920824 17.1916940791764 97 314.62 294.501688287106 20.1183117128938 98 332.62 318.626349263052 13.9936507369484 99 355.51 328.080495580866 27.4295044191337 100 370.32 352.340395720063 17.979604279937 101 408.13 380.485158421405 27.6448415785947 102 433.58 414.694198974621 18.8858010253791 103 440.51 422.813281062557 17.6967189374425 104 386.29 435.441061327431 -49.1510613274305 105 342.84 400.222905935782 -57.3829059357818 106 254.97 351.509404824083 -96.5394048240827 107 203.42 262.739092371358 -59.3190923713579 108 170.09 193.980810218526 -23.8908102185262 109 174.03 168.390105644253 5.63989435574683 110 167.85 176.012232952996 -8.1622329529965 111 177.01 166.826799469627 10.1832005303732 112 188.19 174.892212235496 13.2977877645044 113 211.2 192.890568864660 18.3094311353403 114 240.91 213.433724813631 27.4762751863690 115 230.26 233.155433530494 -2.89543353049393 116 251.25 225.150196244658 26.0998037553421 117 241.66 254.445458589964 -12.7854585899641 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 118 241.267117570009 205.495043998350 277.039191141669 119 242.915317003428 194.071266861086 291.759367145769 120 229.23257997572 172.282020809341 286.183139142099 121 227.813035915904 162.157040952779 293.469030879029 122 229.770997095142 155.641243594516 303.900750595768 123 229.728772663041 148.396942294544 311.060603031539 124 228.513633017624 140.898044244985 316.129221790262 125 236.037082278896 139.504752943477 332.569411614314 126 240.828593914365 136.688345597029 344.968842231701 127 232.842577490626 126.509019616902 339.176135364351 128 229.589120588057 119.311451647316 339.866789528798 129 231.457709368691 112.476456961079 350.438961776304

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/19ejg1259955133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/19ejg1259955133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/2nbk31259955133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/2nbk31259955133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/3uair1259955133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955185606htjzu5ua42i1/3uair1259955133.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=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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