Jonas Cloots, smoothing, eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:28:47 +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/May/18/t1305728677lrwphkx2ximmsiw.htm/, Retrieved Wed, 18 May 2011 16:24:49 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

193.230 199.068 195.076 191.563 191.067 186.665 185.508 184.371 183.046 175.714 175.768 171.029 170.465 170.102 156.389 124.291 99.360 86.675 85.056 128.236 164.257 162.401 152.779 156.005 153.387 153.190 148.840 144.211 145.953 145.542 150.271 147.489 143.824 134.754 131.736 126.304 125.511 125.495 130.133 126.257 110.323 98.417 105.749 120.665 124.075 127.245 146.731 144.979 148.210 144.670 142.970 142.524 146.142 146.522 148.128 148.798 150.181 152.388 155.694 160.662 155.520 158.262 154.338 158.196 160.371 154.856 150.636 145.899 141.242 140.834 141.119 139.104 134.437 129.425 123.155 119.273 120.472 121.523 121.983 123.658 124.794 124.827 120.382 117.395 115.790 114.283 117.271 117.448 118.764 120.550 123.554 125.412 124.182 119.828 115.361 114.226 115.214 115.864 114.276 113.469

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.552989692908948 beta 0.0295901195828147 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 170.465 207.245518963675 -36.7805189636754 14 170.102 187.558447053806 -17.4564470538065 15 156.389 161.51912234837 -5.13012234836955 16 124.291 122.042933804743 2.24806619525653 17 99.36 94.025592655242 5.33440734475802 18 86.675 80.1195450903846 6.55545490961539 19 85.056 130.497241356276 -45.4412413562759 20 128.236 99.9960774077362 28.2399225922638 21 164.257 111.177345083743 53.0796549162567 22 162.401 132.55235608923 29.8486439107699 23 152.779 151.164438409331 1.61456159066933 24 156.005 150.76003333926 5.24496666073952 25 153.387 140.547132329907 12.8398676700929 26 153.19 158.197271180859 -5.00727118085931 27 148.84 146.015501938256 2.82449806174367 28 144.211 115.829719848577 28.3812801514226 29 145.953 105.664478587721 40.2885214122787 30 145.542 114.226547554182 31.3154524458176 31 150.271 158.051387579526 -7.78038757952632 32 147.489 184.926952533316 -37.4379525333157 33 143.824 173.432384685126 -29.6083846851264 34 134.754 139.8839698318 -5.12996983180008 35 131.736 127.146666456924 4.58933354307621 36 126.304 130.673137371871 -4.36913737187135 37 125.511 119.044448346111 6.46655165388854 38 125.495 125.593780731209 -0.0987807312086346 39 130.133 120.108982090509 10.0240179094909 40 126.257 105.928155649467 20.3288443505326 41 110.323 97.100448071531 13.2225519284691 42 98.417 86.709167380079 11.7078326199209 43 105.749 101.919018999165 3.82998100083454 44 120.665 121.851808429496 -1.1868084294959 45 124.075 134.390873293255 -10.3158732932555 46 127.245 123.256032233518 3.98896776648211 47 146.731 120.85815970985 25.8728402901501 48 144.979 133.450047896591 11.5289521034087 49 148.21 137.017030346185 11.1929696538152 50 144.67 144.883117628554 -0.213117628554159 51 142.97 145.496081997442 -2.52608199744199 52 142.524 130.412180425555 12.1118195744453 53 146.142 115.160138580635 30.9818614193645 54 146.522 115.499255680241 31.0227443197592 55 148.128 139.771401851636 8.35659814836379 56 148.798 161.941704836099 -13.1437048360992 57 150.181 165.569189583037 -15.3881895830371 58 152.388 159.722069264883 -7.33406926488345 59 155.694 162.357959314038 -6.66395931403792 60 160.662 151.526034917473 9.13596508252749 61 155.52 154.560944171429 0.959055828571394 62 158.262 152.443097741046 5.81890225895393 63 154.338 156.23044388111 -1.89244388110993 64 158.196 148.923254632426 9.27274536757426 65 160.371 141.372905452981 18.9980945470185 66 154.856 135.743875556654 19.1121244433456 67 150.636 143.74315438448 6.89284561552034 68 145.899 155.914792482287 -10.0157924822865 69 141.242 160.741487049079 -19.4994870490792 70 140.834 156.626677459884 -15.7926774598837 71 141.119 155.15172300185 -14.0327230018497 72 139.104 147.45423456936 -8.35023456936031 73 134.437 137.024722977956 -2.58772297795556 74 129.425 134.920339864682 -5.49533986468185 75 123.155 128.62123421982 -5.46623421982039 76 119.273 123.887511080068 -4.61451108006807 77 120.472 112.336526591919 8.13547340808147 78 121.523 99.9053493451403 21.6176506548597 79 121.983 103.022810403794 18.9601895962059 80 123.658 113.701483802268 9.95651619773177 81 124.794 125.052411468094 -0.258411468094167 82 124.827 133.268604243429 -8.44160424342937 83 120.382 136.799624923598 -16.4176249235977 84 117.395 130.438606619549 -13.043606619549 85 115.79 120.027978352996 -4.23797835299553 86 114.283 115.722650746629 -1.43965074662866 87 117.271 111.757037709689 5.51396229031072 88 117.448 113.733376190592 3.71462380940821 89 118.764 112.881378924381 5.8826210756188 90 120.55 105.587893252327 14.9621067476727 91 123.554 104.084913276361 19.4690867236391 92 125.412 111.276512460469 14.1354875395305 93 124.182 120.696816620875 3.48518337912515 94 119.828 127.711090173143 -7.88309017314333 95 115.361 128.380621834525 -13.0196218345246 96 114.226 125.857508714401 -11.631508714401 97 115.214 120.637692373302 -5.42369237330206 98 115.864 117.38188628516 -1.51788628516026 99 114.276 116.934394197804 -2.6583941978038 100 113.469 113.906504100356 -0.437504100355554 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 101 111.978921795121 79.9180345773319 144.039809012909 102 105.646155242575 68.7529674352971 142.539343049853 103 97.7942497985221 56.3968842244165 139.191615372628 104 91.4271964570385 45.7505652645833 137.103827649494 105 87.6303521197984 37.8358139991373 137.42489024046 106 86.9390177189667 33.1457422714544 140.732293166479 107 89.1041236341715 31.4017281424934 146.80651912585 108 94.0466577788818 32.5032068585045 155.590108699259 109 97.869660210806 32.5369988634746 163.202321558137 110 99.2835401806917 30.200997188216 168.366083173167 111 99.1149464915032 26.3119924844305 171.917900498576 112 98.5427228563867 22.0409308872323 175.044514825541

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/1wu931305728924.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/1wu931305728924.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/222hp1305728924.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/222hp1305728924.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/3sumw1305728924.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728677lrwphkx2ximmsiw/3sumw1305728924.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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