*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 05:13:58 +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/20/t1305868185r4a318h7dmcukkb.htm/, Retrieved Fri, 20 May 2011 07:09:49 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

116 111 104 100 93 91 119 139 134 124 113 109 109 106 101 98 93 91 122 139 140 132 117 114 113 110 107 103 98 98 137 148 147 139 130 128 127 123 118 114 108 111 151 159 158 148 138 137 136 133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135 124 118 121 121 118 113 107 100 102 130 136 133 120 112 109 110

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 1 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.704179612610166 beta 0.524677975873149 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 109 109.640224358974 -0.640224358974436 14 106 105.919778207331 0.0802217926689366 15 101 100.611294895552 0.388705104447524 16 98 97.3303198257394 0.669680174260606 17 93 92.5779600874895 0.422039912510485 18 91 90.9321471712922 0.0678528287077569 19 122 120.270325682248 1.7296743177517 20 139 143.084450176702 -4.08445017670226 21 140 135.128648336621 4.87135166337885 22 132 130.154145852221 1.84585414777933 23 117 122.606132879058 -5.60613287905841 24 114 114.655965145873 -0.655965145872997 25 113 113.634855366808 -0.634855366807756 26 110 109.796566294657 0.203433705343414 27 107 104.376878439113 2.62312156088674 28 103 103.288772862142 -0.288772862142409 29 98 97.9704365423685 0.0295634576314967 30 98 95.9806701845395 2.01932981546045 31 137 127.942843306923 9.05715669307683 32 148 157.662365409917 -9.6623654099169 33 147 149.83263003488 -2.83263003487951 34 139 137.096377620493 1.90362237950694 35 130 125.964178420336 4.03582157966406 36 128 128.410012365075 -0.41001236507546 37 127 129.801187176186 -2.80118717618612 38 123 126.117850090049 -3.1178500900493 39 118 119.280524046228 -1.28052404622775 40 114 113.345231915681 0.654768084318576 41 108 107.897174848097 0.102825151903474 42 111 105.686365734644 5.31363426535576 43 151 142.406146500465 8.59385349953482 44 159 166.446521110303 -7.4465211103028 45 158 163.200913059292 -5.20091305929236 46 148 150.326440336971 -2.32644033697068 47 138 135.411790656281 2.58820934371946 48 137 133.553756986083 3.44624301391727 49 136 136.408510850104 -0.408510850104221 50 133 134.655829420832 -1.65582942083194 51 126 130.27117331286 -4.27117331285996 52 120 122.577104284392 -2.57710428439202 53 114 113.270559174847 0.729440825152636 54 116 111.854584324156 4.14541567584354 55 153 147.102586969709 5.89741303029055 56 162 161.88336800229 0.116631997709533 57 161 164.806469005864 -3.80646900586419 58 149 154.458058981884 -5.45805898188368 59 139 138.328805442612 0.671194557387906 60 135 134.203162743373 0.79683725662747 61 130 131.901564742916 -1.90156474291572 62 127 126.02650843609 0.973491563910187 63 122 120.989128754157 1.01087124584305 64 117 117.736686186467 -0.73668618646721 65 112 111.605222384555 0.39477761544515 66 113 111.741405286567 1.25859471343276 67 149 145.185563138167 3.81443686183283 68 157 155.730609003913 1.26939099608742 69 157 157.671960226961 -0.671960226960522 70 147 149.567366715528 -2.56736671552824 71 137 138.879988156976 -1.87998815697571 72 132 133.645593352486 -1.64559335248589 73 125 128.574015451709 -3.57401545170879 74 123 121.502009749007 1.4979902509933 75 117 116.169070283643 0.830929716357488 76 114 111.530512151983 2.46948784801722 77 111 108.433616722441 2.56638327755869 78 112 111.599008477868 0.400991522131619 79 144 146.122947035791 -2.12294703579136 80 150 150.468078343708 -0.468078343708015 81 149 148.703655886303 0.29634411369662 82 134 139.169987762389 -5.16998776238887 83 123 124.341418228908 -1.34141822890814 84 116 117.242777366841 -1.242777366841 85 117 109.720380344381 7.27961965561892 86 111 113.637744340642 -2.6377443406417 87 105 105.513213568765 -0.513213568765011 88 102 100.234277517794 1.76572248220648 89 95 96.2318715322436 -1.23187153224357 90 93 94.2401138450171 -1.24011384501715 91 124 124.413523012446 -0.413523012445992 92 130 128.635252475746 1.36474752425391 93 124 127.248082740082 -3.24808274008224 94 115 111.152380790358 3.84761920964181 95 106 104.689039888543 1.31096011145678 96 105 101.349942165713 3.65005783428663 97 105 103.464434892445 1.53556510755456 98 101 101.951308819141 -0.951308819141275 99 95 97.8140087446414 -2.81400874464141 100 93 92.9101839332579 0.0898160667421024 101 84 87.5428249343067 -3.54282493430665 102 87 83.7694160169246 3.23058398307543 103 116 118.835412855658 -2.83541285565775 104 120 122.482826865252 -2.48282686525222 105 117 116.205231948774 0.794768051226427 106 109 105.732706012088 3.2672939879122 107 105 98.5731347242782 6.42686527572175 108 107 101.881485057785 5.11851494221469 109 109 107.300051655613 1.69994834438724 110 109 108.123273538321 0.876726461679084 111 108 108.353874353415 -0.353874353414867 112 107 110.582036718822 -3.58203671882218 113 99 104.738394300042 -5.73839430004222 114 103 103.795400768742 -0.795400768742255 115 131 135.117243154089 -4.11724315408915 116 137 138.378033310129 -1.37803331012915 117 135 134.667889024532 0.332110975467685 118 124 125.249954354437 -1.24995435443698 119 118 114.824079243152 3.17592075684782 120 121 113.235010330306 7.76498966969389 121 121 118.262541580103 2.73745841989678 122 118 118.712810177377 -0.712810177376781 123 113 116.012751793762 -3.01275179376238 124 107 112.983958647061 -5.98395864706129 125 100 101.493933084416 -1.49393308441631 126 102 103.253127330707 -1.25312733070673 127 130 131.351950659423 -1.35195065942264 128 136 136.473974686256 -0.47397468625627 129 133 133.344023063385 -0.344023063384981 130 120 122.169829299251 -2.16982929925145 131 112 111.253465058658 0.746534941342077 132 109 107.261637104054 1.73836289594612 133 110 102.281876250964 7.7181237490357 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 134 102.782744018951 96.4486997256334 109.116788312269 135 97.7315986100171 88.4381973980278 107.024999822006 136 94.8858304672028 81.8504686086489 107.921192325757 137 90.089156306739 72.7186793600399 107.459633253438 138 94.6748714162685 72.476695095659 116.873047736878 139 125.793165763538 98.3350041215887 153.251327405487 140 134.792709206092 101.68286792142 167.902550490764 141 134.875861623607 95.7524009696718 173.999322277542 142 126.371814921793 80.8959456519968 171.84768419159 143 121.61580545876 69.4675224480622 173.764088469457 144 120.885550547207 61.7605585974631 180.010542496952 145 119.302201302618 52.909643464552 185.694759140685

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/1rq1o1305868436.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/1rq1o1305868436.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/2b3mr1305868436.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/2b3mr1305868436.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/3yh381305868437.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305868185r4a318h7dmcukkb/3yh381305868437.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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