Exponential Smoothing eigen reeks - Jesse De Meyer

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 12:59:43 -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/26/t1211828426low7uv6dl673mnt.htm/, Retrieved Mon, 26 May 2008 21:00:26 +0200

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Dataseries X:

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36409 33163 34122 35225 28249 30374 26311 22069 23651 28628 23187 14727 43080 32519 39657 33614 28671 34243 27336 22916 24537 26128 22602 15744 41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.51705592571119 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 34122 33163 959 4 35225 33658.856632757 1566.14336724297 5 28249 34468.6403413033 -6219.64034130328 6 30374 31252.7384470401 -878.73844704005 7 26311 30798.3815258477 -4487.38152584774 8 22069 28478.1543169812 -6409.15431698124 9 23651 25164.2630985886 -1513.26309858864 10 28628 24381.8214463033 4246.1785536967 11 23187 26577.3332291200 -3390.33322911995 12 14727 24824.3413428679 -10097.3413428679 13 43080 19603.4511676095 23476.5488323905 14 32519 31742.1398566451 776.860143354876 15 39657 32143.8199972156 7513.1800027844 16 33614 36028.5542385901 -2414.5542385901 17 28671 34780.094661576 -6109.09466157602 18 34243 31621.3510660775 2621.64893392246 19 27336 32976.8901824966 -5640.89018249657 20 22916 30060.2344873506 -7144.23448735064 21 24537 26366.2657109957 -1829.26571099574 22 26128 25420.4330354251 707.5669645749 23 22602 25786.2847272960 -3184.28472729603 24 15744 24139.831439896 -8395.83143989598 25 41086 19798.7170426254 21287.2829573746 26 39690 30805.4328380268 8884.5671619732 27 43129 35399.2509365041 7729.7490634959 28 37863 39395.9634940452 -1532.96349404518 29 35953 38603.3356355502 -2650.33563555019 30 29133 37232.9638900654 -8099.96389006543 31 24693 33044.8295626604 -8351.82956266044 32 22205 28726.4665967570 -6521.46659675696 33 21725 25354.5036485762 -3629.50364857618 34 27192 23477.8472796895 3714.15272031052 35 21790 25398.2719527224 -3608.27195272237 36 13253 23532.5935579898 -10279.5935579898 37 37702 18217.4687949286 19484.5312050714 38 30364 28292.0611142154 2071.93888578464 39 32609 29363.3693928218 3245.63060717825 40 30212 31041.5419309329 -829.541930932872 41 29965 30612.6223599181 -647.622359918128 42 28352 30277.7653810994 -1925.76538109939 43 25814 29282.0369792725 -3468.03697927249 44 22414 27488.8679085541 -5074.86790855411 45 20506 24864.8773842346 -4358.87738423465 46 28806 22611.0940032676 6194.90599673237 47 22228 25814.2068581019 -3586.20685810189 48 13971 23959.9373512942 -9988.9373512942 49 36845 18795.0981022497 18049.9018977503 50 35338 28127.9068369871 7210.09316301285 51 35022 31855.9282318527 3166.07176814732 52 34777 33492.9644008002 1284.03559919984 53 26887 34156.8826161906 -7269.88261619055 54 23970 30397.9467302645 -6427.94673026446 55 22780 27074.3387832253 -4294.33878322535 56 17351 24853.9254683473 -7502.9254683473 57 21382 20974.4933947689 407.506605231083 58 24561 21185.1970997701 3375.8029002299 59 17409 22930.675993367 -5521.67599336699 60 11514 20075.6607011394 -8561.66070113936 61 31514 15648.8033016866 15865.1966983134 62 27071 23851.9972671232 3219.00273287683 63 29462 25516.4017050376 3945.59829496235 64 26105 27556.4966839239 -1451.49668392390 65 22397 26805.9917223509 -4408.99172235091 66 23843 24526.2964258978 -683.296425897785 67 21705 24172.9939598701 -2467.99395987006 68 18089 22896.9030582998 -4807.90305829982 69 20764 20410.9482917609 353.051708239058 70 25316 20593.4957695884 4722.5042304116 71 17704 23035.2945661189 -5331.29456611889 72 15548 20278.7171189952 -4730.71711899525 73 28029 17832.6717997554 10196.3282002446 74 29383 23104.743716188 6278.25628381202 75 36438 26350.9533308665 10087.0466691335 76 32034 31566.5205840673 467.479415932699 77 22679 31808.2335862233 -9129.2335862233 78 24319 27087.9092632649 -2768.90926326493 79 18004 25656.2283209372 -7652.22832093719 80 17537 21699.5983227016 -4162.59832270162 81 20366 19547.3021935933 818.697806406715 82 22782 19970.6147457626 2811.38525423737 83 19169 21424.2581509231 -2255.25815092312 84 13807 20258.1635599799 -6451.16355997986 85 29743 16922.5512135602 12820.4487864398 86 25591 23551.4402288657 2039.55977113427 87 29096 24606.0066943729 4489.99330562714 88 26482 26927.5843394510 -445.58433945095 89 22405 26697.1923163337 -4292.19231633373 90 27044 24477.8888448813 2566.11115511867 91 17970 25804.7118236690 -7834.71182366903 92 18730 21753.7276490014 -3023.72764900143 93 19684 20190.2913503485 -506.291350348474 94 19785 19928.5104075145 -143.510407514474 95 18479 19854.3075009079 -1375.30750090789 96 10698 19143.1966078884 -8445.19660788841 97 31956 14776.5576579837 17179.4423420163 98 29506 23659.2901213369 5846.70987866306 99 34506 26682.3661100138 7823.63388998617 100 27165 30727.6223734261 -3562.62237342607 101 26736 28885.5473641749 -2149.54736417485 102 23691 27774.1111619314 -4083.11116193137 103 18157 25662.9143403173 -7505.91434031725 104 17328 21781.9368527756 -4453.93685277562 105 18205 19479.0024103045 -1274.00241030453 106 20995 18820.2719146862 2174.72808531376 107 17382 19944.7279580083 -2562.72795800827 108 9367 18619.6542813344 -9252.65428133435 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 13835.5145566134 199.380103088879 27471.6490101379 110 13835.5145566134 -1515.56831671000 29186.5974299368 111 13835.5145566134 -3057.30427070751 30728.3333839343 112 13835.5145566134 -4469.64620426856 32140.6753174954 113 13835.5145566134 -5780.56285531525 33451.5919685421 114 13835.5145566134 -7009.19881584202 34680.2279290688 115 13835.5145566134 -8169.34077417364 35840.3698874005 116 13835.5145566134 -9271.30782721756 36942.3369404444 117 13835.5145566134 -10323.0620410870 37994.0911543138 118 13835.5145566134 -11330.8996849110 39001.9287981378 119 13835.5145566134 -12299.9018036638 39970.9309168906 120 13835.5145566134 -13234.2392448915 40905.2683581183

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/15axu1211828377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/15axu1211828377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/27d3x1211828377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/27d3x1211828377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/3lkjr1211828377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211828426low7uv6dl673mnt/3lkjr1211828377.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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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