Exponential Smoothing Australische chocoladeproductie

*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 14:38:47 +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/t1305729338xwigcsb4uebf70m.htm/, Retrieved Wed, 18 May 2011 16:35:41 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

7992 6114 5965 8460 8323 6333 5675 10090 9035 6976 6459 10896 9978 7466 7199 10977 9412 6341 7784 11911 10079 7721 8197 12038 11963 8033 8618 13625 11734 8895 8727 13974 12583 9525 9662 15490 13839 10047 9788 14978 13045 9489 8741 13149 14106 9998 10034 15081 13266 9997 9027 14324 13149 11209 10332 15354 13800 11786 10550 16114 13255 11403 10269 14009 15847 12967 11328 15814 18626 13219 13818 18062 15722 12111 11702 15589 14852 13612 12380 15501 16322 12157 11124 14621 14035 11159 10944 15824 14378 11816 12233 17344 16812 12181 13275 18458 17375 14609 13323 18327 16053 15070 13806 18245 17461 14999 16022 20564 16372 15854 15115 18207 19488 16644 18631 21093 22212 19762 19403 21227 23176 20823 20647 21336 23458 22003 21647 26416 25226 24723 19945 24040 25034 24885 21168 23541 26019 24657 20599 24534 28717 26138 22968 26577 28660 30430 27356 25454 30194

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 0.287307754775613 beta 0.027589438558662 gamma 0.712133275623715 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 9978 9386.09748931624 591.902510683758 14 7466 6998.52798744672 467.472012553277 15 7199 6868.28913007211 330.710869927892 16 10977 10791.2125017103 185.787498289668 17 9412 9302.05427242776 109.945727572243 18 6341 6269.43594997768 71.5640500223217 19 7784 7019.77420446043 764.225795539574 20 11911 11648.677307642 262.32269235799 21 10079 10696.7924331671 -617.792433167131 22 7721 8434.6049610162 -713.6049610162 23 8197 7687.27496962728 509.72503037272 24 12038 12353.9992549104 -315.999254910381 25 11963 11683.8911152053 279.108884794712 26 8033 9153.87106686948 -1120.87106686948 27 8618 8495.85796346025 122.142036539752 28 13625 12281.6310843359 1343.36891566409 29 11734 11092.0650330551 641.93496694486 30 8895 8202.53049305412 692.469506945883 31 8727 9497.4483855628 -770.448385562791 32 13974 13433.1718175674 540.828182432624 33 12583 12119.3008181279 463.699181872054 34 9525 10132.4625362716 -607.462536271631 35 9662 10050.6045645543 -388.604564554298 36 15490 14047.1271812126 1442.87281878738 37 13839 14205.3117263854 -366.311726385366 38 10047 10795.1256242294 -748.125624229424 39 9788 10893.8312855813 -1105.83128558134 40 14978 14955.6333273051 22.3666726949014 41 13045 13029.0854992492 15.9145007507577 42 9489 9978.9285532754 -489.9285532754 43 8741 10175.8746426824 -1434.87464268243 44 13149 14565.1689897207 -1416.16898972072 45 14106 12613.3307423609 1492.66925763915 46 9998 10350.0697768555 -352.069776855466 47 10034 10426.2848676984 -392.284867698396 48 15081 15324.8734089377 -243.873408937714 49 13266 14040.4437919933 -774.443791993306 50 9997 10276.2002518646 -279.200251864599 51 9027 10288.7865885669 -1261.78658856691 52 14324 14837.8434696582 -513.843469658186 53 13149 12709.1788669694 439.821133030637 54 11209 9482.65752000142 1726.34247999858 55 10332 9812.9082447306 519.091755269395 56 15354 14764.7174620363 589.28253796366 57 13800 14872.9170739222 -1072.9170739222 58 11786 10923.470879416 862.529120583973 59 10550 11325.0583832429 -775.058383242913 60 16114 16182.7817247224 -68.7817247224102 61 13255 14674.5488790263 -1419.54887902626 62 11403 10966.3729404933 436.627059506718 63 10269 10681.6616793044 -412.661679304374 64 14009 15856.7479589871 -1847.74795898709 65 15847 13820.7482808249 2026.25171917507 66 12967 11707.4372709921 1259.56272900793 67 11328 11291.6262908921 36.3737091079402 68 15814 16137.3105341784 -323.310534178414 69 18626 15129.401604233 3496.59839576697 70 13219 13501.0400372728 -282.040037272765 71 13818 12759.5102837041 1058.48971629593 72 18062 18533.8722073789 -471.872207378889 73 15722 16252.4638947119 -530.463894711938 74 12111 13777.0377982419 -1666.03779824192 75 11702 12475.7468122093 -773.746812209287 76 15589 16834.4496112836 -1245.44961128355 77 14852 16958.1584988835 -2106.15849888353 78 13612 13256.1839920238 355.816007976216 79 12380 11940.4775718912 439.52242810879 80 15501 16703.1993805035 -1202.1993805035 81 16322 17358.2987389232 -1036.29873892317 82 12157 12450.6849102469 -293.684910246871 83 11124 12326.9423933936 -1202.94239339356 84 14621 16597.715629711 -1976.71562971105 85 14035 13765.1343352184 269.86566478157 86 11159 10860.5704800092 298.429519990841 87 10944 10509.3852502924 434.614749707562 88 15824 14918.2667222788 905.733277721189 89 14378 15182.6528711644 -804.652871164444 90 11816 13073.9210451995 -1257.92104519953 91 12233 11294.0470992906 938.952900709393 92 17344 15327.9798112103 2016.02018878971 93 16812 16978.3549851478 -166.354985147769 94 12181 12690.9351862109 -509.935186210945 95 13275 12035.2232643293 1239.77673567068 96 18458 16626.0948007599 1831.90519924012 97 17375 16069.1617603121 1305.83823968788 98 14609 13526.1400931463 1082.8599068537 99 13323 13525.0662196025 -202.066219602486 100 18327 18040.7053022856 286.294697714413 101 16053 17304.709722194 -1251.70972219404 102 15070 14879.6065351839 190.39346481611 103 13806 14684.4279822451 -878.427982245119 104 18245 18782.0531569268 -537.053156926835 105 17461 18610.2423950517 -1149.24239505168 106 14999 13877.2192805782 1121.78071942182 107 16022 14602.446359179 1419.55364082098 108 20564 19571.0181028372 992.981897162761 109 16372 18524.9351343924 -2152.93513439244 110 15854 14866.4709132621 987.52908673793 111 15115 14176.5696170696 938.430382930368 112 18207 19267.4840847362 -1060.48408473621 113 19488 17353.0299513007 2134.97004869934 114 16644 16648.7721840988 -4.77218409878697 115 18631 15869.4258161338 2761.57418386615 116 21093 21229.3292296624 -136.329229662362 117 22212 20908.339205214 1303.66079478602 118 19762 18098.5093102657 1663.49068973432 119 19403 19200.6355792502 202.364420749836 120 21227 23663.4848939663 -2436.48489396629 121 23176 20068.7363982841 3107.26360171587 122 20823 19590.4495367119 1232.5504632881 123 20647 19022.963640381 1624.03635961902 124 21336 23378.7178180538 -2042.71781805381 125 23458 22878.4418534809 579.558146519143 126 22003 20703.5723498222 1299.4276501778 127 21647 21775.5371092259 -128.537109225865 128 26416 24883.9973640401 1532.00263595991 129 25226 25836.0836874781 -610.08368747808 130 24723 22706.7865433313 2016.21345666872 131 19945 23219.2218185703 -3274.22181857028 132 24040 25366.9002791367 -1326.90027913674 133 25034 24936.3477917563 97.6522082436677 134 24885 22649.8181621519 2235.1818378481 135 21168 22584.953695019 -1416.95369501903 136 23541 24197.7744690695 -656.774469069544 137 26019 25429.3264840353 589.673515964714 138 24657 23625.5471977599 1031.45280224012 139 20599 23896.4862279825 -3297.48622798252 140 24534 26912.8436135164 -2378.8436135164 141 28717 25598.7204283244 3118.27957167564 142 26138 24847.6779196253 1290.32208037466 143 22968 22434.8780834207 533.121916579283 144 26577 26663.3267530722 -86.326753072226 145 28660 27320.6031421277 1339.39685787234 146 30430 26493.9403663909 3936.05963360905 147 27356 25095.8979992204 2260.10200077961 148 25454 28211.8492078771 -2757.84920787708 149 30194 29516.5723603997 677.427639600257 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 150 28007.1323109466 25448.779621704 30565.4850001893 151 25821.3862181696 23153.8653924354 28488.9070439039 152 30314.2491739756 27536.262172844 33092.2361751073 153 32555.2794699745 29665.5348027203 35445.0241372287 154 30037.5949384304 27034.8083597161 33040.3815171446 155 26916.5549594248 23799.4500115957 30033.6599072539 156 30720.0003617357 27487.3087914611 33952.6919320102 157 32168.920270655 28819.3823433112 35518.4581979988 158 32307.9515580529 28840.3162886613 35775.5868274446 159 28929.871100649 25342.896416581 32516.845784717 160 28833.2165583113 25125.6694061176 32540.763710505 161 32679.1733717696 28849.8297782159 36508.5169653234

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/10q831305729524.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/10q831305729524.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/2vza11305729524.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/2vza11305729524.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/3muyi1305729524.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729338xwigcsb4uebf70m/3muyi1305729524.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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