evelyne van haevermaet opd10 oef2

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 06:51:18 -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/28/t12119792086veotonx3p4skeb.htm/, Retrieved Wed, 28 May 2008 14:53:31 +0200

User-defined keywords:

Dataseries X:

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13328 12873 14000 13477 14237 13674 13529 14058 12975 14326 14008 16193 14483 14011 15057 14884 15414 14440 14900 15074 14442 15307 14938 17193 15528 14765 15838 15723 16150 15486 15986 15983 15692 16490 15686 18897 16316 15636 17163 16534 16518 16375 16290 16352 15943 16362 16393 19051 16747 16320 17910 16961 17480 17049 16879 17473 16998 17307 17418 20169 17871 17226 19062 17804 19100 18522 18060 18869 18127 18871 18890 21263 19547 18450 20254 19240 20216 19420 19415 20018 18652 19978 19514 22148

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.257708065841373 beta 0.273715620885234 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 14000 12418 1582 4 13477 12482.2864203408 994.713579659181 5 14237 12465.3902191082 1771.60978089179 6 13674 12773.6735272941 900.326472705858 7 13529 12920.9279792195 608.072020780533 8 14058 13035.7587255948 1022.24127440517 9 12975 13329.4318236016 -354.431823601633 10 14326 13243.3239919096 1082.67600809039 11 14008 13603.9410232314 404.058976768649 12 16193 13818.1747763027 2374.82522369733 13 14483 14707.8080263143 -224.808026314342 14 14011 14911.6371484163 -900.637148416263 15 15057 14877.7698600622 179.230139937794 16 14884 15134.8357471942 -250.835747194178 17 15414 15263.3765530168 150.623446983245 18 14440 15506.0014169266 -1066.00141692658 19 14900 15359.8978613722 -459.897861372154 20 15074 15337.5514728531 -263.551472853147 21 14442 15347.2145479489 -905.214547948883 22 15307 15127.6631945612 179.336805438779 23 14938 15200.2596620479 -262.259662047925 24 17193 15140.5536962957 2052.4463037043 25 15528 15822.1430697692 -294.143069769201 26 14765 15878.2489578869 -1113.24895788689 27 15838 15644.737491711 193.262508289017 28 15723 15761.5570590694 -38.5570590694279 29 16150 15815.9150883808 334.084911619244 30 15486 15989.8718823319 -503.871882331925 31 15986 15912.3379723946 73.6620276054164 32 15983 15988.8352347242 -5.83523472421257 33 15692 16044.4338013319 -352.433801331887 34 16490 15985.85089134 504.149108660005 35 15686 16183.5783407668 -497.578340766839 36 18897 16088.0540058277 2808.94599417232 37 16316 17042.7871260072 -726.787126007159 38 15636 17035.0666665116 -1399.06666651162 39 17163 16755.4059705321 407.59402946788 40 16534 16970.0874705877 -436.087470587663 41 16518 16936.5843896776 -418.58438967765 42 16375 16878.0655854754 -503.065585475437 43 16290 16762.2896915943 -472.289691594313 44 16352 16621.1302819512 -269.130281951151 45 15943 16513.3425843482 -570.342584348153 46 16362 16287.6988091724 74.3011908276039 47 16393 16233.4260455907 159.573954409281 48 19051 16212.3849039884 2838.61509601157 49 16747 17081.9865579657 -334.986557965658 50 16320 17110.095943841 -790.095943840988 51 17910 16965.1876110135 944.81238898655 52 16961 17334.0250086798 -373.025008679841 53 17480 17336.932371648 143.067628351993 54 17049 17482.9327777428 -433.932777742819 55 16879 17449.6264610754 -570.626461075422 56 17473 17340.8418176473 132.158182352658 57 16998 17422.4927148302 -424.492714830190 58 17307 17330.7470118186 -23.7470118185993 59 17418 17340.6016249297 77.3983750702973 60 20169 17381.9818026237 2787.01819737628 61 17871 18318.2455692040 -447.245569204042 62 17226 18389.4653446477 -1163.46534464774 63 19062 18194.0401470887 867.959852911303 64 17804 18583.3543879497 -779.354387949694 65 19100 18493.1677984811 606.832201518948 66 18522 18803.0178426011 -281.01784260109 67 18060 18864.2391292665 -804.239129266534 68 18869 18733.8920687731 135.107931226878 69 18127 18855.1526633628 -728.152663362791 70 18871 18702.5810805998 168.418919400217 71 18890 18792.9432818644 97.0567181355837 72 21263 18871.7611252470 2391.23887475303 73 19547 19710.4831521074 -163.483152107427 74 18450 19879.3008138410 -1429.30081384095 75 20254 19621.0859997143 632.914000285673 76 19240 19938.9655221922 -698.965522192208 77 20216 19864.3048134681 351.695186531859 78 19420 20085.2159732756 -665.215973275623 79 19415 19997.1374395170 -582.13743951697 80 20018 19889.4056822673 128.594317732717 81 18652 19973.9061105004 -1321.90611050038 82 19978 19591.3553095818 386.644690418172 83 19514 19676.3852537728 -162.385253772791 84 22148 19608.4713044817 2539.52869551828 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20415.9974849681 18496.9693575898 22335.0256123463 86 20569.0666371838 18549.2989190126 22588.834355355 87 20722.1357893995 18562.2478166066 22882.0237621923 88 20875.2049416152 18535.0596450627 23215.3502381676 89 21028.2740938308 18469.0552103407 23587.492977321 90 21181.3432460465 18366.7868502205 23995.8996418726 91 21334.4123982622 18231.2999219965 24437.524874528 92 21487.4815504779 18065.6418267054 24909.3212742504 93 21640.5507026936 17872.6048875126 25408.4965178747 94 21793.6198549093 17654.6295735028 25932.6101363158 95 21946.689007125 17413.7970448276 26479.5809694223 96 22099.7581593407 17151.8626027075 27047.6537159738

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/1bqxo1211979072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/1bqxo1211979072.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/28t8c1211979072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/28t8c1211979072.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/35zfd1211979072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119792086veotonx3p4skeb/35zfd1211979072.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')

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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