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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 14:57:18 +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/19/t1305816816q65hmkv39cu074u.htm/, Retrieved Thu, 19 May 2011 16:53:40 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

6827 6178 7084 8162 8462 9644 10466 10748 9963 8194 6848 7027 7269 6775 7819 8371 9069 10248 11030 10882 10333 9109 7685 7602 8350 7829 8829 9948 10638 11253 11424 11391 10665 9396 7775 7933 8186 7444 8484 9948 10252 12282 11637 11577 12417 9637 8094 9280 8334 7899 9994 10078 10801 12950 12222 12246 13281 10366 8730 9614 8639 8772 10894 10455 11179 10588 10794 12770 13812 10857 9290 10925 9491 8919 11607 8852 12537 14759 13667 13731 15110 12185 10645 12161 10840 10436 13589 13402 13103 14933 14147 14057 16234 12389 11595 12772

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.194526868697057 beta 0 gamma 0.414248667899734 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7269 6992.55582264958 276.444177350425 14 6775 6566.94396801391 208.056031986088 15 7819 7674.11211493786 144.887885062141 16 8371 8244.45069337263 126.54930662737 17 9069 8937.7635922348 131.236407765207 18 10248 10127.1549248712 120.845075128766 19 11030 10919.066530775 110.933469225016 20 10882 11223.0500630185 -341.050063018516 21 10333 10359.9023206987 -26.9023206987495 22 9109 8590.03142166736 518.968578332639 23 7685 7354.68041267073 330.319587329269 24 7602 7591.17377283802 10.826227161976 25 8350 7922.54882708647 427.451172913534 26 7829 7503.49307979763 325.50692020237 27 8829 8612.4315064763 216.568493523706 28 9948 9190.59492596117 757.40507403883 29 10638 10008.1901489503 629.809851049738 30 11253 11291.100176145 -38.1001761449879 31 11424 12048.7854924272 -624.78549242717 32 11391 12058.8403039573 -667.840303957295 33 10665 11236.943553866 -571.943553865962 34 9396 9543.18614354233 -147.186143542331 35 7775 8115.30435581386 -340.304355813862 36 7933 8114.73921388684 -181.739213886838 37 8186 8547.66876654046 -361.668766540461 38 7444 7941.0926398772 -497.092639877204 39 8484 8853.66428216425 -369.664282164253 40 9948 9498.24854678723 449.751453212772 41 10252 10213.4226646954 38.5773353045988 42 12282 11158.4631001354 1123.53689986458 43 11637 11946.3609959165 -309.360995916528 44 11577 12003.4084129279 -426.408412927929 45 12417 11260.4741540808 1156.52584591916 46 9637 10044.6776627278 -407.677662727778 47 8094 8501.68626088138 -407.686260881383 48 9280 8540.92135182203 739.078648177969 49 8334 9092.93831481898 -758.938314818981 50 7899 8363.89622153124 -464.896221531242 51 9994 9325.24946454283 668.75053545717 52 10078 10445.2446234768 -367.244623476776 53 10801 10864.296159036 -63.296159036021 54 12950 12151.5337669436 798.466233056408 55 12222 12398.0871285241 -176.087128524134 56 12246 12442.0051301003 -196.005130100317 57 13281 12272.062114556 1008.93788544398 58 10366 10505.6340029493 -139.634002949339 59 8730 9014.78142600075 -284.781426000747 60 9614 9460.56146663124 153.438533368757 61 8639 9398.81810676915 -759.818106769153 62 8772 8767.71676988577 4.28323011422981 63 10894 10198.5975959148 695.402404085171 64 10455 10978.1007208464 -523.100720846443 65 11179 11468.2513783323 -289.251378332334 66 10588 12999.0755832242 -2411.07558322419 67 10794 12296.1113360835 -1502.11133608346 68 12770 12075.4360374134 694.563962586637 69 13812 12480.7813619065 1331.21863809346 70 10857 10393.8059310646 463.194068935351 71 9290 8971.78882632496 318.211173675043 72 10925 9681.08630541064 1243.91369458936 73 9491 9526.74681718453 -35.7468171845321 74 8919 9291.45156882427 -372.451568824266 75 11607 10879.6504430341 727.3495569659 76 8852 11258.794874714 -2406.79487471398 77 12537 11460.5440217296 1076.45597827041 78 14759 12549.0540428522 2209.94595714779 79 13667 13048.2932666712 618.706733328803 80 13731 13973.1303034321 -242.130303432106 81 15110 14408.6935536831 701.306446316854 82 12185 11909.5528417133 275.447158286737 83 10645 10402.6380307182 242.361969281776 84 12161 11406.0564178401 754.943582159947 85 10840 10729.6196807541 110.380319245894 86 10436 10410.4031012122 25.5968987878405 87 13589 12442.9995286584 1146.0004713416 88 13402 11857.8248378055 1544.17516219452 89 13103 13990.3867915028 -887.386791502795 90 14933 15075.0838898878 -142.083889887843 91 14147 14585.8474124561 -438.84741245612 92 14057 15017.729554271 -960.729554271045 93 16234 15628.2988709111 605.701129088944 94 12389 12968.4655176424 -579.465517642378 95 11595 11284.2078124351 310.792187564877 96 12772 12471.968860082 300.031139918039 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 11491.9704737389 10051.0585333696 12932.8824141082 98 11122.9925970028 9655.07123781813 12590.9139561875 99 13524.4505106603 12030.0078006167 15018.8932207039 100 12849.2053613453 11328.703828806 14369.7068938845 101 13870.0537877494 12323.932574097 15416.1750014018 102 15376.053825926 13804.7305924193 16947.3770594327 103 14815.4365342194 13219.3091580336 16411.5639104052 104 15158.5518726922 13537.9999611937 16779.1037841908 105 16478.6738304944 14834.0600780549 18123.287582934 106 13305.5653154105 11637.2367232066 14973.8939076144 107 12031.0781031655 10339.367079256 13722.789127075 108 13154.7911221783 11440.0164765561 14869.5657678006

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/1gg281305817031.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/1gg281305817031.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/2fhz31305817031.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/2fhz31305817031.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/3gbsz1305817031.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816816q65hmkv39cu074u/3gbsz1305817031.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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