smoothing champagne Katrien Broux

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 10:27:48 -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/27/t1211905700aar27iwki509kau.htm/, Retrieved Tue, 27 May 2008 18:28:24 +0200

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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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0 beta 0 gamma 0.89588635004732 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2541 2368.49607099695 172.503929003050 14 2475 2299.23063554187 175.769364458128 15 3031 2808.66370689647 222.336293103529 16 3266 2997.43890828896 268.561091711039 17 3776 3417.25819820299 358.741801797015 18 3230 2855.58006291701 374.419937082992 19 3028 2630.60624337706 397.393756622937 20 1759 1510.29684667595 248.70315332405 21 3595 3036.94605462600 558.053945374004 22 4474 3730.0172037031 743.982796296901 23 6838 5676.50441952317 1161.49558047683 24 8357 6872.94896809105 1484.05103190895 25 3113 2523.03998632031 589.960013679685 26 3006 2456.7000099164 549.299990083599 27 4047 3007.85175700804 1039.14824299196 28 3523 3238.03912450669 284.960875493313 29 3937 3738.65008162431 198.349918375688 30 3986 3191.01777373524 794.982226264764 31 3260 2986.62588552958 273.374114470421 32 1573 1733.10660695269 -160.106606952692 33 3528 3536.89896687662 -8.89896687661849 34 5211 4396.54123557553 814.458764424472 35 7614 6717.07245571265 896.927544287351 36 9254 8202.49003035192 1051.50996964808 37 5375 3051.57710964967 2323.42289035033 38 3088 2948.81037311343 139.189626886575 39 3718 3938.81048358019 -220.810483580192 40 4514 3493.33168315868 1020.66831684132 41 4520 3916.34906603009 603.650933969909 42 4539 3903.23149877607 635.768501223933 43 3663 3231.5380231399 431.461976860098 44 1643 1589.66928323138 53.330716768616 45 4739 3528.92650392233 1210.07349607767 46 5428 5126.20372529982 301.796274700182 47 8314 7520.61759962115 793.382400378851 48 10651 9144.52345909831 1506.47654090169 49 3633 5133.09996250202 -1500.09996250202 50 4292 3073.50845990929 1218.49154009071 51 4154 3740.98938539335 413.01061460665 52 4121 4407.73449614259 -286.734496142591 53 4647 4457.15169796705 189.848302032951 54 4753 4472.80782081263 280.192179187369 55 3965 3618.07891877330 346.921081226703 56 1723 1637.44754442263 85.5524555773732 57 5048 4613.01483161235 434.985168387647 58 6922 5396.57888829884 1525.42111170116 59 9858 8231.39806248834 1626.60193751166 60 11331 10494.1552287586 836.844771241364 61 4016 3789.18088238996 226.819117610035 62 4276 4165.13839832469 110.861601675308 63 4968 4110.9999574441 857.0000425559 64 4677 4150.85297496075 526.147025039253 65 3523 4627.23420033803 -1104.23420033803 66 1821 4723.82816953661 -2902.82816953661 67 5222 3928.88077998796 1293.11922001204 68 6872 1714.09282158742 5157.90717841258 69 10803 5002.71210644388 5800.28789355612 70 13916 6763.18284034592 7152.81715965408 71 2639 9688.64853526556 -7049.64853526556 72 2899 11243.8730364222 -8344.87303642225 73 3370 3992.38503378657 -622.385033786572 74 3740 4264.45779400998 -524.457794009983 75 2927 4878.7745975599 -1951.77459755990 76 3986 4622.22091281142 -636.220912811418 77 4217 3637.96585299977 579.034147000228 78 1738 2123.22403591592 -385.224035915915 79 5221 5087.36863818058 133.631361819417 80 6424 6334.99145753833 89.0085424616655 81 9842 10199.1108566255 -357.110856625526 82 13076 13171.2940980642 -95.294098064247 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 83 3372.96463989007 -115.882675313725 6861.81195509386 84 3767.81519021363 278.967875009838 7256.66250541742 85 3434.79877754344 -54.0485376603492 6923.64609274723 86 3794.60321518051 305.755899976718 7283.4505303843 87 3130.20637723689 -358.640937966906 6619.05369244068 88 4052.23928140902 563.39196620523 7541.08659661281 89 4156.71464150857 667.867326304777 7645.56195671236 90 1778.10708042871 -1710.74023477508 5266.9543956325 91 5207.08715117283 1718.23983596904 8695.93446637663 92 6414.73299576735 2925.88568056356 9903.58031097114 93 9879.180114721 6390.33279951722 13368.0274299248 94 13085.9214163684 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/1gz4q1211905662.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/1gz4q1211905662.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/2ub901211905662.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/2ub901211905662.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/3c18d1211905662.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211905700aar27iwki509kau/3c18d1211905662.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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