*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Jun 2010 12:18:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8.htm/, Retrieved Fri, 04 Jun 2010 14:18:31 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

2953 2635 2404 2413 2136 1565 1451 2037 2477 2785 2994 2681 3098 2708 2517 2445 2087 1801 1216 2173 2286 3121 3458 3511 3524 2767 2744 2603 2527 1846 1066 2327 3066 3048 3806 4042 3583 3438 2957 2885 2744 1837 1447 2504 3248 3098 4318 3561 3316 3379 2717 2354 2445 1542 1606 2590 3588 3202 4704 4005 3810 3488 2781 2944 2817 1960 1937 2903 3357 3552 4581 3905 4581 4037 3345 3175 2808 2050 1719 3143 3756 4776 4540 4309 4563 3506 3665 3361 3094 2440 1633 2935 4159 4159 4894 4921 4577 4155 3851 3429 3370 2726

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0739209572408732 beta 0.0457595802441608 gamma 0.330408735129191 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3098 3043.75133958815 54.248660411848 14 2708 2676.14760474331 31.8523952566948 15 2517 2499.03150563822 17.968494361784 16 2445 2429.67297843909 15.3270215609109 17 2087 2052.48331231898 34.5166876810194 18 1801 1740.229682197 60.7703178030013 19 1216 1479.02638528787 -263.026385287868 20 2173 2046.24268410856 126.757315891436 21 2286 2498.10879770803 -212.108797708034 22 3121 2790.63405895328 330.365941046718 23 3458 3035.43251390506 422.56748609494 24 3511 2745.82958857622 765.170411423783 25 3524 3268.87831897298 255.121681027018 26 2767 2885.73433583387 -118.734335833874 27 2744 2683.65008135413 60.3499186458675 28 2603 2614.73872898148 -11.7387289814774 29 2527 2216.85245011382 310.147549886176 30 1846 1910.12665563092 -64.1266556309245 31 1066 1512.13470404602 -446.134704046022 32 2327 2238.36363532242 88.636364677583 33 3066 2610.05431782677 455.945682173229 34 3048 3166.8416959311 -118.841695931104 35 3806 3430.05153765498 375.948462345018 36 4042 3222.6200002145 819.379999785502 37 3583 3622.01234825892 -39.0123482589183 38 3438 3065.99529840135 372.004701598646 39 2957 2946.1970596661 10.8029403338951 40 2885 2846.34520494443 38.6547950555669 41 2744 2525.2917641732 218.708235826795 42 1837 2059.96935124306 -222.969351243057 43 1447 1488.53965796715 -41.5396579671487 44 2504 2510.41768909839 -6.41768909838584 45 3248 3039.95282066349 208.047179336514 46 3098 3440.21107317002 -342.211073170018 47 4318 3880.64978432776 437.35021567224 48 3561 3802.38664979137 -241.386649791374 49 3316 3865.93410822792 -549.934108227915 50 3379 3369.51064679066 9.48935320933651 51 2717 3096.84754101386 -379.847541013864 52 2354 2969.45203176324 -615.45203176324 53 2445 2643.90816159447 -198.908161594466 54 1542 2002.43623879537 -460.436238795372 55 1606 1466.69192742223 139.308072577772 56 2590 2509.86199499966 80.1380050003377 57 3588 3106.16889657423 481.831103425772 58 3202 3352.77704040259 -150.777040402587 59 4704 4044.55265104991 659.447348950087 60 4005 3765.26463767186 239.735362328138 61 3810 3763.65058303625 46.3494169637484 62 3488 3471.66967622237 16.3303237776299 63 2781 3065.73113731036 -284.731137310358 64 2944 2863.35170761191 80.648292388094 65 2817 2709.43587516602 107.564124833983 66 1960 1968.08867639479 -8.0886763947949 67 1937 1626.66791923682 310.332080763182 68 2903 2755.36853261452 147.631467385484 69 3357 3546.86017041421 -189.860170414209 70 3552 3554.69355056176 -2.69355056176073 71 4581 4582.35179879189 -1.35179879189491 72 3905 4097.16659814172 -192.166598141725 73 4581 4000.65408916199 580.345910838008 74 4037 3720.09301337571 316.906986624292 75 3345 3208.18326799286 136.816732007139 76 3175 3146.52909511546 28.4709048845352 77 2808 2987.08280068018 -179.082800680183 78 2050 2127.23032372058 -77.2303237205765 79 1719 1858.74341484165 -139.743414841654 80 3143 2966.90568577197 176.094314228026 81 3756 3697.44968667812 58.5503133218754 82 4776 3786.76089529729 989.239104702712 83 4540 4981.53083543739 -441.530835437393 84 4309 4364.64607760225 -55.6460776022477 85 4563 4528.985696435 34.0143035649944 86 3506 4098.53767225567 -592.537672255672 87 3665 3430.0431700927 234.956829907297 88 3361 3335.59103266362 25.4089673363828 89 3094 3098.50112839995 -4.50112839995199 90 2440 2232.42957136688 207.570428633124 91 1633 1946.07136552366 -313.071365523663 92 2935 3216.87679167235 -281.876791672346 93 4159 3912.437485424 246.562514576004 94 4159 4314.22352711335 -155.223527113348 95 4894 5002.97302409231 -108.973024092307 96 4921 4506.96988076895 414.030119231046 97 4577 4739.32609311007 -162.326093110073 98 4155 4072.13353871192 82.8664612880757 99 3851 3685.92421974168 165.07578025832 100 3429 3512.22381455546 -83.2238145554611 101 3370 3244.77846622642 125.22153377358 102 2726 2411.44519592482 314.554804075179 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 103 1947.58190806176 1726.60026838129 2168.56354774222 104 3337.57580194295 3103.66115244467 3571.49045144124 105 4282.25322354332 4032.08312618455 4532.42332090209 106 4562.61424411506 4302.00907671979 4823.21941151034 107 5331.33592189944 5049.29564316104 5613.37620063784 108 4980.99350540246 4699.38145406586 5262.60555673906 109 5009.49402399384 4720.0000381381 5298.98800984958 110 4389.90553887547 4108.79305144498 4671.01802630597 111 3998.2870441714 3720.50055246462 4276.07353587817 112 3719.66254320856 3442.82090306382 3996.5041833533 113 3509.41703288083 3232.09811092984 3786.73595483183 114 2672.44929115105 2536.40344186298 2808.49514043912

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/1m52r1275653876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/1m52r1275653876.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/2fekc1275653876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/2fekc1275653876.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/3fekc1275653876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/04/t12756539108jp94jq6d9fxfv8/3fekc1275653876.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=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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