*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 12 Dec 2009 10:11:35 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t.htm/, Retrieved Sat, 12 Dec 2009 18:12:10 +0100

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/2009/Dec/12/t1260637926p73o0h5ahk76o4t.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

4716.99 4926.65 4920.10 5170.09 5246.24 5283.61 4979.05 4825.20 4695.12 4711.54 4727.22 4384.96 4378.75 4472.93 4564.07 4310.54 4171.38 4049.38 3591.37 3720.46 4107.23 4101.71 4162.34 4136.22 4125.88 4031.48 3761.36 3408.56 3228.47 3090.45 2741.14 2980.44 3104.33 3181.57 2863.86 2898.01 3112.33 3254.33 3513.47 3587.61 3727.45 3793.34 3817.58 3845.13 3931.86 4197.52 4307.13 4229.43 4362.28 4217.34 4361.28 4327.74 4417.65 4557.68 4650.35 4967.18 5123.42 5290.85 5535.66 5514.06 5493.88 5694.83 5850.41 6116.64 6175.00 6513.58 6383.78 6673.66 6936.61 7300.68 7392.93 7497.31 7584.71 7160.79 7196.19 7245.63 7347.51 7425.75 7778.51 7822.33 8181.22 8371.47 8347.71 8672.11 8802.79 9138.46 9123.29 9023.21 8850.41 8864.58 9163.74 8516.66 8553.44 7555.20 7851.22 7442.00 7992.53 8264.04 7517.39 7200.40 7193.69 6193.58 5104.21 4800.46 4461.61 4398.59 4243.63 4293.82

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.917492764005406 beta 0.110092205215912 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4378.75 4816.92751819308 -438.177518193077 14 4472.93 4496.21089354897 -23.2808935489729 15 4564.07 4513.10358455271 50.9664154472939 16 4310.54 4239.8733072642 70.666692735802 17 4171.38 4106.45589796015 64.9241020398476 18 4049.38 3977.94887623674 71.4311237632651 19 3591.37 4149.49506581446 -558.125065814463 20 3720.46 3399.82009621670 320.639903783297 21 4107.23 3505.15520732032 602.074792679677 22 4101.71 4060.68418394558 41.0258160544163 23 4162.34 4131.56555974045 30.7744402595526 24 4136.22 3894.08387464931 242.136125350693 25 4125.88 4154.94897685148 -29.068976851484 26 4031.48 4325.45935120328 -293.979351203282 27 3761.36 4154.43857173772 -393.078571737716 28 3408.56 3533.71369017903 -125.15369017903 29 3228.47 3243.4310620317 -14.9610620316980 30 3090.45 3058.57649918596 31.8735008140447 31 2741.14 3093.76311739398 -352.62311739398 32 2980.44 2619.18289770903 361.257102290968 33 3104.33 2805.84420711042 298.485792889582 34 3181.57 3018.1441663724 163.425833627598 35 2863.86 3178.15656141591 -314.296561415905 36 2898.01 2666.39603585652 231.613964143483 37 3112.33 2845.94875378530 266.381246214703 38 3254.33 3205.72400635576 48.6059936442371 39 3513.47 3336.80918577878 176.660814221217 40 3587.61 3351.7434447048 235.866555295201 41 3727.45 3514.10829742696 213.341702573044 42 3793.34 3668.52619479052 124.813805209481 43 3817.58 3918.55387384301 -100.97387384301 44 3845.13 3923.99556679087 -78.865566790866 45 3931.86 3813.57699870634 118.283001293661 46 4197.52 3958.53144217852 238.988557821479 47 4307.13 4271.77025223961 35.3597477603889 48 4229.43 4224.39398643604 5.03601356396393 49 4362.28 4336.93915489609 25.3408451039068 50 4217.34 4616.91599552967 -399.575995529669 51 4361.28 4449.25934087327 -87.9793408732712 52 4327.74 4228.69829515672 99.0417048432819 53 4417.65 4269.9900805267 147.659919473294 54 4557.68 4355.87501902967 201.804980970327 55 4650.35 4693.94957717584 -43.5995771758407 56 4967.18 4796.15524089788 171.024759102120 57 5123.42 4969.59510852716 153.824891472836 58 5290.85 5214.32273245127 76.527267548734 59 5535.66 5405.21553752457 130.444462475433 60 5514.06 5448.8532705348 65.2067294652006 61 5493.88 5685.92969523329 -192.049695233293 62 5694.83 5801.12967084213 -106.299670842128 63 5850.41 6061.60435771929 -211.194357719291 64 6116.64 5743.8688776575 372.771122342502 65 6175 6085.83500647657 89.1649935234327 66 6513.58 6155.59766721843 357.982332781573 67 6383.78 6731.26288163338 -347.482881633385 68 6673.66 6665.48576003458 8.17423996541947 69 6936.61 6705.65235616964 230.957643830358 70 7300.68 7063.28912002935 237.390879970652 71 7392.93 7478.45176447565 -85.5217644756458 72 7497.31 7294.2860237131 203.023976286897 73 7584.71 7704.13622379215 -119.426223792146 74 7160.79 8031.94951232763 -871.15951232763 75 7196.19 7636.49312696004 -440.303126960045 76 7245.63 7084.15881646387 161.471183536134 77 7347.51 7129.29084442936 218.219155570639 78 7425.75 7276.55492610909 149.195073890907 79 7778.51 7542.82985474693 235.68014525307 80 7822.33 8071.68707261266 -249.35707261266 81 8181.22 7850.98990210087 330.230097899135 82 8371.47 8279.82570997482 91.6442900251823 83 8347.71 8500.08610434749 -152.376104347488 84 8672.11 8206.79113280938 465.318867190617 85 8802.79 8819.95727301461 -17.1672730146129 86 9138.46 9200.11413671316 -61.6541367131595 87 9123.29 9759.3846864971 -636.094686497105 88 9023.21 9098.31483897915 -75.104838979154 89 8850.41 8927.78492225431 -77.3749222543138 90 8864.58 8775.42105991466 89.1589400853445 91 9163.74 9000.88602495431 162.853975045686 92 8516.66 9441.0806518963 -924.420651896304 93 8553.44 8567.95779799683 -14.5177979968266 94 7555.2 8549.0755763182 -993.8755763182 95 7851.22 7534.92877157304 316.291228426959 96 7442 7566.61549329302 -124.615493293017 97 7992.53 7373.89045050445 618.639549495546 98 8264.04 8144.3513033938 119.688696606198 99 7517.39 8625.34025516097 -1107.95025516096 100 7200.4 7399.17629217925 -198.776292179252 101 7193.69 6945.38035085194 248.309649148064 102 6193.58 6961.52078944754 -767.940789447538 103 5104.21 6128.92308453093 -1024.71308453093 104 4800.46 4961.83056552194 -161.370565521944 105 4461.61 4540.5469052901 -78.9369052900956 106 4398.59 4113.92388901846 284.666110981540 107 4243.63 4156.72896436101 86.9010356389854 108 4293.82 3851.46523822392 442.35476177608 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 4072.20688461099 3414.03653462214 4730.37723459984 110 3940.97750440011 2991.7661078309 4890.18890096933 111 3837.97900358632 2609.53229277538 5066.42571439726 112 3600.04735284454 2132.45031964165 5067.64438604742 113 3325.07845796578 1638.79122102413 5011.36569490742 114 3016.92775947944 1138.42270039448 4895.43281856441 115 2808.12376982676 685.807296425495 4930.44024322802 116 2658.59980265358 238.944757062995 5078.25484824416 117 2457.07454951061 -228.977495821141 5143.12659484237 118 2227.64673066096 -699.371999981562 5154.66546130347 119 2030.17168991497 -1184.40237592737 5244.74575575732 120 1770.22206128955 -1566.95727954501 5107.40140212411

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/1cwc91260637893.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/1cwc91260637893.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/2kd5i1260637893.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/2kd5i1260637893.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/35ql71260637893.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260637926p73o0h5ahk76o4t/35ql71260637893.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

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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