Exponential smoothing Toegekende bouwvergunningen voor het aantal woningen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 07:53:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c.htm/, Retrieved Sat, 16 Jan 2010 15:55:45 +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/2010/Jan/16/t12636537410e1w5z5o7pk6q1c.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 «

2766 3851 3289 3848 3348 3682 4058 3655 3811 3341 3032 3475 3353 3186 3902 4164 3499 4145 3796 3711 3949 3740 3243 4407 4814 3908 5250 3937 4004 5560 3922 3759 4138 4634 3996 4308 4143 4429 5219 4929 5761 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5526 4248 3830 4430 4837 4408 4569 4104 4807 3944 3794 4390 4041 4104 4823

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.246198542886314 beta 0 gamma 0.397334337843492 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3353 3222.9249465812 130.075053418801 14 3186 3111.84798228501 74.152017714986 15 3902 3853.3361814181 48.6638185818956 16 4164 4120.25755639716 43.7424436028359 17 3499 3455.92562936072 43.0743706392841 18 4145 4080.22089040077 64.7791095992334 19 3796 4206.10982654648 -410.109826546484 20 3711 3720.70679858029 -9.70679858029416 21 3949 3891.79907933332 57.2009206666844 22 3740 3412.48894307279 327.511056927212 23 3243 3179.97876848701 63.0212315129947 24 4407 3628.22658427599 778.773415724014 25 4814 3743.85881392609 1070.14118607391 26 3908 3847.47518601694 60.5248139830587 27 5250 4577.97438626735 672.025613732649 28 3937 4996.89251996398 -1059.89251996398 29 4004 4060.6471776821 -56.6471776821008 30 5560 4666.89195130402 893.108048695985 31 3922 4854.47970881134 -932.479708811336 32 3759 4360.39516950586 -601.395169505861 33 4138 4405.85424696435 -267.854246964353 34 4634 3927.47691612331 706.523083876686 35 3996 3709.06128456337 286.938715436627 36 4308 4426.81305624074 -118.813056240736 37 4143 4408.72871574138 -265.728715741384 38 4429 3881.06445052013 547.935549479871 39 5219 4914.71480370012 304.285196299883 40 4929 4724.36689904177 204.633100958234 41 5761 4399.92914127151 1361.07085872849 42 5592 5639.67635992577 -47.6763599257747 43 4163 5048.86038174167 -885.860381741668 44 4962 4665.41698143613 296.583018563868 45 5208 5031.85622324376 176.143776756239 46 4755 4954.6274852554 -199.627485255402 47 4491 4387.44868506034 103.551314939656 48 5732 4938.52354476708 793.476455232923 49 5731 5101.04066679174 629.95933320826 50 5040 5037.59505687693 2.40494312307237 51 6102 5863.96055932165 238.039440678354 52 4904 5627.45612721679 -723.456127216791 53 5369 5420.89021762652 -51.8902176265246 54 5578 5890.83290418776 -312.832904187757 55 4619 4983.69026660452 -364.690266604521 56 4731 5082.71323434286 -351.713234342859 57 5011 5253.46998114473 -242.469981144732 58 5299 4960.63144325579 338.368556744208 59 4146 4616.71193179793 -470.71193179793 60 4625 5233.04432555503 -608.044325555029 61 4736 5001.53386362427 -265.533863624275 62 4219 4529.65956327045 -310.659563270452 63 5116 5349.52421220215 -233.524212202151 64 4205 4708.94280182617 -503.942801826167 65 4121 4757.56226645068 -636.562266450677 66 5103 5005.404288604 97.5957113960058 67 4300 4183.77671714341 116.223282856590 68 4578 4405.08666655518 172.913333444816 69 3809 4737.72528807202 -928.725288072015 70 5526 4449.89934270139 1076.10065729861 71 4248 4045.27972913278 202.720270867217 72 3830 4786.27755947736 -956.277559477362 73 4430 4571.6183032043 -141.6183032043 74 4837 4116.73618068735 720.263819312652 75 4408 5213.51556601744 -805.515566017442 76 4569 4351.1173207433 217.882679256702 77 4104 4537.72815166057 -433.728151660567 78 4807 5055.39617633328 -248.396176333275 79 3944 4154.16507259718 -210.165072597176 80 3794 4312.09798972122 -518.097989721216 81 4390 4144.65752174464 245.342478255357 82 4041 4746.3531800518 -705.353180051795 83 4104 3641.55501744207 462.444982557926 84 4823 4099.36385911524 723.636140884755 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 4542.29648178718 3518.12874103289 5566.46422254147 86 4380.42393037592 3325.67349523520 5435.17436551664 87 4842.88739394754 3758.41637097951 5927.35841691558 88 4485.32514671298 3371.92660221729 5598.72369120868 89 4423.12883573348 3281.53554646057 5564.72212500638 90 5103.08910220651 3933.98082777649 6272.19737663652 91 4274.46341900762 3078.47300242038 5470.45383559486 92 4391.90931237261 3169.62784078094 5614.19078396429 93 4580.68278738876 3332.66399144692 5828.70158333059 94 4837.23148489865 3563.99551531096 6110.46745448634 95 4255.85887978116 2957.89557002248 5553.82218953983 96 4678.04411858192 3355.81582032647 6000.27241683736

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/1uhw51263653630.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/1uhw51263653630.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/29cj61263653630.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/29cj61263653630.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/35pra1263653630.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c/35pra1263653630.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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