Exponential Smoothing bij Time Series Analysis-Inschrijvingen nieuwe personenwagen (eigen reeks)-Ling Weng

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 May 2011 10:00:51 +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/17/t1305626298kbn2l00oje8u8st.htm/, Retrieved Tue, 17 May 2011 11:58:31 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

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26281 23899 25727 30733 28599 16723 43738 45272 46532 41032 37967 35366 33892 21560 26588 33527 24859 17952 45504 40129 40357 41913 33730 37842 33025 24050 30429 34507 25189 20253 48527 44446 46380 48950 38883 42928 37107 30186 32602 39892 32194 21629 59968 45694 55756 48554 41052 49822 39191 31994 35735 38930 33658 23849 58972 59249 63955 53785 52760 44795 37348 32370 32717 40974 33591 21124 58608 46865 51378 46235 47206 45382 41227 33795 31295 42625 33625 21538 56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.299879412252782 beta 0 gamma 0.349182850776405 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 33892 33798.3976961584 93.6023038415951 14 21560 21552.9720026785 7.02799732148924 15 26588 26888.1310517072 -300.131051707198 16 33527 33929.5240389334 -402.524038933356 17 24859 25109.3522847842 -250.35228478421 18 17952 18072.0832006946 -120.08320069464 19 45504 42850.4365793122 2653.56342068777 20 40129 44771.087406539 -4642.08740653903 21 40357 44549.5657657189 -4192.56576571891 22 41913 37901.5707251791 4011.42927482095 23 33730 36129.7009680399 -2399.70096803994 24 37842 32996.4593697799 4845.54063022006 25 33025 32829.7714509667 195.228549033258 26 24050 20941.1724818495 3108.82751815046 27 30429 27209.3888990417 3219.6111009583 28 34507 35671.1619825215 -1164.16198252153 29 25189 26248.5428154518 -1059.5428154518 30 20253 18736.401931757 1516.59806824305 31 48527 46355.3389409546 2171.66105904542 32 44446 46275.7477951946 -1829.74779519455 33 46380 47090.2980031004 -710.298003100448 34 48950 43101.0793392308 5848.92066076915 35 38883 39770.2737958123 -887.273795812296 36 42928 38731.2217916038 4196.7782083962 37 37107 36906.5305457332 200.4694542668 38 30186 24327.4526078805 5858.54739211946 39 32602 32244.5889745158 357.41102548422 40 39892 39535.1691910924 356.830808907573 41 32194 29409.9055566125 2784.0944433875 42 21629 22508.9016903962 -879.901690396178 43 59968 53324.3310286009 6643.66897139913 44 45694 53339.683081199 -7645.683081199 45 55756 52905.9993039098 2850.00069609021 46 48554 51211.8180620544 -2657.81806205442 47 41052 43089.3371452171 -2037.33714521712 48 49822 42959.2621826019 6862.73781739811 49 39191 40569.2102791524 -1378.21027915242 50 31994 27845.4380757448 4148.56192425518 51 35735 34183.8893229551 1551.1106770449 52 38930 42327.2384151215 -3397.23841512149 53 33658 31269.5484101878 2388.45158981219 54 23849 23057.1729841271 791.827015872852 55 58972 58047.8843362817 924.115663718301 56 59249 52638.3474655253 6610.65253447473 57 63955 59536.0061775168 4418.99382248316 58 53785 56508.9716928303 -2723.97169283033 59 52760 47666.9318429067 5093.06815709334 60 44795 52234.4682698308 -7439.46826983076 61 37348 43085.2062658501 -5737.20626585011 62 32370 29937.2873490857 2432.71265091434 63 32717 35205.7453001402 -2488.74530014017 64 40974 40801.3467616453 172.653238354709 65 33591 32136.1037191569 1454.89628084312 66 21124 23250.7063630654 -2126.70636306539 67 58608 56096.8941821823 2511.1058178177 68 46865 52618.1462843655 -5753.14628436547 69 51378 54823.7040192324 -3445.70401923241 70 46235 48471.9813162077 -2236.98131620768 71 47206 42443.7826692697 4762.21733073031 72 45382 43768.4281423932 1613.57185760684 73 41227 38220.5277659155 3006.47223408447 74 33795 29875.0224689907 3919.97753100931 75 31295 34350.2593572568 -3055.25935725682 76 42625 40339.3898095476 2285.61019045239 77 33625 32590.077885417 1034.92211458299 78 21538 22697.0158892503 -1159.01588925028 79 56421 57362.1369654417 -941.136965441707 80 53152 50821.4691753984 2330.53082460164 81 53536 56187.9243639391 -2651.9243639391 82 52408 50134.6584614178 2273.3415385822 83 41454 46861.8263071366 -5407.82630713655 84 38271 44359.0796649402 -6088.07966494024 85 35306 37091.4423342542 -1785.44233425417 86 26414 28241.0030737985 -1827.00307379846 87 31917 29045.7384414805 2871.26155851945 88 38030 37403.5710188032 626.428981196754 89 27534 29681.4224998943 -2147.4224998943 90 18387 19621.4912786712 -1234.49127867119 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 91 49828.0146536114 46267.7779824663 53388.2513247564 92 45023.5806222922 41044.7615949402 49002.3996496443 93 47981.5267531921 43435.5218056609 52527.5317007233 94 44408.7143520964 39627.0498209403 49190.3788832525 95 39313.1389102739 34442.0215017634 44184.2563187844 96 38308.7427464306 33123.0707046436 43494.4147882176 97 34199.8574762959 28990.1887014171 39409.5262511746 98 26305.3913238751 21451.3660678557 31159.4165798945 99 28698.2859829984 23194.1208503441 34202.4511156527 100 35206.5751187632 28487.8801630226 41925.2700745039 101 27180.6106619964 21313.3861514725 33047.8351725202 102 18409.6071120149 14974.5163881951 21844.6978358347

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/19m541305626450.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/19m541305626450.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/2b9xe1305626450.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/2b9xe1305626450.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/3bxsq1305626450.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305626298kbn2l00oje8u8st/3bxsq1305626450.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')

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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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