IKO - opgave 10 - oefening 2 - Melino Olivini

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Jun 2010 18:00:21 +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/03/t1275588133opfz08o5tm19zth.htm/, Retrieved Thu, 03 Jun 2010 20:02:17 +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/03/t1275588133opfz08o5tm19zth.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 «

5221,3 5115,9 5107,4 5202,1 5307,5 5266,1 5329,8 5263,4 5177,1 5204,9 5185,2 5189,8 5253,8 5372,3 5478,4 5590,5 5699,8 5797,9 5854,3 5902,4 5956,9 6007,8 6101,7 6148,6 6207,4 6232 6291,7 6323,4 6365 6435 6493,4 6606,8 6639,1 6723,5 6759,4 6848,6 6918,1 6963,5 7013,1 7030,9 7112,1 7130,3 7130,8 7076,9 7040,8 7086,5 7120,7 7154,1 7228,2 7297,9 7369,5 7450,7 7459,7 7497,5 7536 7637,4 7715,1 7815,7 7859,5 7951,6 7973,7 7988 8053,1 8112 8169,2 8303,1 8372,7 8470,6 8536,1 8665,8 8773,7 8838,4 8936,2 8995,3 9098,9 9237,1 9315,5 9392,6 9502,2 9671,1 9695,6 9847,9 9836,6 9887,7 9875,6 9905,9 9871,1 9910 9977,3 10031,6 10090,7 10095,8 10126 10212,7 10398,7 10467 10543,6 10634,2 10728,7 10796,4 10875,8 10946,1 11050 11086,1 11217,3 11291,7 11314,1 11356,4 11357,8 11491,4 11625,7 11620,7

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 1 beta 0.384583602218265 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 5107.4 5010.5 96.9000000000005 4 5202.1 5039.26615105495 162.833848945051 5 5307.5 5196.5893792453 110.910620754697 6 5266.1 5344.64378529941 -78.5437852994073 7 5329.8 5273.03713341710 56.7628665828961 8 5263.4 5358.56720111979 -95.1672011197888 9 5177.1 5255.56745610011 -78.4674561001093 10 5204.9 5139.09015917623 65.8098408237729 11 5185.2 5192.19954482164 -6.99954482164321 12 5189.8 5169.80763466025 19.9923653397527 13 5253.8 5182.09637053947 71.7036294605268 14 5372.3 5273.67241064953 98.6275893504735 15 5478.4 5430.10296424004 48.2970357599643 16 5590.5 5554.77721222907 35.7227877709338 17 5699.8 5680.61561063129 19.1843893687092 18 5797.9 5797.29361220107 0.606387798932701 19 5854.3 5895.62681900512 -41.3268190051213 20 5902.4 5936.13320208391 -33.7332020839103 21 5956.9 5971.25996571212 -14.3599657121231 22 6007.8 6020.23735837082 -12.4373583708229 23 6101.7 6066.35415428649 35.3458457135066 24 6148.6 6173.84758695444 -25.2475869544442 25 6207.4 6211.03777901619 -3.63777901618596 26 6232 6268.43874885807 -36.438748858066 27 6291.7 6279.0250035619 12.6749964380951 28 6323.4 6343.59959935017 -20.1995993501714 29 6365 6367.53116466872 -2.53116466871597 30 6435 6408.15772024261 26.8422797573858 31 6493.4 6488.48082088346 4.91917911653945 32 6606.8 6548.77265650806 58.0273434919445 33 6639.1 6684.48902129535 -45.3890212953447 34 6723.5 6699.33314798442 24.1668520155799 35 6759.4 6793.02732298685 -33.6273229868475 36 6848.6 6815.99480597961 32.6051940203924 37 6918.1 6917.734228947 0.365771053004210 38 6963.5 6987.37489849615 -23.8748984961476 39 7013.1 7023.5930040299 -10.4930040299032 40 7030.9 7069.15756674199 -38.2575667419933 41 7112.1 7072.24433391225 39.8556660877493 42 7130.3 7168.77216954509 -38.4721695450862 43 7130.8 7172.17640399629 -41.3764039962853 44 7076.9 7156.76371750056 -79.863717500556 45 7040.8 7072.14944133765 -31.3494413376493 46 7086.5 7023.99296026049 62.5070397395139 47 7120.7 7093.7321427675 26.9678572324910 48 7154.1 7138.30353844609 15.7964615539122 49 7228.2 7177.7785985328 50.4214014672052 50 7297.9 7271.26984273795 26.6301572620541 51 7369.5 7351.21136454542 18.2886354545753 52 7450.7 7429.8448738482 20.8551261517978 53 7459.7 7519.06541338838 -59.3654133883765 54 7497.5 7505.2344488603 -7.73444886029847 55 7536 7540.05990665643 -4.05990665643185 56 7637.4 7576.99853312983 60.4014668701684 57 7715.1 7701.62794683803 13.4720531619723 58 7815.7 7784.50907757234 31.1909224276642 59 7859.5 7897.10459487608 -37.6045948760766 60 7951.6 7926.44248431868 25.1575156813233 61 7973.7 8028.21765232226 -54.5176523222635 62 7988 8029.35105720768 -41.3510572076839 63 8053.1 8027.74811867122 25.351881328781 64 8112 8102.59803651565 9.40196348434802 65 8169.2 8165.11387750039 4.08612249961334 66 8303.1 8223.88533321039 79.2146667896068 67 8372.7 8388.24999511286 -15.5499951128604 68 8470.6 8451.86972197788 18.7302780221198 69 8536.1 8556.97307977018 -20.8730797701755 70 8665.8 8614.44563556277 51.3543644372257 71 8773.7 8763.89568202767 9.80431797232995 72 8838.4 8875.56626195076 -37.1662619507642 73 8936.2 8925.97272704875 10.2272729512515 74 8995.3 9027.70596852121 -32.4059685212142 75 9098.9 9074.34316441395 24.5568355860487 76 9237.1 9187.38732070272 49.7126792972849 77 9315.5 9344.70600198279 -29.2060019827877 78 9392.6 9411.87385253385 -19.2738525338518 79 9502.2 9481.56144489776 20.6385551022395 80 9671.1 9599.09869476356 72.0013052364393 81 9695.6 9795.6892160958 -100.089216095806 82 9847.9 9781.69654482648 66.2034551735196 83 9836.6 9959.4573080964 -122.857308096407 84 9887.7 9900.90840198985 -13.2084019898521 85 9875.6 9946.92866717305 -71.3286671730475 86 9905.9 9907.3968314102 -1.49683141020978 87 9871.1 9937.12117459456 -66.0211745945562 88 9910 9876.9305134463 33.0694865536989 89 9977.3 9928.54849570863 48.7515042913674 90 10031.6 10014.5975248426 17.0024751574365 91 10090.7 10075.4363979852 15.263602014762 92 10095.8 10140.4065290309 -44.6065290309034 93 10126 10128.3515894137 -2.35158941374175 94 10212.7 10157.6472066861 55.0527933139329 95 10398.7 10265.5196082509 133.180391749082 96 10467 10502.7386030546 -35.7386030546204 97 10543.6 10557.2941223536 -13.6941223536251 98 10634.2 10628.6275874497 5.57241255034933 99 10728.7 10721.3706459413 7.3293540586892 100 10796.4 10818.6893953271 -22.2893953271359 101 10875.8 10877.8172593810 -2.01725938095842 102 10946.1 10956.4414545016 -10.3414545016185 103 11050 11022.7643006772 27.2356993227877 104 11086.1 11137.1387040317 -51.0387040317019 105 11217.3 11153.6100553826 63.6899446173593 106 11291.7 11309.3041637087 -17.6041637086637 107 11314.1 11376.9338910155 -62.8338910155471 108 11356.4 11375.1690068674 -18.7690068673983 109 11357.8 11410.2507545963 -52.4507545962751 110 11491.4 11391.4790544546 99.9209455454275 111 11625.7 11563.5070116295 62.1929883705125 112 11620.7 11721.7254151297 -101.025415129739 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 113 11677.8726970635 11578.6811236784 11777.0642704487 114 11735.0453941271 11565.6317692625 11904.4590189917 115 11792.2180911906 11548.2990873031 12036.1370950782 116 11849.3907882542 11525.144065813 12173.6375106954

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/1tscp1275588019.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/1tscp1275588019.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/241ta1275588019.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/241ta1275588019.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/341ta1275588019.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275588133opfz08o5tm19zth/341ta1275588019.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; par2 = Double ; 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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