Exponential Smoothing - Koers BEL 20 van Januari 2000 tot Januari 2009 - Claus Wesley

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 01:41:47 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt.htm/, Retrieved Tue, 02 Jun 2009 09:43:26 +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/2009/Jun/02/t12439286024q0yhdl9etcouyt.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 «

1635,25 1765,9 1833,42 1862,83 1905,41 1910,43 1940,49 1946,81 1959,67 1969,6 1995,37 2014,45 2042 2061,41 2065,81 2091,48 2120,88 2174,56 2196,72 2197,82 2214,95 2304,98 2350,44 2407,6 2408,64 2440,25 2448,05 2452,62 2472,81 2497,84 2555,28 2604,42 2638,53 2641,65 2645,64 2659,81 2720,25 2735,7 2745,88 2756,76 2767,63 2794,83 2799,43 2803,47 2811,7 2833,18 2845,26 2848,96 2849,27 2863,36 2882,6 2892,63 2897,06 2915,02 2921,44 2962,34 2981,85 2987,1 2995,55 3012,61 3013,24 3030,29 3032,6 3032,93 3045,78 3047,03 3061,26 3080,58 3097,31 3106,22 3110,52 3119,31 3142,95 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3504,37 3570,12 3667,03 3674,4 3701,61 3720,98 3801,06 3801,06 3813,06 3844,49 3857,62 3862,27 3895,51 3917,96 3970,1 4105,18 4116,68 4138,52 4199,75 4202,52 4290,89 4296,49 4356,98 4435,23 4443,91 4502,64 4562,84 4591,27 4621,4 4696,96

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 0.0887765523093223 gamma 0.518290651633152 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2042 1916.84015491453 125.159845085471 14 2061.41 2073.58958995384 -12.1795899538370 15 2065.81 2076.94791128253 -11.1379112825284 16 2091.48 2098.11370925227 -6.63370925227082 17 2120.88 2122.76687474917 -1.8868747491656 18 2174.56 2173.87228118096 0.687718819038764 19 2196.72 2228.46166782001 -31.7416678200075 20 2197.82 2201.51041865307 -3.69041865306599 21 2214.95 2216.08779600847 -1.13779600846965 22 2304.98 2232.97261973494 72.0073802650613 23 2350.44 2345.94018669570 4.49981330430319 24 2407.6 2383.63133127356 23.9686687264434 25 2408.64 2449.6908537132 -41.0508537132 26 2440.25 2439.49316711785 0.756832882145773 27 2448.05 2456.19993946514 -8.14993946514005 28 2452.62 2481.03099927123 -28.4109992712279 29 2472.81 2482.6508520416 -9.8408520415992 30 2497.84 2523.84013179223 -26.0001317922256 31 2555.28 2547.41026306546 7.86973693454229 32 2604.42 2559.25557784475 45.1644221552451 33 2638.53 2626.21011953074 12.3198804692597 34 2641.65 2661.269669377 -19.6196693769971 35 2645.64 2679.19290277226 -33.5529027722582 36 2659.81 2672.03585841083 -12.2258584108349 37 2720.25 2691.89215551876 28.3578444812356 38 2735.7 2747.2563338494 -11.5563338493994 39 2745.88 2746.70998570625 -0.829985706248408 40 2756.76 2774.57088577011 -17.8108857701141 41 2767.63 2783.4417800712 -15.8117800712025 42 2794.83 2814.78098141727 -19.9509814172734 43 2799.43 2841.05813540519 -41.6281354051944 44 2803.47 2795.66919973152 7.80080026847736 45 2811.7 2814.20672788461 -2.50672788461179 46 2833.18 2822.07002255877 11.1099774412291 47 2845.26 2861.08132805224 -15.8213280522368 48 2848.96 2863.58843176147 -14.6284317614727 49 2849.27 2872.76143669066 -23.4914366906628 50 2863.36 2863.39261459914 -0.0326145991393787 51 2882.6 2862.50930252081 20.0906974791924 52 2892.63 2901.28746870983 -8.65746870983185 53 2897.06 2910.12097181938 -13.0609718193814 54 2915.02 2935.26438043811 -20.2443804381132 55 2921.44 2952.27548747251 -30.8354874725128 56 2962.34 2909.66468587259 52.6753141274071 57 2981.85 2969.04601865264 12.8039813473647 58 2987.1 2989.54854530582 -2.44854530581961 59 2995.55 3011.12617189540 -15.5761718953950 60 3012.61 3010.02503972301 2.58496027698720 61 3013.24 3034.08619025093 -20.8461902509262 62 3030.29 3025.27220401833 5.01779598166922 63 3032.6 3027.79724997911 4.80275002089047 64 3032.93 3048.2882049009 -15.3582049009001 65 3045.78 3046.82683975347 -1.04683975347189 66 3047.03 3081.45682159600 -34.4268215960042 67 3061.26 3080.49886040108 -19.2388604010766 68 3080.58 3046.72756737098 33.8524326290240 69 3097.31 3082.85786962706 14.4521303729357 70 3106.22 3100.72671326843 5.49328673156879 71 3110.52 3126.66938832531 -16.1493883253056 72 3119.31 3121.36736797455 -2.05736797454892 73 3142.95 3136.7463886056 6.20361139439774 74 3161.69 3153.34379050373 8.3462094962697 75 3257.16 3157.85432154099 99.3056784590049 76 3277.01 3279.89492063266 -2.88492063265585 77 3295.32 3299.06089065854 -3.74089065853696 78 3363.99 3338.91170394997 25.0782960500283 79 3494.17 3410.65640194442 83.513598055581 80 3504.37 3501.95711791741 2.41288208259266 81 3570.12 3526.17632526983 43.9436747301711 82 3667.03 3595.68332654151 71.3466734584918 83 3674.4 3715.47223822989 -41.0722382298923 84 3701.61 3711.02765319088 -9.4176531908829 85 3720.98 3744.17325307642 -23.1932530764170 86 3801.06 3753.89090269812 47.1690973018781 87 3801.06 3823.18799586546 -22.1279958654600 88 3813.06 3838.97813201634 -25.9181320163420 89 3844.49 3848.24929294697 -3.75929294696743 90 3857.62 3901.21847254668 -43.5984725466801 91 3862.27 3911.32628380137 -49.056283801367 92 3895.51 3865.32790272304 30.1820972769592 93 3917.96 3915.05236526075 2.90763473924517 94 3970.1 3937.61632838161 32.4836716183877 95 4105.18 4009.18511675424 95.9948832457599 96 4116.68 4144.6188781948 -27.9388781948019 97 4138.52 4160.41022757995 -21.8902275799446 98 4199.75 4172.7135553128 27.0364446872036 99 4202.52 4221.37334099216 -18.8533409921629 100 4290.89 4240.2241897127 50.6658102873016 101 4296.49 4332.6642090033 -36.1742090032985 102 4356.98 4356.92570411213 0.0542958878668287 103 4435.23 4418.26885764720 16.9611423528031 104 4443.91 4451.73127605517 -7.82127605517326 105 4502.64 4473.52193013234 29.1180698676644 106 4562.84 4534.69276531842 28.147234681579 107 4591.27 4613.93657977049 -22.6665797704927 108 4621.4 4632.18598563249 -10.7859856324922 109 4696.96 4668.13010968145 28.8298903185523 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 4738.65619461405 4675.7402815835 4801.5721076446 111 4765.38197256144 4672.3720272642 4858.39191785867 112 4809.86233384215 4690.95182920173 4928.77283848258 113 4853.91477845621 4710.78064080881 4997.0489161036 114 4919.84013973692 4753.23802588022 5086.44225359363 115 4986.61383435098 4796.85411329068 5176.37355541127 116 5007.09419563169 4794.23922569959 5219.9491655638 117 5041.37955691241 4805.34117341531 5277.41794040952 118 5075.52075152646 4816.11414561032 5334.92735744261 119 5126.20694614052 4843.18284993936 5409.23104234167 120 5168.72480742123 4861.78984904207 5475.6597658004 121 5218.01433536862 4886.84448347111 5549.18418726612

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/1muqk1243928504.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/1muqk1243928504.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/27fxv1243928504.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/27fxv1243928504.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/3drwi1243928504.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439286024q0yhdl9etcouyt/3drwi1243928504.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=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')

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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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