review WS 9 exponential smoothing

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Dec 2009 13:44:29 -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/06/t1260132346t2rwamkzoahp6h6.htm/, Retrieved Sun, 06 Dec 2009 21:45:50 +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/06/t1260132346t2rwamkzoahp6h6.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:

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2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2537 2069 2063 2524 2437 2189 2793 2074 2622 2278 2144 2427 2139 1828 2072 1800 1758 2246 1987 1868 2514 2121

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 0.347167391002761 beta 0.0325187100821525 gamma 0.393036024342864 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2260 2165.71971681071 94.2802831892864 14 2498 2431.59066431542 66.4093356845774 15 2695 2639.21051460026 55.7894853997418 16 2799 2762.94788953861 36.052110461389 17 2947 2925.69536649647 21.3046335035256 18 2930 2894.17629876157 35.8237012384334 19 2318 2379.93135935169 -61.9313593516904 20 2540 2391.95263488983 148.047365110167 21 2570 2436.04022753511 133.959772464894 22 2669 2938.60901177949 -269.609011779486 23 2450 2290.93533203163 159.064667968373 24 2842 2464.45787164299 377.542128357005 25 3440 2771.97809928578 668.021900714218 26 2678 3318.28871966593 -640.288719665934 27 2981 3327.19077198552 -346.190771985524 28 2260 3326.35191724600 -1066.35191724600 29 2844 3102.7683529705 -258.768352970502 30 2546 2966.09141466652 -420.091414666524 31 2456 2275.01908045422 180.980919545777 32 2295 2414.64068780833 -119.640687808334 33 2379 2350.55625820821 28.4437417917884 34 2479 2675.19009901314 -196.190099013143 35 2057 2178.13929213336 -121.139292133362 36 2280 2273.9620716808 6.03792831920009 37 2351 2459.59702725275 -108.597027252746 38 2276 2375.02088656453 -99.020886564529 39 2548 2562.43586993791 -14.4358699379077 40 2311 2458.22504011548 -147.225040115482 41 2201 2709.82987514301 -508.829875143014 42 2725 2437.61449401645 287.385505983555 43 2408 2163.01083964412 244.989160355882 44 2139 2240.54876701044 -101.548767010440 45 1898 2213.24299379638 -315.242993796379 46 2537 2320.30445896899 216.695541031008 47 2069 2005.29631666276 63.7036833372424 48 2063 2187.28515469447 -124.285154694467 49 2524 2282.83423077301 241.165769226993 50 2437 2319.83412911981 117.165870880190 51 2189 2608.49296364284 -419.492963642839 52 2793 2329.36548710150 463.634512898496 53 2074 2703.75440279794 -629.75440279794 54 2622 2595.60012289522 26.39987710478 55 2278 2216.36500646009 61.6349935399085 56 2144 2140.46243674390 3.53756325610357 57 2427 2089.09653730266 337.903462697335 58 2139 2595.01466406412 -456.014664064122 59 1828 2007.89160094113 -179.891600941129 60 2072 2046.60869385472 25.3913061452845 61 1800 2276.25230583301 -476.252305833008 62 1758 2031.79577134451 -273.795771344512 63 2246 2006.10271408423 239.897285915774 64 1987 2156.21535900778 -169.215359007781 65 1868 2017.54965846487 -149.549658464873 66 2514 2189.25953005690 324.740469943095 67 2121 1959.88673775854 161.113262241463 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 68 1909.36570395408 1549.43102452977 2269.3003833784 69 1928.65391285178 1508.70071383447 2348.60711186910 70 2067.64642735290 1577.97032461735 2557.32253008844 71 1742.12508008275 1246.45952430926 2237.79063585623 72 1879.59065444489 1307.60976946457 2451.57153942521 73 1950.78838144931 1313.69986587277 2587.87689702584 74 1921.70191536672 1243.71899427583 2599.68483645761 75 2131.0523856025 1344.97357805235 2917.13119315265 76 2093.66164578083 1272.09814697024 2915.22514459141 77 2019.88847155494 1176.42674110791 2863.35020200197 78 2384.09597578782 1357.62091446766 3410.57103710799 79 2000.90322925556 1147.67823346131 2854.12822504982

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/1r7q61260132267.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/1r7q61260132267.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/258531260132267.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/258531260132267.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/3t0qj1260132267.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132346t2rwamkzoahp6h6/3t0qj1260132267.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=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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