Opgave 10 - Aantal nieuwe gebouwen - Christophe Morre

*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 01:32:33 -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/t1243928004m0x7l2ea7ysxyj8.htm/, Retrieved Tue, 02 Jun 2009 09:33:28 +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/t1243928004m0x7l2ea7ysxyj8.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 «

2194 2419 2742 2137 2710 2173 2363 2126 1905 2121 1983 1734 2074 2049 2406 2558 2251 2059 2397 1747 1707 2319 1631 1627 1791 2034 1997 2169 2028 2253 2218 1855 2187 1852 1570 1851 1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2945 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2259 2844 2546 2456 2295 2379 2479 2057 2280 2351 2275 2543 2305 2188 2720 2398 2147 1898 2538 2081 2057 2497 2460 2195 2823 2100 2640 2342 2171 2482

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.243472330170413 beta 0.0205562664353707 gamma 0.397243808484191 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2074 2141.93536324786 -67.9353632478637 14 2049 2102.77000853926 -53.7700085392644 15 2406 2458.45107986328 -52.4510798632814 16 2558 2585.14909568857 -27.1490956885655 17 2251 2265.28823320274 -14.2882332027352 18 2059 2076.19545728523 -17.1954572852301 19 2397 2224.14212484319 172.857875156807 20 1747 2037.68498672405 -290.684986724054 21 1707 1761.91314380543 -54.9131438054333 22 2319 1947.31205372759 371.687946272413 23 1631 1889.56177944909 -258.561779449087 24 1627 1588.36073130781 38.6392686921906 25 1791 1907.75529479443 -116.755294794434 26 2034 1859.44629684248 174.553703157516 27 1997 2270.74258262418 -273.742582624177 28 2169 2349.68694120936 -180.686941209358 29 2028 1994.0612437758 33.9387562241989 30 2253 1813.83043889310 439.169561106896 31 2218 2130.28309877620 87.7169012237955 32 1855 1783.64150072934 71.3584992706608 33 2187 1668.53642928732 518.463570712676 34 1852 2126.27472463116 -274.274724631161 35 1570 1723.14439010108 -153.144390101079 36 1851 1538.75414635396 312.245853646036 37 1954 1881.26157993508 72.7384200649212 38 1828 1970.7806937783 -142.780693778301 39 2251 2172.64768095312 78.3523190468832 40 2277 2369.6027385011 -92.6027385011012 41 2085 2104.68424549635 -19.6842454963517 42 2282 2037.67226268747 244.327737312528 43 2266 2204.58270454306 61.4172954569367 44 1878 1850.00714303399 27.9928569660087 45 2267 1861.87875317538 405.121246824616 46 2069 2056.38399510040 12.616004899603 47 1746 1763.54335798965 -17.5433579896455 48 2299 1756.74565401575 542.254345984248 49 2360 2089.14236508221 270.857634917789 50 2214 2168.98727518902 45.0127248109839 51 2825 2490.83118453767 334.168815462334 52 2355 2707.77259984061 -352.772599840605 53 2333 2409.20027051493 -76.200270514933 54 3016 2415.26421869386 600.73578130614 55 2155 2623.25817848311 -468.258178483112 56 2172 2136.30277337822 35.6972266217767 57 2150 2270.05199379037 -120.051993790372 58 2533 2222.77059727665 310.229402723346 59 2058 1998.8529550737 59.1470449263002 60 2160 2184.87083389630 -24.8708338962956 61 2260 2300.69797605381 -40.6979760538079 62 2498 2238.32763409113 259.672365908869 63 2695 2701.92064729472 -6.92064729471576 64 2799 2630.25191113638 168.748088863620 65 2945 2545.2621503655 399.737849634501 66 2930 2876.51226824777 53.487731752226 67 2318 2633.13871952370 -315.138719523695 68 2540 2338.81433512761 201.185664872394 69 2570 2470.77598263163 99.2240173683713 70 2669 2612.01764729391 56.982352706093 71 2450 2255.54182604720 194.458173952797 72 2842 2454.48911570999 387.510884290008 73 3440 2673.26169729084 766.738302709157 74 2678 2909.08831638889 -231.088316388890 75 2981 3181.9598610077 -200.959861007702 76 2259 3123.75310501022 -864.753105010216 77 2844 2859.29241091157 -15.2924109115679 78 2546 2986.09942425485 -440.099424254849 79 2456 2509.96132662118 -53.9613266211827 80 2295 2433.89451418500 -138.894514185003 81 2379 2450.21110390858 -71.2111039085758 82 2479 2534.20598417388 -55.2059841738787 83 2057 2188.11313454535 -131.113134545352 84 2280 2360.56339693259 -80.563396932594 85 2351 2571.75109163386 -220.751091633858 86 2275 2254.74689883006 20.2531011699407 87 2543 2586.59374778731 -43.5937477873131 88 2305 2356.72804265566 -51.7280426556558 89 2188 2539.08435742891 -351.084357428911 90 2720 2448.37213505697 271.627864943031 91 2398 2257.02889800291 140.971101997091 92 2147 2199.33817364837 -52.3381736483684 93 1898 2253.94272245668 -355.942722456683 94 2538 2268.87150259653 269.128497403467 95 2081 1976.00453059727 104.995469402734 96 2057 2219.38538054769 -162.385380547686 97 2497 2366.36530768190 130.634692318104 98 2460 2206.94414390802 253.055856091976 99 2195 2577.05184215065 -382.051842150655 100 2823 2261.40990062501 561.590099374991 101 2100 2505.27097288365 -405.27097288365 102 2640 2590.37887889006 49.621121109943 103 2342 2306.47817788752 35.5218221124765 104 2171 2165.25204089819 5.7479591018132 105 2482 2143.28164944744 338.718350552561 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 106 2519.19172175873 2006.53626811179 3031.84717540566 107 2114.12665028470 1585.88230031074 2642.37100025866 108 2253.71711360180 1709.72370354922 2797.71052365438 109 2531.23422242952 1971.33334610173 3091.13509875732 110 2379.08475290284 1803.11969916223 2955.04980664345 111 2497.73439679447 1905.55009094956 3089.91870263938 112 2561.63288466798 1953.07583340372 3170.18993593224 113 2378.31729143701 1753.23553098585 3003.39905188818 114 2700.95448008141 2059.19752736499 3342.71143279784 115 2402.63699990829 1744.05580640828 3061.2181934083 116 2245.53847742671 1569.98538556802 2921.09156928539 117 2323.9300998666 1631.25880171814 3016.60139801507

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/1hn9t1243927951.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/1hn9t1243927951.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/2fz8k1243927951.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/2fz8k1243927951.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/3xn9d1243927951.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8/3xn9d1243927951.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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