Exponential Smoothing - Aantal Bouwvergunningen - Wouter Schuurbiers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 01:54:10 +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/20/t1305856259n2wxbz3hgkee2id.htm/, Retrieved Fri, 20 May 2011 03:51:02 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

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1394 1657 2411 3595 3336 3249 2920 2113 2040 1853 1832 2093 2164 2368 2072 2521 1819 1947 2226 1754 1787 2072 1846 2137 2467 2154 2289 2628 2074 2798 2194 2442 2565 2063 2069 2539 1898 2139 2408 2725 2201 2311 2548 2276 2351 2280 2057 2479 2379 2295 2456 2546 2844 2260 2981 2678 3440 2842 2450 2669 2570 2540 2318 2930 2947 2799 2695 2498 2260 2160 2058 2533 2150 2172 2155 3016 2333 2355 2825 2214 2360 2299 1746 2069 2267 1878 2266 2282 2085 2277 2251 1828 1954 1851 1570 1852 2187 1855 2218

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.71784635643899 beta 0.0864815573358333 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 2411 1920 491 4 3595 2565.9440721904 1029.0559278096 5 3336 3662.01390823092 -326.013908230917 6 3249 3765.11270282839 -516.112702828388 7 2920 3699.7092507663 -779.709250766298 8 2113 3396.6792597969 -1283.6792597969 9 2040 2652.184821244 -612.184821244003 10 1853 2351.71549683589 -498.715496835888 11 1832 2101.7392206666 -269.739220666598 12 2093 1999.38719223537 93.6128077646267 13 2164 2163.67762070022 0.322379299781915 14 2368 2261.01986845966 106.980131540341 15 2072 2441.56737198673 -369.567371986726 16 2521 2257.08406997945 263.915930020547 17 1819 2543.72847337897 -724.728473378966 18 1947 2075.68660913111 -128.686609131111 19 2226 2027.52230013396 198.477699866041 20 1754 2226.53328736477 -472.533287364767 21 1787 1914.52639331768 -127.526393317683 22 2072 1842.26454256787 229.735457432127 23 1846 2040.72389503782 -194.723895037816 24 2137 1922.39809679443 214.601903205567 25 2467 2111.22791860914 355.772081390862 26 2154 2423.48273679387 -269.482736793874 27 2289 2270.17104671733 18.8289532826734 28 2628 2324.99176316607 303.008236833929 29 2074 2602.62043689636 -528.620436896363 30 2798 2250.45049166486 547.549508335137 31 2194 2704.7973518086 -510.797351808599 32 2442 2367.70323444914 74.2967655508633 33 2565 2455.22917559679 109.770824403205 34 2063 2575.03466510235 -512.034665102354 35 2069 2216.69199646037 -147.691996460368 36 2539 2110.72259631981 428.277403680191 37 1898 2444.79839435797 -546.798394357972 38 2139 2044.97408175029 94.0259182497055 39 2408 2111.00034034098 296.999659659024 40 2725 2341.16843836391 383.83156163609 41 2201 2657.49694491057 -456.496944910566 42 2311 2342.25914954715 -31.2591495471515 43 2548 2330.3361734838 217.663826516204 44 2276 2510.61432165484 -234.614321654843 45 2351 2351.6612815119 -0.661281511903326 46 2280 2360.60952614579 -80.6095261457858 47 2057 2307.16293732881 -250.162937328812 48 2479 2116.47281713804 362.527182861963 49 2379 2388.1059255541 -9.10592555409949 50 2295 2392.39826101583 -97.3982610158287 51 2456 2327.26373526272 128.736264737282 52 2546 2432.45106281467 113.54893718533 53 2844 2533.78539410243 310.214605897574 54 2260 2795.5537279052 -535.553727905205 55 2981 2416.94291731162 564.057082688378 56 2678 2862.70064987338 -184.700649873379 57 3440 2759.49906895291 680.500931047085 58 2842 3319.62510868295 -477.625108682951 59 2450 3018.74339886711 -568.743398867108 60 2669 2617.14489845296 51.8551015470407 61 2570 2664.25995949173 -94.2599594917256 62 2540 2600.63515367704 -60.6351536770353 63 2318 2557.38353331311 -239.383533313106 64 2930 2370.95699745038 559.043002549622 65 2947 2792.38369405492 154.616305945082 66 2799 2933.09281312672 -134.092813126716 67 2695 2858.22859802793 -163.228598027926 68 2498 2752.31605767688 -254.316057676878 69 2260 2565.22865569865 -305.22865569865 70 2160 2322.64509207625 -162.645092076246 71 2058 2172.31753619355 -114.317536193551 72 2533 2049.58485374552 483.415146254479 73 2150 2385.94303940445 -235.943039404448 74 2172 2191.26511753763 -19.2651175376263 75 2155 2150.93266483629 4.06733516370832 76 3016 2127.60183037539 888.398169624607 77 2333 2794.2368399761 -461.236839976103 78 2355 2463.40747522134 -108.407475221341 79 2825 2379.12539729694 445.874602703057 80 2214 2720.41279471815 -506.412794718154 81 2360 2346.66580888598 13.3341911140242 82 2299 2346.84509596611 -47.8450959661054 83 1746 2300.13680864162 -554.136808641618 84 2069 1855.58778609156 213.412213908442 85 2267 1975.26976348825 291.730236511749 86 1878 2169.28279849302 -291.282798493017 87 2266 1926.69907728726 339.300922712737 88 2282 2157.84154381477 124.158456185226 89 2085 2242.25259004805 -157.252590048055 90 2277 2114.89142725125 162.108572748754 91 2251 2226.8462880785 24.1537119214959 92 1828 2241.27022851631 -413.270228516311 93 1954 1916.03497672422 37.965023275776 94 1851 1917.07419284805 -66.0741928480511 95 1570 1839.32731974872 -269.327319748723 96 1852 1598.95596325081 253.044036749194 97 2187 1749.27607466581 437.723925334192 98 1855 2059.34207858859 -204.342078588593 99 2218 1895.81768855235 322.182311447648 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 100 2130.25814306852 1385.63121130967 2874.88507482738 101 2133.42119920291 1189.09864813712 3077.7437502687 102 2136.5842553373 1003.07173018513 3270.09678048947 103 2139.74731147169 821.39235452716 3458.10226841621 104 2142.91036760607 641.029428168894 3644.79130704326 105 2146.07342374046 460.284537718964 3831.86230976196 106 2149.23647987485 278.127968646776 4020.34499110292 107 2152.39953600924 93.9027868649605 4210.89628515351 108 2155.56259214362 -92.8242555538754 4403.94943984112 109 2158.72564827801 -282.344720453299 4599.79601700932 110 2161.8887044124 -474.856653629889 4798.63406245469 111 2165.05176054679 -670.494370871455 5000.59789196503

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/1g5sj1305856448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/1g5sj1305856448.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/26tcx1305856448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/26tcx1305856448.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/3c39s1305856448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305856259n2wxbz3hgkee2id/3c39s1305856448.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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