WS09 - Seasonal decomposition by Loess

*The author of this computation has been verified*

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

Title produced by software: Decomposition by Loess

Date of computation: Wed, 02 Dec 2009 13:35:37 -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/02/t1259786267cofwv4ldrqqjm09.htm/, Retrieved Wed, 02 Dec 2009 21:37:53 +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/02/t1259786267cofwv4ldrqqjm09.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 «

423.4 404.1 500 472.6 496.1 562 434.8 538.2 577.6 518.1 625.2 561.2 523.3 536.1 607.3 637.3 606.9 652.9 617.2 670.4 729.9 677.2 710 844.3 748.2 653.9 742.6 854.2 808.4 1819 1936.5 1966.1 2083.1 1620.1 1527.6 1795 1685.1 1851.8 2164.4 1981.8 1726.5 2144.6 1758.2 1672.9 1837.3 1596.1 1446 1898.4 1964.1 1755.9 2255.3 1881.2 2117.9 1656.5 1544.1 2098.9 2133.3 1963.5 1801.2 2365.4 1936.5 1667.6 1983.5 2058.6 2448.3 1858.1 1625.4 2130.6 2515.7 2230.2 2086.9 2235 2100.2 2288.6 2490 2573.7 2543.8 2004.7 2390 2338.4 2724.5 2292.5 2386 2477.9 2337 2605.1 2560.8 2839.3 2407.2 2085.2 2735.6 2798.7 3053.2 2405 2471.9 2727.3 2790.7 2385.4 3206.6 2705.6 3518.4 1954.9 2584.3 2535.8 2685.9 2866 2236.6 2934.9 2668.6 2371.2 3165.9 2887.2 3112.2 2671.2 2432.6 2812.3 3095.7 2862.9 2607.3 2862.5

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 Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 1201 0 121 Trend 19 1 2 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 423.4 463.322686523912 -66.0208557168566 449.498169192945 39.9226865239119 2 404.1 501.154507793702 -153.035594154971 460.081086361269 97.0545077937021 3 500 387.976487009375 141.359509461032 470.664003529593 -112.023512990625 4 472.6 418.664232967553 45.2854523382474 481.2503146942 -53.9357670324474 5 496.1 383.242109779647 117.121264361546 491.836625858807 -112.857890220353 6 562 757.259334313481 -135.468075298591 502.20874098511 195.259334313481 7 434.8 442.456596092553 -85.4374522039657 512.580856111413 7.65659609255317 8 538.2 504.528736727737 48.6483392588324 523.222924013431 -33.6712632722632 9 577.6 401.570865195521 219.764142889030 533.864991915449 -176.029134804479 10 518.1 532.324534471057 -41.2407767260136 545.116242254957 14.2245344710568 11 625.2 869.108052318109 -175.075544912573 556.367492594465 243.908052318109 12 561.2 471.128896695863 84.0995508852252 567.171552418912 -90.0711033041373 13 523.3 534.645243473497 -66.0208557168566 577.97561224336 11.3452434734971 14 536.1 636.327906995482 -153.035594154971 588.907687159489 100.227906995482 15 607.3 473.40072846335 141.359509461032 599.839762075618 -133.899271536651 16 637.3 617.617045456213 45.2854523382474 611.69750220554 -19.6829545437873 17 606.9 473.123493302993 117.121264361546 623.555242335461 -133.776506697007 18 652.9 802.504014186664 -135.468075298591 638.764061111927 149.604014186664 19 617.2 665.864572315574 -85.4374522039657 653.972879888392 48.6645723155735 20 670.4 620.59983620884 48.6483392588324 671.551824532328 -49.80016379116 21 729.9 550.905087934707 219.764142889030 689.130769176263 -178.994912065293 22 677.2 682.944263410715 -41.2407767260136 712.696513315299 5.74426341071489 23 710 858.813287458239 -175.075544912573 736.262257454335 148.813287458239 24 844.3 805.873013353573 84.0995508852252 798.627435761202 -38.4269866464274 25 748.2 701.428241648787 -66.0208557168566 860.99261406807 -46.7717583512131 26 653.9 500.984325645147 -153.035594154971 959.851268509824 -152.915674354853 27 742.6 285.13056758739 141.359509461032 1058.70992295158 -457.46943241261 28 854.2 502.65962067085 45.2854523382474 1160.45492699090 -351.540379329149 29 808.4 237.478804608228 117.121264361546 1262.19993103023 -570.921195391772 30 1819 2416.61379615754 -135.468075298591 1356.85427914105 597.613796157541 31 1936.5 2506.92882495209 -85.4374522039657 1451.50862725187 570.428824952093 32 1966.1 2334.75211703859 48.6483392588324 1548.79954370258 368.652117038587 33 2083.1 2300.34539695768 219.764142889030 1646.09046015329 217.245396957681 34 1620.1 1562.15069101655 -41.2407767260136 1719.29008570946 -57.9493089834493 35 1527.6 1437.78583364694 -175.075544912573 1792.48971126564 -89.814166353063 36 1795 1686.38845749023 84.0995508852252 1819.51199162455 -108.611542509774 37 1685.1 1589.68658373340 -66.0208557168566 1846.53427198346 -95.4134162666041 38 1851.8 2013.50547877509 -153.035594154971 1843.13011537988 161.705478775091 39 2164.4 2347.71453176267 141.359509461032 1839.7259587763 183.314531762670 40 1981.8 2084.93174618030 45.2854523382474 1833.38280148145 103.131746180305 41 1726.5 1508.83909145186 117.121264361546 1827.03964418660 -217.660908548142 42 2144.6 2601.91323288714 -135.468075298591 1822.75484241145 457.313232887144 43 1758.2 1783.36741156767 -85.4374522039657 1818.47004063630 25.1674115676683 44 1672.9 1478.91315801974 48.6483392588324 1818.23850272143 -193.986841980260 45 1837.3 1636.82889230441 219.764142889030 1818.00696480656 -200.471107695588 46 1596.1 1412.49916462104 -41.2407767260136 1820.94161210498 -183.600835378965 47 1446 1243.19928550918 -175.075544912573 1823.87625940340 -202.800714490824 48 1898.4 1884.35032923647 84.0995508852252 1828.35011987830 -14.0496707635284 49 1964.1 2161.39687536365 -66.0208557168566 1832.82398035321 197.296875363648 50 1755.9 1817.15299409908 -153.035594154971 1847.68260005590 61.2529940990755 51 2255.3 2506.69927078039 141.359509461032 1862.54121975858 251.399270780386 52 1881.2 1832.05328917656 45.2854523382474 1885.06125848520 -49.1467108234444 53 2117.9 2211.09743842664 117.121264361546 1907.58129721181 93.1974384266423 54 1656.5 1525.07041290989 -135.468075298591 1923.39766238870 -131.429587090105 55 1544.1 1234.42342463839 -85.4374522039657 1939.21402756558 -309.676575361614 56 2098.9 2206.32267341156 48.6483392588324 1942.82898732961 107.422673411555 57 2133.3 2100.39191001733 219.764142889030 1946.44394709364 -32.9080899826738 58 1963.5 2012.36898478299 -41.2407767260136 1955.87179194303 48.8689847829858 59 1801.2 1812.17590812016 -175.075544912573 1965.29963679241 10.9759081201619 60 2365.4 2668.15941835215 84.0995508852252 1978.54103076262 302.759418352154 61 1936.5 1947.23843098403 -66.0208557168566 1991.78242473283 10.7384309840265 62 1667.6 1483.95517168938 -153.035594154971 2004.28042246559 -183.644828310617 63 1983.5 1808.86207034062 141.359509461032 2016.77842019835 -174.637929659377 64 2058.6 2041.06979821069 45.2854523382474 2030.84474945106 -17.5302017893114 65 2448.3 2734.56765693467 117.121264361546 2044.91107870378 286.267656934672 66 1858.1 1786.74668809703 -135.468075298591 2064.92138720156 -71.3533119029689 67 1625.4 1251.30575650463 -85.4374522039657 2084.93169569934 -374.094243495371 68 2130.6 2097.28017925516 48.6483392588324 2115.27148148601 -33.3198207448409 69 2515.7 2666.02458983829 219.764142889030 2145.61126727268 150.324589838291 70 2230.2 2321.55954626065 -41.2407767260136 2180.08123046536 91.3595462606495 71 2086.9 2134.32435125453 -175.075544912573 2214.55119365805 47.424351254525 72 2235 2141.07303791425 84.0995508852252 2244.82741120053 -93.926962085754 73 2100.2 1991.31722697385 -66.0208557168566 2275.10362874301 -108.882773026152 74 2288.6 2430.65341074924 -153.035594154971 2299.58218340574 142.053410749235 75 2490 2514.57975247051 141.359509461032 2324.06073806846 24.5797524705058 76 2573.7 2760.92592263109 45.2854523382474 2341.18862503067 187.225922631086 77 2543.8 2612.16222364559 117.121264361546 2358.31651199287 68.3622236455849 78 2004.7 1769.28175920011 -135.468075298591 2375.58631609849 -235.418240799894 79 2390 2472.58133199986 -85.4374522039657 2392.8561202041 82.5813319998642 80 2338.4 2219.0508147211 48.6483392588324 2409.10084602007 -119.349185278898 81 2724.5 2803.89028527494 219.764142889030 2425.34557183603 79.3902852749397 82 2292.5 2187.8337624522 -41.2407767260136 2438.40701427381 -104.666237547799 83 2386 2495.60708820098 -175.075544912573 2451.46845671160 109.607088200979 84 2477.9 2405.12450172899 84.0995508852252 2466.57594738579 -72.7754982710103 85 2337 2258.33741765688 -66.0208557168566 2481.68343805998 -78.6625823431186 86 2605.1 2860.50015633824 -153.035594154971 2502.73543781673 255.400156338237 87 2560.8 2456.45305296548 141.359509461032 2523.78743757349 -104.346947034524 88 2839.3 3089.8189311377 45.2854523382474 2543.49561652405 250.518931137703 89 2407.2 2134.07494016385 117.121264361546 2563.20379547461 -273.125059836153 90 2085.2 1726.18288051748 -135.468075298591 2579.68519478112 -359.017119482525 91 2735.6 2960.47085811634 -85.4374522039657 2596.16659408762 224.870858116341 92 2798.7 2932.83798648281 48.6483392588324 2615.91367425836 134.137986482811 93 3053.2 3250.97510268188 219.764142889030 2635.66075442909 197.775102681882 94 2405 2187.75331212636 -41.2407767260136 2663.48746459965 -217.24668787364 95 2471.9 2427.56137014235 -175.075544912573 2691.31417477022 -44.3386298576456 96 2727.3 2664.92905578375 84.0995508852252 2705.57139333103 -62.3709442162512 97 2790.7 2927.59224382502 -66.0208557168566 2719.82861189183 136.892243825023 98 2385.4 2210.56236611158 -153.035594154971 2713.27322804339 -174.83763388842 99 3206.6 3565.12264634402 141.359509461032 2706.71784419495 358.522646344019 100 2705.6 2665.36066590353 45.2854523382474 2700.55388175822 -40.2393340964713 101 3518.4 4225.28881631696 117.121264361546 2694.3899193215 706.888816316956 102 1954.9 1355.56107817446 -135.468075298591 2689.70699712413 -599.338921825538 103 2584.3 2569.01337727721 -85.4374522039657 2685.02407492676 -15.2866227227937 104 2535.8 2343.49536244969 48.6483392588324 2679.45629829148 -192.304637550308 105 2685.9 2478.14733545478 219.764142889030 2673.88852165619 -207.752664545222 106 2866 3093.60256400708 -41.2407767260136 2679.63821271894 227.602564007076 107 2236.6 1962.88764113089 -175.075544912573 2685.38790378168 -273.71235886911 108 2934.9 3082.88716148172 84.0995508852252 2702.81328763306 147.987161481719 109 2668.6 2682.98218423243 -66.0208557168566 2720.23867148443 14.3821842324282 110 2371.2 2155.71000192470 -153.035594154971 2739.72559223027 -215.489998075303 111 3165.9 3431.22797756285 141.359509461032 2759.21251297612 265.327977562848 112 2887.2 2960.16035982984 45.2854523382474 2768.95418783191 72.9603598298381 113 3112.2 3328.58287295075 117.121264361546 2778.69586268771 216.382872950746 114 2671.2 2690.54770980086 -135.468075298591 2787.32036549773 19.3477098008630 115 2432.6 2154.69258389622 -85.4374522039657 2795.94486830775 -277.907416103782 116 2812.3 2773.35706380058 48.6483392588324 2802.59459694059 -38.9429361994189 117 3095.7 3162.39153153754 219.764142889030 2809.24432557343 66.6915315375445 118 2862.9 2952.40032950512 -41.2407767260136 2814.6404472209 89.500329505116 119 2607.3 2569.63897604420 -175.075544912573 2820.03656886837 -37.6610239557963 120 2862.5 2816.14878945376 84.0995508852252 2824.75165966101 -46.3512105462355

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/18hlt1259786135.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/18hlt1259786135.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/26nr11259786135.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/26nr11259786135.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/3conr1259786135.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/3conr1259786135.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/4hdi81259786135.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786267cofwv4ldrqqjm09/4hdi81259786135.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ; par9 = 1 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #seasonal period if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window par3 <- as.numeric(par3) #s.degree if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window par5 <- as.numeric(par5)#t.degree if (par6 != '') par6 <- as.numeric(par6)#l.window par7 <- as.numeric(par7)#l.degree if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust nx <- length(x) x <- ts(x,frequency=par1) if (par6 != '') { m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8) } else { m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8) } m$time.series m$win m$deg m$jump m$inner m$outer bitmap(file='test1.png') plot(m,main=main) dev.off() mylagmax <- nx/2 bitmap(file='test2.png') op <- par(mfrow = c(2,2)) acf(as.numeric(x),lag.max = mylagmax,main='Observed') acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend') acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal') acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder') par(op) dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) spectrum(as.numeric(x),main='Observed') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder') par(op) dev.off() bitmap(file='test4.png') op <- par(mfrow = c(2,2)) cpgram(as.numeric(x),main='Observed') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder') par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Component',header=TRUE) a<-table.element(a,'Window',header=TRUE) a<-table.element(a,'Degree',header=TRUE) a<-table.element(a,'Jump',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Seasonal',header=TRUE) a<-table.element(a,m$win['s']) a<-table.element(a,m$deg['s']) a<-table.element(a,m$jump['s']) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Trend',header=TRUE) a<-table.element(a,m$win['t']) a<-table.element(a,m$deg['t']) a<-table.element(a,m$jump['t']) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Low-pass',header=TRUE) a<-table.element(a,m$win['l']) a<-table.element(a,m$deg['l']) a<-table.element(a,m$jump['l']) 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,'Seasonal Decomposition by Loess - Time Series Components',6,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,'Seasonal',header=TRUE) a<-table.element(a,'Trend',header=TRUE) a<-table.element(a,'Remainder',header=TRUE) a<-table.row.end(a) for (i in 1:nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]+m$time.series[i,'remainder']) a<-table.element(a,m$time.series[i,'seasonal']) a<-table.element(a,m$time.series[i,'trend']) a<-table.element(a,m$time.series[i,'remainder']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.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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