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*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, 29 Dec 2010 14:40:33 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7.htm/, Retrieved Wed, 29 Dec 2010 15:38:16 +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/2010/Dec/29/t129363349583w5s64fh4i5lb7.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

1856 1834 2095 2164 2368 2072 2521 1823 1947 2226 1754 1786 2072 1846 2137 2466 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 2253 2028 2169 1997 2034 1791 1627 1631 2319 1707 1747 2397 2059 2251 2558 2406 2049 2074 1734

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	1091	0	110
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	1856	1717.0461780852	-167.932921731244	2162.88674364604	-138.953821914796
2	1834	1862.49484899914	-340.322436087578	2145.82758708844	28.4948489991393
3	2095	2019.70184129498	41.5297281741834	2128.76843053084	-75.2981587050203
4	2164	2273.81230133391	-59.3608400385585	2113.54853870464	109.812301333914
5	2368	2768.58944401808	-130.918090896529	2098.32864687845	400.589444018078
6	2072	2028.24561886508	28.5986948118474	2087.15568632307	-43.7543811349224
7	2521	2672.34595227068	293.671321961627	2075.9827257677	151.345952270675
8	1823	1548.36173961312	30.1931141919941	2067.44514619488	-274.638260386879
9	1947	1705.93337153961	129.159061838314	2058.90756662207	-241.066628460386
10	2226	2193.88895345562	202.133109182978	2055.9779373614	-32.1110465443771
11	1754	1513.0669634892	-58.1152715899228	2053.04830810073	-240.933036510804
12	1786	1469.46836806809	31.3645801052525	2071.16705182666	-316.531631931911
13	2072	2222.64712617865	-167.932921731244	2089.28579555259	150.647126178654
14	1846	1909.33516127068	-340.322436087578	2122.9872748169	63.3351612706765
15	2137	2075.7815177446	41.5297281741834	2156.68875408121	-61.2184822553963
16	2466	2796.48800268567	-59.3608400385585	2194.87283735288	330.488002685674
17	2154	2205.86117027197	-130.918090896529	2233.05692062456	51.8611702719741
18	2289	2285.00600429952	28.5986948118474	2264.39530088864	-3.99399570048354
19	2628	2666.59499688566	293.671321961627	2295.73368115272	38.5949968856567
20	2074	1807.41889715609	30.1931141919941	2310.38798865191	-266.581102843908
21	2798	3141.79864201057	129.159061838314	2325.04229615111	343.798642010574
22	2194	1860.33969433202	202.133109182978	2325.52719648501	-333.660305667984
23	2442	2616.10317477102	-58.1152715899228	2326.0120968189	174.103174771022
24	2565	2773.06277897289	31.3645801052525	2325.57264092186	208.062778972885
25	2063	1968.79973670642	-167.932921731244	2325.13318502482	-94.20026329358
26	2069	2155.69740957742	-340.322436087578	2322.62502651015	86.6974095774231
27	2539	2716.35340383033	41.5297281741834	2320.11686799549	177.353403830331
28	1898	1541.58710901897	-59.3608400385585	2313.77373101959	-356.41289098103
29	2139	2101.48749685284	-130.918090896529	2307.43059404369	-37.5125031471621
30	2408	2483.30305814808	28.5986948118474	2304.09824704007	75.3030581480775
31	2725	2855.56277800192	293.671321961627	2300.76590003646	130.562778001915
32	2201	2064.11386096162	30.1931141919941	2307.69302484638	-136.886139038376
33	2311	2178.22078850538	129.159061838314	2314.62014965631	-132.779211494621
34	2548	2565.77005108346	202.133109182978	2328.09683973356	17.7700510834634
35	2276	2268.54174177911	-58.1152715899228	2341.57352981081	-7.45825822088818
36	2351	2315.67884636866	31.3645801052525	2354.95657352609	-35.3211536313438
37	2280	2359.59330448987	-167.932921731244	2368.33961724137	79.593304489872
38	2057	2070.07024346866	-340.322436087578	2384.25219261892	13.0702434686559
39	2479	2516.30550382935	41.5297281741834	2400.16476799647	37.3055038293451
40	2379	2388.47512987157	-59.3608400385585	2428.88571016699	9.47512987157006
41	2295	2263.31143855902	-130.918090896529	2457.60665233751	-31.6885614409757
42	2456	2379.50224345927	28.5986948118474	2503.89906172888	-76.4977565407303
43	2546	2248.13720691811	293.671321961627	2550.19147112026	-297.862793081887
44	2844	3063.23925690894	30.1931141919941	2594.56762889906	219.239256908944
45	2260	1751.89715148382	129.159061838314	2638.94378667786	-508.102848516178
46	2981	3092.90376149681	202.133109182978	2666.96312932021	111.903761496813
47	2678	2719.13279962737	-58.1152715899228	2694.98247196255	41.1327996273685
48	3440	4138.64663505943	31.3645801052525	2709.98878483531	698.646635059433
49	2842	3126.93782402317	-167.932921731244	2724.99509770807	284.937824023169
50	2450	2508.91632230913	-340.322436087578	2731.40611377845	58.9163223091291
51	2669	2558.65314197699	41.5297281741834	2737.81712984882	-110.346858023006
52	2570	2479.91937771896	-59.3608400385585	2719.4414623196	-90.0806222810397
53	2540	2509.85229610616	-130.918090896529	2701.06579479037	-30.1477038938428
54	2318	1950.49845659041	28.5986948118474	2656.90284859774	-367.501543409588
55	2930	2953.58877563326	293.671321961627	2612.73990240511	23.588775633265
56	2947	3288.32171511708	30.1931141919941	2575.48517069093	341.321715117077
57	2799	2930.61049918494	129.159061838314	2538.23043897675	131.610499184937
58	2695	2676.73160502789	202.133109182978	2511.13528578914	-18.2683949721149
59	2498	2570.0751389884	-58.1152715899228	2484.04013260153	72.0751389883976
60	2260	2030.1164887359	31.3645801052525	2458.51893115885	-229.883511264099
61	2160	2054.93519201508	-167.932921731244	2432.99772971617	-105.064807984923
62	2058	2047.23172509917	-340.322436087578	2409.0907109884	-10.7682749008263
63	2533	2639.28657956518	41.5297281741834	2385.18369226064	106.286579565176
64	2150	1985.15973668612	-59.3608400385585	2374.20110335244	-164.840263313884
65	2172	2111.69957645228	-130.918090896529	2363.21851444425	-60.3004235477156
66	2155	1920.40000590708	28.5986948118474	2361.00129928107	-234.599994092921
67	3016	3379.54459392047	293.671321961627	2358.7840841179	363.544593920471
68	2333	2285.21915108226	30.1931141919941	2350.58773472575	-47.7808489177423
69	2355	2238.44955282809	129.159061838314	2342.39138533359	-116.550447171908
70	2825	3120.56174302162	202.133109182978	2327.3051477954	295.561743021622
71	2214	2173.89636133272	-58.1152715899228	2312.21891025721	-40.1036386672836
72	2360	2398.60557905971	31.3645801052525	2290.02984083504	38.6055790597111
73	2299	2498.09215031838	-167.932921731244	2267.84077141287	199.092150318377
74	1746	1593.46222273484	-340.322436087578	2238.86021335274	-152.53777726516
75	2069	1886.59061653321	41.5297281741834	2209.87965529261	-182.409383466792
76	2267	2414.6986940088	-59.3608400385585	2178.66214602976	147.698694008799
77	1878	1739.47345412962	-130.918090896529	2147.44463676691	-138.526545870381
78	2266	2385.87053113854	28.5986948118474	2117.53077404961	119.870531138544
79	2282	2182.71176670607	293.671321961627	2087.61691133231	-99.2882332939328
80	2085	2075.20401153888	30.1931141919941	2064.60287426913	-9.79598846112049
81	2277	2383.25210095574	129.159061838314	2041.58883720595	106.252100955739
82	2251	2270.20167464266	202.133109182978	2029.66521617436	19.2016746426634
83	1828	1696.37367644715	-58.1152715899228	2017.74159514277	-131.626323552847
84	1954	1863.87314669283	31.3645801052525	2012.76227320192	-90.1268533071716
85	1851	1862.14997047018	-167.932921731244	2007.78295126107	11.149970470176
86	1570	1475.19802919509	-340.322436087578	2005.12440689249	-94.8019708049128
87	1852	1660.0044093019	41.5297281741834	2002.46586252391	-191.995590698097
88	2187	2433.9731058805	-59.3608400385585	1999.38773415806	246.973105880498
89	1855	1844.60848510432	-130.918090896529	1996.30960579221	-10.391514895678
90	2218	2415.50906040726	28.5986948118474	1991.89224478089	197.50906040726
91	2253	2224.8537942688	293.671321961627	1987.47488376958	-28.1462057312049
92	2028	2042.87061750543	30.1931141919941	1982.93626830258	14.8706175054267
93	2169	2230.4432853261	129.159061838314	1978.39765283558	61.4432853261046
94	1997	1819.555241928	202.133109182978	1972.31164888902	-177.444758071996
95	2034	2159.88962664747	-58.1152715899228	1966.22564494246	125.889626647467
96	1791	1586.03049596563	31.3645801052525	1964.60492392911	-204.969504034366
97	1627	1458.94871881547	-167.932921731244	1962.98420291577	-168.051281184527
98	1631	1625.16144107206	-340.322436087578	1977.16099501552	-5.83855892794077
99	2319	2605.13248471055	41.5297281741834	1991.33778711527	286.132484710551
100	1707	1458.74110643959	-59.3608400385585	2014.61973359897	-248.258893560414
101	1747	1587.01641081385	-130.918090896529	2037.90168008268	-159.983589186149
102	2397	2714.6796731202	28.5986948118474	2050.72163206795	317.679673120201
103	2059	1760.78709398515	293.671321961627	2063.54158405322	-298.212906014851
104	2251	2396.3825842477	30.1931141919941	2075.4243015603	145.382584247704
105	2558	2899.53391909431	129.159061838314	2087.30701906738	341.533919094305
106	2406	2510.41409072215	202.133109182978	2099.45280009487	104.414090722154
107	2049	2044.51669046757	-58.1152715899228	2111.59858112235	-4.48330953243203
108	2074	1994.395157246	31.3645801052525	2122.24026264875	-79.6048427540036
109	1734	1503.0509775561	-167.932921731244	2132.88194417515	-230.949022443903

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/11fcb1293633628.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/11fcb1293633628.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/21fcb1293633628.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/21fcb1293633628.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/3u7bw1293633628.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/3u7bw1293633628.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/4u7bw1293633628.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363349583w5s64fh4i5lb7/4u7bw1293633628.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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')

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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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