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Seizoenale decompositie met de Loess techniek

*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: Fri, 11 Dec 2009 09:44:09 -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/11/t12605499008i5ctgndcddg58c.htm/, Retrieved Fri, 11 Dec 2009 17:45:05 +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/11/t12605499008i5ctgndcddg58c.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 «

21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485 18730

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	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	21790	22279.4514224485	-4969.10442504701	26269.6530025985	489.451422448474
2	13253	11506.5592112009	-11364.7483778249	26364.189166624	-1746.44078879906
3	37702	41206.8079722223	7738.46669712823	26458.7253306495	3504.80797222231
4	30364	29294.0123645075	4879.4871552399	26554.5004802526	-1069.98763549248
5	32609	30602.2161679453	7965.50820219897	26650.2756298557	-2006.78383205466
6	30212	28463.264056446	5219.75794957985	26740.9779939742	-1748.73594355401
7	29965	32116.0881315082	982.231510399147	26831.6803580926	2151.08813150824
8	28352	28309.8163899307	1469.02397387064	26925.1596361987	-42.1836100693399
9	25814	27830.2136858763	-3220.85260018113	27018.6389143048	2016.21368587635
10	22414	22971.1822369874	-5311.68167809179	27168.4994411044	557.182236987392
11	20506	17076.8184255081	-3383.17839341211	27318.359967904	-3429.1815744919
12	28806	30201.4561371599	-4.90964384195788	27415.4535066821	1395.45613715985
13	22228	21912.5573795868	-4969.10442504701	27512.5470454602	-315.442620413185
14	13971	11935.5654279328	-11364.7483778249	27371.1829498922	-2035.43457206722
15	36845	38721.7144485476	7738.46669712823	27229.8188543241	1876.71444854765
16	35338	38811.6108030272	4879.4871552399	26984.9020417329	3473.61080302721
17	35022	35338.5065686594	7965.50820219897	26739.9852291417	316.506568659363
18	34777	37906.2187349761	5219.75794957985	26428.0233154440	3129.21873497610
19	26887	26675.7070878544	982.231510399147	26116.0614017464	-211.29291214556
20	23970	20788.7950604075	1469.02397387064	25682.1809657219	-3181.20493959254
21	22780	23532.5520704838	-3220.85260018113	25248.3005296974	752.552070483751
22	17351	15284.5387127359	-5311.68167809179	24729.1429653559	-2066.46128726415
23	21382	21937.1929923976	-3383.17839341211	24209.9854010145	555.19299239762
24	24561	25358.7008577858	-4.90964384195788	23768.2087860561	797.700857785814
25	17409	16460.6722539492	-4969.10442504701	23326.4321710978	-948.32774605079
26	11514	11291.8903959135	-11364.7483778249	23100.8579819114	-222.109604086487
27	31514	32414.2495101467	7738.46669712823	22875.2837927251	900.249510146718
28	27071	26438.9955680138	4879.4871552399	22823.5172767463	-632.004431986214
29	29462	28186.7410370335	7965.50820219897	22771.7507607676	-1275.25896296654
30	26105	24157.271501553	5219.75794957985	22832.9705488672	-1947.72849844701
31	22397	20917.5781526341	982.231510399147	22894.1903369667	-1479.42184736589
32	23843	23198.0068700880	1469.02397387064	23018.9691560413	-644.993129911978
33	21705	23487.1046250652	-3220.85260018113	23143.7479751159	1782.10462506520
34	18089	18103.4907883817	-5311.68167809179	23386.1908897101	14.4907883817323
35	20764	21282.5445891079	-3383.17839341211	23628.6338043042	518.544589107922
36	25316	26743.1277767362	-4.90964384195788	23893.7818671058	1427.12777673619
37	17704	16218.1744951397	-4969.10442504701	24158.9299299074	-1485.82550486034
38	15548	18253.3242094717	-11364.7483778249	24207.4241683533	2705.32420947166
39	28029	24063.6148960726	7738.46669712823	24255.9184067992	-3965.38510392744
40	29383	29747.0633896838	4879.4871552399	24139.4494550763	364.063389683757
41	36438	40887.5112944476	7965.50820219897	24022.9805033535	4449.51129444755
42	32034	34919.0699639174	5219.75794957985	23929.1720865027	2885.06996391742
43	22679	20540.4048199489	982.231510399147	23835.363669652	-2138.59518005112
44	24319	23434.2091995291	1469.02397387064	23734.7668266003	-884.790800470924
45	18004	15594.6826166325	-3220.85260018113	23634.1699835486	-2409.31738336746
46	17537	16981.8984633569	-5311.68167809179	23403.7832147349	-555.101536643098
47	20366	20941.7819474909	-3383.17839341211	23173.3964459212	575.781947490934
48	22782	22632.3387146269	-4.90964384195788	22936.5709292150	-149.661285373069
49	19169	20607.3590125381	-4969.10442504701	22699.7454125089	1438.35901253813
50	13807	16319.0215261833	-11364.7483778249	22659.7268516416	2512.02152618329
51	29743	29127.8250120974	7738.46669712823	22619.7082907744	-615.174987902643
52	25591	23704.7196492856	4879.4871552399	22597.7931954745	-1886.28035071444
53	29096	27650.6136976264	7965.50820219897	22575.8781001747	-1445.38630237363
54	26482	25257.6529931132	5219.75794957985	22486.589057307	-1224.34700688684
55	22405	21430.4684751616	982.231510399147	22397.3000144393	-974.531524838447
56	27044	30219.6789089989	1469.02397387064	22399.2971171304	3175.67890899895
57	17970	16759.5583803596	-3220.85260018113	22401.2942198215	-1210.44161964040
58	18730	20174.2804751038	-5311.68167809179	22597.401202988	1444.28047510380
59	19684	19957.6702072577	-3383.17839341211	22793.5081861544	273.670207257663
60	19785	16578.9439782000	-4.90964384195788	22995.9656656419	-3206.05602179998
61	18479	18728.6812799176	-4969.10442504701	23198.4231451294	249.681279917582
62	10698	9503.116288489	-11364.7483778249	23257.6320893359	-1194.883711511
63	31956	32856.6922693293	7738.46669712823	23316.8410335424	900.692269329324
64	29506	30838.5805147819	4879.4871552399	23293.9323299782	1332.5805147819
65	34506	37775.4681713871	7965.50820219897	23271.0236264140	3269.46817138708
66	27165	25915.8888763761	5219.75794957985	23194.3531740441	-1249.11112362394
67	26736	29372.0857679266	982.231510399147	23117.6827216742	2636.08576792664
68	23691	22956.3767007239	1469.02397387064	22956.5993254054	-734.623299276063
69	18157	16739.3366710445	-3220.85260018113	22795.5159291366	-1417.66332895551
70	17328	17385.6075022776	-5311.68167809179	22582.0741758142	57.6075022776095
71	18205	17424.5459709204	-3383.17839341211	22368.6324224917	-780.454029079614
72	20995	19750.2919950398	-4.90964384195788	22244.6176488021	-1244.70800496018
73	17382	17612.5015499345	-4969.10442504701	22120.6028751126	230.501549934452
74	9367	7918.7687710315	-11364.7483778249	22179.9796067934	-1448.2312289685
75	31124	32270.1769643975	7738.46669712823	22239.3563384743	1146.17696439745
76	26551	25793.0930468058	4879.4871552399	22429.4197979543	-757.906953194215
77	30651	30717.0085403667	7965.50820219897	22619.4832574343	66.0085403667144
78	25859	23642.1588912285	5219.75794957985	22856.0831591916	-2216.84110877147
79	25100	26125.0854286519	982.231510399147	23092.6830609489	1025.08542865194
80	25778	26769.6707172353	1469.02397387064	23317.3053088940	991.670717235316
81	20418	20514.9250433420	-3220.85260018113	23541.9275568392	96.925043341951
82	18688	18963.0548139022	-5311.68167809179	23724.6268641896	275.054813902181
83	20424	20323.8522218721	-3383.17839341211	23907.3261715400	-100.147778127925
84	24776	25489.6547470625	-4.90964384195788	24067.2548967794	713.654747062541
85	19814	20369.9208030282	-4969.10442504701	24227.1836220188	555.92080302821
86	12738	12534.6599947769	-11364.7483778249	24306.0883830481	-203.340005223126
87	31566	31008.5401587944	7738.46669712823	24384.9931440773	-557.459841205557
88	30111	30976.5021763005	4879.4871552399	24366.0106684596	865.502176300459
89	30019	27725.4636049591	7965.50820219897	24347.0281928420	-2293.53639504093
90	31934	34444.7483796717	5219.75794957985	24203.4936707485	2510.74837967168
91	25826	26609.8093409459	982.231510399147	24059.959148655	783.809340945878
92	26835	28428.4716252958	1469.02397387064	23772.5044008336	1593.47162529575
93	20205	20145.8029471689	-3220.85260018113	23485.0496530123	-59.1970528311176
94	17789	17818.7926350153	-5311.68167809179	23070.8890430765	29.7926350152593
95	20520	21766.4499602713	-3383.17839341211	22656.7284331408	1246.44996027130
96	22518	22827.4322232011	-4.90964384195788	22213.4774206409	309.432223201085
97	15572	14342.8780169061	-4969.10442504701	21770.2264081409	-1229.12198309393
98	11509	12936.1894583820	-11364.7483778249	21446.5589194430	1427.18945838198
99	25447	22032.6418721268	7738.46669712823	21122.8914307450	-3414.3581278732
100	24090	22189.0271569096	4879.4871552399	21111.4856878505	-1900.97284309044
101	27786	26506.4118528449	7965.50820219897	21100.0799449561	-1279.58814715508
102	26195	25905.7284348317	5219.75794957985	21264.5136155885	-289.271565168343
103	20516	18620.8212033800	982.231510399147	21428.9472862209	-1895.17879662002
104	22759	22428.8791903696	1469.02397387064	21620.0968357598	-330.1208096304
105	19028	19465.6062148825	-3220.85260018113	21811.2463852987	437.606214882479
106	16971	17210.7677032240	-5311.68167809179	22042.9139748678	239.767703223981
107	20036	21180.5968289751	-3383.17839341211	22274.5815644370	1144.59682897515
108	22485	22430.1033027007	-4.90964384195788	22544.8063411412	-54.8966972992748
109	18730	19614.0733072015	-4969.10442504701	22815.0311178455	884.073307201506

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/1bisu1260549846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/1bisu1260549846.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/2km3f1260549846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/2km3f1260549846.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/336o81260549846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/336o81260549846.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/45sqe1260549846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605499008i5ctgndcddg58c/45sqe1260549846.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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