Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 20 »

*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: Mon, 20 Dec 2010 10:15:16 +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/20/t1292840004tpniojb75vswyy7.htm/, Retrieved Mon, 20 Dec 2010 11:13:26 +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/20/t1292840004tpniojb75vswyy7.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 «

377 370 358 357 349 348 369 381 368 361 351 351 358 354 347 345 343 340 362 370 373 371 354 357 363 364 363 358 357 357 380 378 376 380 379 384 392 394 392 396 392 396 419 421 420 418 410 418 426 428 430 424 423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441 439 454 460 457 451 444 437 443 471 469 454 444 436

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	1311	0	132
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	377	382.428098174186	3.83527790809046	367.736623917723	5.4280981741864
2	370	371.49778468648	1.88092257262018	366.6212927409	1.49778468647992
3	358	353.385652604302	-2.89161416837898	365.505961564077	-4.61434739569762
4	357	355.517107940219	-5.89575270014044	364.378644759922	-1.48289205978108
5	349	345.466742134595	-10.7180700903614	363.251327955766	-3.53325786540506
6	348	343.84196007035	-9.92232934353665	362.080369273187	-4.15803992965044
7	369	366.308089160281	10.7825002491113	360.909410590608	-2.69191083971896
8	381	389.107135357275	13.1397900208043	359.753074621921	8.10713535727473
9	368	371.360720577115	6.04254076965048	358.596738653234	3.36072057711522
10	361	363.114307971305	1.19226840949127	357.693423619204	2.11430797130492
11	351	351.686077795541	-6.47618638071424	356.790108585173	0.686077795540882
12	351	347.024052300319	-0.969349629556216	355.945297329238	-3.97594769968129
13	358	357.064236018608	3.83527790809046	355.100486073302	-0.935763981392085
14	354	351.434883079667	1.88092257262018	354.684194347713	-2.56511692033331
15	347	342.623711546254	-2.89161416837898	354.267902622125	-4.37628845374564
16	345	341.289600776253	-5.89575270014044	354.606151923887	-3.71039922374678
17	343	341.773668864712	-10.7180700903614	354.94440122565	-1.22633113528843
18	340	334.213289525198	-9.92232934353665	355.709039818339	-5.78671047480213
19	362	356.743821339861	10.7825002491113	356.473678411028	-5.25617866013903
20	370	369.422075392834	13.1397900208043	357.438134586362	-0.577924607165869
21	373	381.554868468654	6.04254076965048	358.402590761695	8.55486846865415
22	371	381.237955085691	1.19226840949127	359.569776504818	10.2379550856911
23	354	353.739224132774	-6.47618638071424	360.73696224794	-0.260775867225789
24	357	353.140693285815	-0.969349629556216	361.828656343741	-3.85930671418527
25	363	359.244371652367	3.83527790809046	362.920350439543	-3.75562834763338
26	364	362.389551457028	1.88092257262018	363.729525970351	-1.61044854297165
27	363	364.352912667219	-2.89161416837898	364.53870150116	1.3529126672189
28	358	356.220667695775	-5.89575270014044	365.675085004366	-1.77933230422542
29	357	357.90660158279	-10.7180700903614	366.811468507572	0.90660158278979
30	357	355.117320054771	-9.92232934353665	368.805009288765	-1.88267994522874
31	380	378.418949680929	10.7825002491113	370.798550069959	-1.58105031907053
32	378	369.532724340587	13.1397900208043	373.327485638609	-8.46727565941296
33	376	370.101038023091	6.04254076965048	375.856421207258	-5.89896197690859
34	380	379.999787964718	1.19226840949127	378.807943625791	-0.000212035281947465
35	379	382.716720336391	-6.47618638071424	381.759466044323	3.71672033639101
36	384	383.866267832976	-0.969349629556216	385.10308179658	-0.133732167023766
37	392	391.718024543073	3.83527790809046	388.446697548837	-0.281975456927171
38	394	394.252764599067	1.88092257262018	391.866312828313	0.252764599066893
39	392	391.60568606059	-2.89161416837898	395.285928107789	-0.394313939410154
40	396	399.472285463411	-5.89575270014044	398.423467236729	3.47228546341114
41	392	393.157063724692	-10.7180700903614	401.56100636567	1.15706372469191
42	396	397.519922304758	-9.92232934353665	404.402407038779	1.51992230475815
43	419	419.973692039001	10.7825002491113	407.243807711888	0.97369203900115
44	421	418.853692364396	13.1397900208043	410.006517614799	-2.14630763560365
45	420	421.188231712638	6.04254076965048	412.769227517711	1.18823171263836
46	418	419.393075573557	1.19226840949127	415.414656016952	1.39307557355664
47	410	408.416101864521	-6.47618638071424	418.060084516193	-1.58389813547888
48	418	416.461828236798	-0.969349629556216	420.507521392758	-1.53817176320206
49	426	425.209763822586	3.83527790809046	422.954958269323	-0.790236177413931
50	428	428.67314251794	1.88092257262018	425.44593490944	0.673142517940278
51	430	434.954702618823	-2.89161416837898	427.936911549556	4.95470261882332
52	424	422.90931447306	-5.89575270014044	430.986438227081	-1.09068552694038
53	423	422.682105185755	-10.7180700903614	434.035964904606	-0.317894814244596
54	427	426.539694266638	-9.92232934353665	437.382635076898	-0.460305733361736
55	441	430.488194501698	10.7825002491113	440.729305249191	-10.511805498302
56	449	440.997681709836	13.1397900208043	443.86252826936	-8.0023182901644
57	452	450.96170794082	6.04254076965048	446.995751289529	-1.03829205917998
58	462	472.911588941539	1.19226840949127	449.89614264897	10.911588941539
59	455	463.679652372304	-6.47618638071424	452.79653400841	8.6796523723043
60	461	467.626159375118	-0.969349629556216	455.343190254438	6.62615937511805
61	461	460.274875591443	3.83527790809046	457.889846500466	-0.725124408556894
62	463	464.561544856292	1.88092257262018	459.557532571088	1.56154485629224
63	462	465.66639552667	-2.89161416837898	461.225218641709	3.66639552667033
64	456	455.964800318236	-5.89575270014044	461.930952381904	-0.0351996817635154
65	455	458.081383968262	-10.7180700903614	462.636686122099	3.08138396826212
66	456	458.923082320565	-9.92232934353665	462.999247022972	2.92308232056456
67	472	469.855691827044	10.7825002491113	463.361807923845	-2.14430817295619
68	472	467.198472822819	13.1397900208043	463.661737156376	-4.80152717718056
69	471	471.995792841442	6.04254076965048	463.961666388908	0.995792841441812
70	465	464.507920009011	1.19226840949127	464.299811581498	-0.492079990988827
71	459	459.838229606627	-6.47618638071424	464.637956774087	0.83822960662684
72	465	465.881306255307	-0.969349629556216	465.088043374249	0.881306255307038
73	468	466.626592117499	3.83527790809046	465.538129974411	-1.37340788250145
74	467	466.372922283053	1.88092257262018	465.746155144326	-0.627077716946644
75	463	462.937433854137	-2.89161416837898	465.954180314242	-0.0625661458629452
76	460	460.571751305548	-5.89575270014044	465.324001394593	0.571751305547934
77	462	470.024247615418	-10.7180700903614	464.693822474943	8.02424761541829
78	461	468.858540698697	-9.92232934353665	463.06378864484	7.85854069869674
79	476	479.783744936152	10.7825002491113	461.433754814737	3.783744936152
80	476	480.039105503396	13.1397900208043	458.8211044758	4.03910550339583
81	471	479.749005093487	6.04254076965048	456.208454136863	8.74900509348652
82	453	452.096719590144	1.19226840949127	452.711012000365	-0.903280409856166
83	443	443.262616516847	-6.47618638071424	449.213569863867	0.262616516847345
84	442	439.781522090252	-0.969349629556216	445.187827539304	-2.21847790974783
85	444	443.002636877168	3.83527790809046	441.162085214741	-0.9973631228317
86	438	436.884081976906	1.88092257262018	437.234995450474	-1.11591802309397
87	427	423.583708482173	-2.89161416837898	433.307905686206	-3.41629151782735
88	424	424.094813066292	-5.89575270014044	429.800939633849	0.0948130662916924
89	416	416.42409650887	-10.7180700903614	426.293973581491	0.424096508870264
90	406	398.567444234079	-9.92232934353665	423.354885109457	-7.43255576592077
91	431	430.801703113465	10.7825002491113	420.415796637424	-0.19829688653499
92	434	436.990172258828	13.1397900208043	417.870037720368	2.99017225882778
93	418	414.633180427037	6.04254076965048	415.324278803312	-3.36681957296258
94	412	409.732237939769	1.19226840949127	413.07549365074	-2.26776206023112
95	404	403.649477882547	-6.47618638071424	410.826708498168	-0.350522117453409
96	409	410.012554405907	-0.969349629556216	408.956795223649	1.012554405907
97	412	413.077840142779	3.83527790809046	407.086881949131	1.07784014277877
98	406	404.574708121955	1.88092257262018	405.544369305425	-1.42529187804507
99	398	394.88975750666	-2.89161416837898	404.001856661719	-3.11024249334002
100	397	396.963304743901	-5.89575270014044	402.932447956239	-0.0366952560989944
101	385	378.855030839602	-10.7180700903614	401.86303925076	-6.14496916039849
102	390	388.16818213107	-9.92232934353665	401.754147212467	-1.83181786892999
103	413	413.572244576715	10.7825002491113	401.645255174173	0.57224457671532
104	413	409.847464782544	13.1397900208043	403.012745196652	-3.15253521745632
105	401	391.577224011219	6.04254076965048	404.380235219131	-9.42277598878115
106	397	385.683461897031	1.19226840949127	407.124269693478	-11.3165381029692
107	397	390.607882212889	-6.47618638071424	409.868304167825	-6.39211778711092
108	409	405.402993676285	-0.969349629556216	413.566355953271	-3.59700632371522
109	419	416.900314353192	3.83527790809046	417.264407738718	-2.09968564680821
110	424	424.806344430562	1.88092257262018	421.312732996818	0.806344430561921
111	428	433.530555913461	-2.89161416837898	425.361058254918	5.53055591346094
112	430	436.717433395931	-5.89575270014044	429.178319304209	6.71743339593132
113	424	425.722489736861	-10.7180700903614	432.9955803535	1.72248973686118
114	433	439.677487572926	-9.92232934353665	436.244841770611	6.677487572926
115	456	461.723396563168	10.7825002491113	439.494103187721	5.72339656316763
116	459	462.881743031211	13.1397900208043	441.978466947984	3.88174303121127
117	446	441.494628522102	6.04254076965048	444.462830708248	-4.50537147789822
118	441	434.794694058862	1.19226840949127	446.013037531646	-6.20530594113757
119	439	436.912942025669	-6.47618638071424	447.563244355045	-2.08705797433072
120	454	460.302253624712	-0.969349629556216	448.667096004845	6.30225362471168
121	460	466.393774437265	3.83527790809046	449.770947654644	6.39377443726534
122	457	461.748481899322	1.88092257262018	450.370595528058	4.74848189932186
123	451	453.921370766907	-2.89161416837898	450.970243401472	2.92137076690727
124	444	443.049331041713	-5.89575270014044	450.846421658428	-0.950668958287338
125	437	433.995470174978	-10.7180700903614	450.722599915384	-3.00452982502247
126	443	445.43155190426	-9.92232934353665	450.490777439277	2.43155190425972
127	471	480.958544787719	10.7825002491113	450.25895496317	9.95854478771867
128	469	474.908805139556	13.1397900208043	449.95140483964	5.9088051395558
129	454	452.31360451424	6.04254076965048	449.64385471611	-1.68639548576027
130	444	437.589233978789	1.19226840949127	449.21849761172	-6.4107660212112
131	436	429.683045873384	-6.47618638071424	448.79314050733	-6.31695412661594

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/13fdh1292840111.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/13fdh1292840111.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/2w6ck1292840111.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/2w6ck1292840111.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/3w6ck1292840111.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/3w6ck1292840111.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/47fb51292840111.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292840004tpniojb75vswyy7/47fb51292840111.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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.

FreeStatistics.org is powered by