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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: Fri, 10 Dec 2010 19:49:25 +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/10/t1292010632x22awpyur4ygr03.htm/, Retrieved Fri, 10 Dec 2010 20:50:38 +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/10/t1292010632x22awpyur4ygr03.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 «

42.33600 42.14710 40.25640 39.18980 39.13170 38.15070 38.27070 39.13350 40.12190 41.28450 42.57490 43.90190 43.18350 43.61880 44.76240 45.19720 44.38810 43.55520 43.56780 44.21350 45.14510 45.80790 42.32820 37.89990 34.79640 35.21440 36.37270 36.25020 36.82610 36.77230 36.90420 37.04940 36.82590 36.13570 36.03000 35.79270 35.91740 35.40080 35.17230 34.92110 35.02920 34.77390 34.89990 34.90540 34.56800 34.40600 34.45780 34.73160 34.26020 33.88490 34.05490 34.27550 34.13930 34.15870 34.53860 33.79870 33.49730 33.68020 34.32840 34.15380 33.91840 34.32620 34.77500 35.01190 34.55130 34.69510 35.47300 35.97940 36.47890 36.39100 36.67040 37.41620 37.11850 36.30010 35.70020 35.58590 35.67770 35.24080 34.80160 34.43890 34.98810 36.06800 36.35660 36.12540 34.87100 35.21990 34.33900 33.82340 34.51990 35.53000 35.79660 33.84840 33.98710 34.11610 33.82350 32.45400 31.87740 31.11500 31.04360 30.88680 31.30010 30.05070 28.6 etc...

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	1431	0	144
Trend	9	1	1
Low-pass	5	1	1

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	42.336	42.3127885773776	0.0722499279578777	42.2869614946645	-0.0232114226224027
2	42.1471	42.7657060135087	0.0735859514229754	41.4549080350683	0.618606013508703
3	40.2564	39.9118835280161	-0.0548654765214136	40.6557819485053	-0.344516471983887
4	39.1898	38.5614333062827	-0.0632640123127906	39.8814307060301	-0.62836669371729
5	39.1317	39.1847998651201	-0.0277064405741964	39.1063065754541	0.0530998651200747
6	38.1507	37.392558949688	0.0722499279578777	38.8365911223542	-0.758141050312034
7	38.2707	37.4906463582351	0.0735859514229754	38.9771676903419	-0.78005364176488
8	39.1335	38.8487892463857	-0.0548654765214136	39.4730762301357	-0.28471075361432
9	40.1219	39.9833997859176	-0.0632640123127906	40.3236642263952	-0.13850021408242
10	41.2845	41.2643159571442	-0.0277064405741964	41.33239048343	-0.0201840428557958
11	42.5749	42.8647562199598	0.0722499279578777	42.2127938520823	0.289856219959844
12	43.9019	44.7928997361466	0.0735859514229754	42.9373143124304	0.890999736146611
13	43.1835	42.8544166404819	-0.0548654765214136	43.5674488360395	-0.329083359518073
14	43.6188	43.2751236168803	-0.0632640123127906	44.0257403954325	-0.343676383119686
15	44.7624	45.3039467436662	-0.0277064405741964	44.248559696908	0.541546743666174
16	45.1972	46.0014935883603	0.0722499279578777	44.3206564836818	0.804293588360295
17	44.3881	44.4257616742017	0.0735859514229754	44.2768523743753	0.0376616742017077
18	43.5552	42.9854332363591	-0.0548654765214136	44.1798322401623	-0.569766763640871
19	43.5678	42.9893023258767	-0.0632640123127906	44.2095616864361	-0.57849767412327
20	44.2135	44.1177176062186	-0.0277064405741964	44.3369888343556	-0.0957823937813771
21	45.1451	46.1348661359213	0.0722499279578777	44.0830839361208	0.989766135921343
22	45.8079	48.5157981670718	0.0735859514229754	43.0264158815052	2.70789816707184
23	42.3282	43.4765371349983	-0.0548654765214136	41.2347283415231	1.14833713499833
24	37.8999	36.6935604958602	-0.0632640123127906	39.1695035164526	-1.20633950413979
25	34.7964	32.2621080268624	-0.0277064405741964	37.3583984137118	-2.53429197313757
26	35.2144	34.0909937031733	0.0722499279578777	36.2655563688689	-1.12340629682674
27	36.3727	36.6472562911728	0.0735859514229754	36.0245577574043	0.274556291172757
28	36.2502	36.2675036683949	-0.0548654765214136	36.2877618081265	0.0173036683948737
29	36.8261	37.1276439388981	-0.0632640123127906	36.5878200734147	0.301543938898121
30	36.7723	36.8109857705189	-0.0277064405741964	36.7613206700553	0.0386857705188817
31	36.9042	36.9141688838947	0.0722499279578777	36.8219811881475	0.00996888389466477
32	37.0494	37.2781874396831	0.0735859514229754	36.7470266088939	0.228787439683103
33	36.8259	37.1244697223615	-0.0548654765214136	36.5821957541599	0.298569722361464
34	36.1357	35.9697209739234	-0.0632640123127906	36.3649430383894	-0.16597902607662
35	36.03	35.9690994123162	-0.0277064405741964	36.118607028258	-0.0609005876837756
36	35.7927	35.6388250415204	0.0722499279578777	35.8743250305217	-0.153874958479555
37	35.9174	36.1022105309878	0.0735859514229754	35.6590035175892	0.184810530987846
38	35.4008	35.396897211605	-0.0548654765214136	35.4595682649164	-0.00390278839498137
39	35.1723	35.1404659554672	-0.0632640123127906	35.2673980568456	-0.031834044532836
40	34.9211	34.7854787405446	-0.0277064405741964	35.0844277000296	-0.135621259455355
41	35.0292	35.0224556301524	0.0722499279578777	34.9636944418897	-0.00674436984756
42	34.7739	34.5760242238521	0.0735859514229754	34.898189824725	-0.197875776147946
43	34.8999	35.0271504330823	-0.0548654765214136	34.8275150434391	0.127250433082338
44	34.9054	35.1404698579972	-0.0632640123127906	34.7335941543156	0.23506985799721
45	34.568	34.5115022936343	-0.0277064405741964	34.6522041469399	-0.0564977063657253
46	34.406	34.1589913088587	0.0722499279578777	34.5807587631835	-0.247008691141346
47	34.4578	34.3588914281455	0.0735859514229754	34.4831226204315	-0.0989085718544658
48	34.7316	35.1429515494802	-0.0548654765214136	34.3751139270412	0.411351549480194
49	34.2602	34.2945940692097	-0.0632640123127906	34.2890699431031	0.0343940692096751
50	33.8849	33.5863519914617	-0.0277064405741964	34.2111544491125	-0.298548008538297
51	34.0549	33.9008405853804	0.0722499279578777	34.1367094866617	-0.154059414619567
52	34.2755	34.3408910568531	0.0735859514229754	34.136522991724	0.065391056853052
53	34.1393	34.1400049324688	-0.0548654765214136	34.1934605440526	0.000704932468764241
54	34.1587	34.2113402701552	-0.0632640123127906	34.1693237421576	0.05264027015523
55	34.5386	35.0511875036286	-0.0277064405741964	34.0537189369456	0.512587503628559
56	33.7987	33.5680197209873	0.0722499279578777	33.9571303510548	-0.230680279012667
57	33.4973	33.0009008112957	0.0735859514229754	33.9201132372813	-0.496399188704309
58	33.6802	33.5065477283203	-0.0548654765214136	33.9087177482011	-0.173652271679714
59	34.3284	34.7591433183714	-0.0632640123127906	33.9609206939414	0.430743318371391
60	34.1538	34.2383942838317	-0.0277064405741964	34.0969121567425	0.0845942838316631
61	33.9184	33.4980149563526	0.0722499279578777	34.2665351156896	-0.420385043647443
62	34.3262	34.1630043475549	0.0735859514229754	34.4158097010221	-0.163195652445104
63	34.775	35.0574737167933	-0.0548654765214136	34.5473917597281	0.282473716793326
64	35.0119	35.3865488546183	-0.0632640123127906	34.7005151576945	0.374648854618265
65	34.5513	34.2382070234051	-0.0277064405741964	34.8920994171691	-0.313092976594938
66	34.6951	34.1861829001019	0.0722499279578777	35.1317671719402	-0.508917099898127
67	35.473	35.4265884631143	0.0735859514229754	35.4458255854627	-0.0464115368856852
68	35.9794	36.1911660062963	-0.0548654765214136	35.8224994702251	0.211766006296351
69	36.4789	36.8126205640526	-0.0632640123127906	36.2084434482602	0.333720564052634
70	36.391	36.2616970624147	-0.0277064405741964	36.5480093781595	-0.129302937585273
71	36.6704	36.5123365646754	0.0722499279578777	36.7562135073667	-0.158063435324557
72	37.4162	37.9801154773645	0.0735859514229754	36.7786985712125	0.563915477364532
73	37.1185	37.6431864670836	-0.0548654765214136	36.6486790094378	0.524686467083626
74	36.3001	36.2673145338049	-0.0632640123127906	36.3961494785079	-0.0327854661950582
75	35.7002	35.373126188466	-0.0277064405741964	36.0549802521082	-0.327073811534042
76	35.5859	35.3896968233865	0.0722499279578777	35.7098532486556	-0.196203176613473
77	35.6777	35.8645582602009	0.0735859514229754	35.4172557883761	0.186858260200879
78	35.2408	35.3521398748504	-0.0548654765214136	35.184325601671	0.11133987485043
79	34.8016	34.6065076445512	-0.0632640123127906	35.0599563677616	-0.19509235544885
80	34.4389	33.7952013015963	-0.0277064405741964	35.1103051389779	-0.643698698403718
81	34.9881	34.5808064327598	0.0722499279578777	35.3231436392823	-0.407293567240202
82	36.068	36.4897396204375	0.0735859514229754	35.5726744281395	0.421739620437499
83	36.3566	37.0570098239384	-0.0548654765214136	35.711055652583	0.700409823938429
84	36.1254	36.6569067945178	-0.0632640123127906	35.657157217795	0.53150679451776
85	34.871	34.4239558776893	-0.0277064405741964	35.3457505628849	-0.447044122310665
86	35.2199	35.4565941380948	0.0722499279578777	34.9109559339473	0.236694138094791
87	34.339	33.9655234161849	0.0735859514229754	34.6388906323921	-0.373476583815126
88	33.8234	33.0527870500059	-0.0548654765214136	34.6488784265155	-0.77061294999411
89	34.5199	34.3555243902719	-0.0632640123127906	34.7475396220409	-0.164375609728097
90	35.53	36.3139216555183	-0.0277064405741964	34.7737847850559	0.783921655518341
91	35.7966	36.7817827168418	0.0722499279578777	34.7391673552003	0.985182716841827
92	33.8484	33.0389989587234	0.0735859514229754	34.5842150898536	-0.809401041276573
93	33.9871	33.8041931140649	-0.0548654765214136	34.2248723624565	-0.182906885935118
94	34.1161	34.5649209557291	-0.0632640123127906	33.7305430565837	0.448820955729104
95	33.8235	34.4418201397887	-0.0277064405741964	33.2328863007855	0.6183201397887
96	32.454	32.1697470451098	0.0722499279578777	32.6660030269324	-0.284252954890228
97	31.8774	31.631728062577	0.0735859514229754	32.049485986	-0.245671937423008
98	31.115	30.7449730575058	-0.0548654765214136	31.5398924190157	-0.370026942494246
99	31.0436	30.9459286121199	-0.0632640123127906	31.2045354001929	-0.0976713878800624
100	30.8868	30.9351145839727	-0.0277064405741964	30.8661918566015	0.0483145839726511
101	31.3001	32.1491794781147	0.0722499279578777	30.3787705939274	0.849079478114724
102	30.0507	30.3075237027302	0.0735859514229754	29.7202903458468	0.256823702730244
103	28.6799	28.4779838225137	-0.0548654765214136	28.9366816540077	-0.201916177486268
104	27.6438	27.2133708959647	-0.0632640123127906	28.1374931163481	-0.430429104035273
105	27.2394	26.9825893197495	-0.0277064405741964	27.5239171208247	-0.256810680250538
106	26.8549	26.4889737077801	0.0722499279578777	27.148576364262	-0.365926292219875
107	27.0158	27.0239844984348	0.0735859514229754	26.9340295501422	0.00818449843480806
108	26.9188	27.0576924065435	-0.0548654765214136	26.8347730699779	0.13889240654348
109	26.4966	26.2725316979561	-0.0632640123127906	26.7839323143567	-0.224068302043928
110	26.785	26.9471536728714	-0.0277064405741964	26.6505527677028	0.162153672871359
111	26.8398	27.2316489651412	0.0722499279578777	26.375701106901	0.391848965141168
112	26.4478	26.7782101769655	0.0735859514229754	26.0438038716115	0.330410176965511
113	25.1728	24.6581546791545	-0.0548654765214136	25.7423107973669	-0.5146453208455
114	24.8784	24.2804200217292	-0.0632640123127906	25.5396439905836	-0.597979978270796
115	25.4015	25.3043899297022	-0.0277064405741964	25.5263165108719	-0.0971100702977488
116	25.7716	25.7340141745592	0.0722499279578777	25.7369358974829	-0.0375858254407859
117	26.1181	26.1772833770969	0.0735859514229754	25.9853306714801	0.0591833770968968
118	26.3969	26.8680791537682	-0.0548654765214136	25.9805863227532	0.471179153768194
119	26.6571	27.7124214768121	-0.0632640123127906	25.6650425355006	1.05532147681215
120	25.1839	25.1998805207479	-0.0277064405741964	25.1956259198263	0.0159805207478563
121	23.8394	22.8613124538601	0.0722499279578777	24.745237618182	-0.97808754613989
122	23.8619	23.1299355926188	0.0735859514229754	24.5202784559582	-0.73196440738122
123	24.2581	23.8581642091803	-0.0548654765214136	24.7129012673411	-0.399935790819676
124	25.1098	25.0932978689205	-0.0632640123127906	25.1895661433923	-0.0165021310794842
125	26.1617	26.6770127246505	-0.0277064405741964	25.6740937159237	0.515312724650471
126	26.8087	27.3922552400495	0.0722499279578777	26.1528948319926	0.58355524004951
127	25.6577	24.6319721072213	0.0735859514229754	26.6098419413557	-1.02572789277869
128	27.0982	27.2145868083865	-0.0548654765214136	27.0366786681349	0.116386808386533
129	27.4665	27.5537947927977	-0.0632640123127906	27.4424692195151	0.087294792797703
130	28.289	28.8777309933091	-0.0277064405741964	27.7279754472651	0.588730993309063
131	28.6933	29.4985394590627	0.0722499279578777	27.8158106129794	0.805239459062744
132	27.2401	26.6598438086402	0.0735859514229754	27.7467702399368	-0.580256191359808
133	27.2798	27.1287268991303	-0.0548654765214136	27.4857385773911	-0.151073100869713
134	27.6404	28.2573338148066	-0.0632640123127906	27.0867301975062	0.616933814806568
135	26.831	27.0236296045273	-0.0277064405741964	26.6660768360469	0.19262960452734
136	26.2467	26.1506370815803	0.0722499279578777	26.2705129904619	-0.0960629184197401
137	25.2212	24.3420470531448	0.0735859514229754	26.0267669954322	-0.879152946855214
138	25.3653	24.7663152059851	-0.0548654765214136	26.0191502705363	-0.598984794014893
139	26.2592	26.4587692471786	-0.0632640123127906	26.1228947651342	0.199569247178619
140	27.2279	28.2642003650266	-0.0277064405741964	26.2193060755476	1.03630036502661
141	26.3315	26.2310316114106	0.0722499279578777	26.3597184606316	-0.100468388589441
142	25.8981	25.2435267043796	0.0735859514229754	26.4790873441975	-0.65457329562043
143	26.6898	26.8662888535133	-0.0548654765214136	26.5681766230082	0.176488853513256

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/1zq301292010560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/1zq301292010560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/2rz2l1292010560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/2rz2l1292010560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/3rz2l1292010560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/3rz2l1292010560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/4k91o1292010560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292010632x22awpyur4ygr03/4k91o1292010560.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 <- 5

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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