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Paper - 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: Tue, 14 Dec 2010 09:48:57 +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/14/t1292320019vksh908iaxb1ib9.htm/, Retrieved Tue, 14 Dec 2010 10:47:04 +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/14/t1292320019vksh908iaxb1ib9.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 «

235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1

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	'George Udny Yule' @ 72.249.76.132

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	1061	0	107
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	235.1	221.975437231718	39.6937187003568	208.530844067926	-13.1245627682823
2	280.7	296.42000945377	52.637641710942	212.342348835288	15.72000945377
3	264.6	279.275687902735	33.7704584946149	216.153853602651	14.6756879027346
4	240.7	253.768790480597	7.31523739464612	220.315972124757	13.0687904805971
5	201.4	189.217452014034	-10.8955426608971	224.478090646863	-12.1825479859660
6	240.8	235.800586049013	16.7684648387020	229.030949112285	-4.99941395098699
7	241.1	235.439265939465	13.1769264828283	233.583807577707	-5.66073406053522
8	223.8	227.394824517345	-18.1797061906026	238.384881673257	3.59482451734513
9	206.1	199.239265488785	-30.2252212575932	243.185955768808	-6.86073451121479
10	174.7	149.161340403322	-50.1298762227587	250.368535819437	-25.5386595966784
11	203.3	178.245340355168	-29.1964562252343	257.551115870066	-25.0546596448319
12	220.5	195.306459211026	-24.7356479452433	270.429188734217	-25.1935407889741
13	299.5	275.999019701275	39.6937187003568	283.307261598369	-23.5009802987255
14	347.4	343.258436179994	52.637641710942	298.903922109064	-4.14156382000607
15	338.3	328.328958885626	33.7704584946149	314.500582619759	-9.97104111437426
16	327.7	317.845864552884	7.31523739464612	330.23889805247	-9.85413544711628
17	351.6	368.118329175716	-10.8955426608971	345.977213485181	16.5183291757162
18	396.6	416.806177760618	16.7684648387020	359.62535740068	20.2061777606179
19	438.8	491.149572200992	13.1769264828283	373.273501316179	52.3495722009924
20	395.6	426.426025785933	-18.1797061906026	382.953680404669	30.8260257859332
21	363.5	364.591361764434	-30.2252212575932	392.633859493160	1.09136176443371
22	378.8	412.122862330418	-50.1298762227587	395.60701389234	33.3228623304184
23	357	344.616287933713	-29.1964562252343	398.580168291521	-12.3837120662867
24	369	368.504093966340	-24.7356479452433	394.231553978903	-0.495906033659537
25	464.8	500.023341633359	39.6937187003568	389.882939666285	35.2233416333585
26	479.1	525.260553248066	52.637641710942	380.301805040992	46.160553248066
27	431.3	458.108871089686	33.7704584946149	370.720670415699	26.8088710896859
28	366.5	367.248239005735	7.31523739464612	358.436523599619	0.748239005735002
29	326.3	317.343165877359	-10.8955426608971	346.152376783539	-8.95683412264145
30	355.1	361.649496684191	16.7684648387020	331.782038477107	6.54949668419141
31	331.6	332.611373346497	13.1769264828283	317.411700170675	1.01137334649707
32	261.3	239.193090053197	-18.1797061906026	301.586616137405	-22.1069099468028
33	249	242.463689153457	-30.2252212575932	285.761532104136	-6.53631084654296
34	205.5	189.918601185967	-50.1298762227587	271.211275036791	-15.5813988140325
35	235.6	243.735438255788	-29.1964562252343	256.661017969446	8.13543825578807
36	240.9	261.480007172285	-24.7356479452433	245.055640772958	20.5800071722853
37	264.9	256.656017723173	39.6937187003568	233.450263576470	-8.24398227682659
38	253.8	229.425571997807	52.637641710942	225.536786291252	-24.3744280021935
39	232.3	213.206232499352	33.7704584946149	217.623309006033	-19.0937675006481
40	193.8	167.059675420479	7.31523739464612	213.225087184875	-26.7403245795213
41	177	156.06867729718	-10.8955426608971	208.826865363717	-20.9313227028200
42	213.2	203.218982337805	16.7684648387020	206.412552823493	-9.98101766219534
43	207.2	197.224833233902	13.1769264828283	203.998240283269	-9.97516676609783
44	180.6	176.803874112352	-18.1797061906026	202.57583207825	-3.79612588764758
45	188.6	206.271797384362	-30.2252212575932	201.153423873231	17.6717973843625
46	175.4	200.965746288116	-50.1298762227587	199.964129934643	25.5657462881157
47	199	228.421620229179	-29.1964562252343	198.774835996055	29.4216202291791
48	179.6	186.330050853176	-24.7356479452433	197.605597092067	6.7300508531759
49	225.8	215.469923111564	39.6937187003568	196.436358188080	-10.3300768884364
50	234	220.180139849312	52.637641710942	195.182218439746	-13.8198601506880
51	200.2	172.701462813973	33.7704584946149	193.928078691412	-27.4985371860273
52	183.6	167.397932602619	7.31523739464612	192.486830002735	-16.2020673973811
53	178.2	176.249961346839	-10.8955426608971	191.045581314058	-1.95003865316056
54	203.2	199.756863672183	16.7684648387020	189.874671489115	-3.44313632781683
55	208.5	215.119311853000	13.1769264828283	188.703761664172	6.61931185299969
56	191.8	214.489590427305	-18.1797061906026	187.290115763297	22.6895904273053
57	172.8	189.948751395171	-30.2252212575932	185.876469862422	17.1487513951708
58	148	162.488714462602	-50.1298762227587	183.641161760157	14.4887144626015
59	159.4	166.590602567342	-29.1964562252343	181.405853657892	7.19060256734244
60	154.5	155.511978555823	-24.7356479452433	178.22366938942	1.01197855582325
61	213.2	211.664796178695	39.6937187003568	175.041485120948	-1.53520382130506
62	196.4	167.657245589024	52.637641710942	172.505112700034	-28.7427544109763
63	182.8	161.860801226265	33.7704584946149	169.968740279120	-20.9391987737353
64	176.4	174.535432808349	7.31523739464612	170.949329797005	-1.86456719165113
65	153.6	146.165623346007	-10.8955426608971	171.929919314890	-7.43437665399253
66	173.2	150.267054468622	16.7684648387020	179.364480692676	-22.9329455313782
67	171	142.024031446709	13.1769264828283	186.799042070463	-28.975968553291
68	151.2	119.318177523871	-18.1797061906026	201.261528666732	-31.8818224761295
69	161.9	138.301205994592	-30.2252212575932	215.724015263001	-23.5987940054081
70	157.2	130.280252526085	-50.1298762227587	234.249623696674	-26.9197474739151
71	201.7	179.821224094888	-29.1964562252343	252.775232130346	-21.8787759051119
72	236.4	226.058017994607	-24.7356479452433	271.477629950636	-10.3419820053926
73	356.1	382.326253528718	39.6937187003568	290.180027770926	26.2262535287176
74	398.3	437.380364571237	52.637641710942	306.581993717821	39.0803645712368
75	403.7	450.645581840668	33.7704584946149	322.983959664717	46.9455818406683
76	384.6	427.684309473492	7.31523739464612	334.200453131862	43.0843094734923
77	365.8	397.078596061891	-10.8955426608971	345.416946599007	31.2785960618906
78	368.1	370.021895284858	16.7684648387020	349.40963987644	1.92189528485778
79	367.9	369.220740363298	13.1769264828283	353.402333153874	1.32074036329772
80	347	361.544842081117	-18.1797061906026	350.634864109486	14.5448420811166
81	343.3	368.957826192495	-30.2252212575932	347.867395065098	25.6578261924952
82	292.9	294.283036640768	-50.1298762227587	341.646839581991	1.38303664076756
83	311.5	316.77017212635	-29.1964562252343	335.426284098884	5.27017212635008
84	300.9	298.837930809539	-24.7356479452433	327.697717135704	-2.06206919046082
85	366.9	374.137131127119	39.6937187003568	319.969150172524	7.23713112711926
86	356.9	349.330610942843	52.637641710942	311.831747346215	-7.56938905715703
87	329.7	321.935196985479	33.7704584946149	303.694344519906	-7.76480301452091
88	316.2	328.052236735423	7.31523739464612	297.032525869930	11.8522367354235
89	269	258.524835440942	-10.8955426608971	290.370707219955	-10.4751645590576
90	289.3	275.985676514299	16.7684648387020	285.845858646999	-13.3143234857011
91	266.2	237.902063443128	13.1769264828283	281.321010074043	-28.2979365568718
92	253.6	247.192468986929	-18.1797061906026	278.187237203673	-6.40753101307081
93	233.8	222.77175692429	-30.2252212575932	275.053464333303	-11.0282430757100
94	228.4	233.04126227799	-50.1298762227587	273.888613944769	4.64126227799011
95	253.6	263.672692669000	-29.1964562252343	272.723763556234	10.0726926690003
96	260.1	271.31237640877	-24.7356479452433	273.623271536473	11.2123764087699
97	306.6	298.983501782930	39.6937187003568	274.522779516713	-7.61649821706965
98	309.2	291.248175833041	52.637641710942	274.514182456017	-17.9518241669588
99	309.5	310.723956110064	33.7704584946149	274.505585395321	1.22395611006431
100	271	260.724169183861	7.31523739464612	273.960593421493	-10.2758308161386
101	279.9	297.279941213233	-10.8955426608971	273.415601447664	17.3799412132328
102	317.9	346.120120169564	16.7684648387020	272.911414991734	28.2201201695644
103	298.4	311.215844981369	13.1769264828283	272.407228535803	12.8158449813689
104	246.7	239.716300903419	-18.1797061906026	271.863405287183	-6.9836990965809
105	227.3	213.505639219029	-30.2252212575932	271.319582038564	-13.7943607809710
106	209.1	197.690713791673	-50.1298762227587	270.639162431086	-11.4092862083274

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/1l3581292320133.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/1l3581292320133.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/2l3581292320133.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/2l3581292320133.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/3vumb1292320133.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/3vumb1292320133.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/46m3e1292320133.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292320019vksh908iaxb1ib9/46m3e1292320133.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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