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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 13:44:44 +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/t1293630161r47sedpbeja5z8l.htm/, Retrieved Wed, 29 Dec 2010 14:42:41 +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/t1293630161r47sedpbeja5z8l.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 «

1203.6 1180.59 1156.85 1191.5 1191.33 1234.18 1220.33 1228.81 1207.01 1249.48 1248.29 1280.08 1280.66 1294.87 1310.61 1270.09 1270.2 1276.66 1303.82 1335.85 1377.94 1400.63 1418.3 1438.24 1406.82 1420.86 1482.37 1530.62 1503.35 1455.27 1473.99 1526.75 1549.38 1481.14 1468.36 1378.55 1330.63 1322.7 1385.59 1400.38 1280 1267.38 1282.83 1166.36 968.75 896.24 903.25 825.88 735.09 797.87 872.81 919.14 919.32 987.48 1020.62 1057.08 1036.19 1095.63 1115.1 1073.87 1104.49 1169.43 1186.69 1089.41 1030.71 1101.6 1049.33 1141.2 1183.26 1180.55

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	701	0	71
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	1203.6	1268.27550820852	-38.0611782605698	1176.98567005205	64.6755082085224
2	1180.59	1194.21882430945	-16.9920843609289	1183.95326005147	13.6288243094539
3	1156.85	1104.77376529599	18.0053846531078	1190.92085005090	-52.0762347040104
4	1191.5	1166.14766058095	18.5780380729517	1198.2743013461	-25.3523394190527
5	1191.33	1193.28993890089	-16.2576915421857	1205.6277526413	1.95993890088675
6	1234.18	1249.94303368385	5.19189777119832	1213.22506854496	15.7630336838454
7	1220.33	1209.74772265374	10.0898928976459	1220.82238444861	-10.5822773462598
8	1228.81	1200.44217196097	28.3566089303243	1228.82121910871	-28.3678280390302
9	1207.01	1170.35162653712	6.84831969407701	1236.82005376880	-36.658373462875
10	1249.48	1248.49643488859	4.57487893124038	1245.88868618017	-0.983565111409234
11	1248.29	1237.13823608589	4.48444532257202	1254.95731859154	-11.1517639141118
12	1280.08	1322.90894586064	-24.8184940996659	1262.06954823902	42.8289458606412
13	1280.66	1330.19940037406	-38.0611782605698	1269.18177788651	49.5394003740605
14	1294.87	1329.07141696694	-16.9920843609289	1277.66066739399	34.2014169669364
15	1310.61	1317.07505844542	18.0053846531078	1286.13955690148	6.46505844541707
16	1270.09	1224.84970462363	18.5780380729517	1296.75225730342	-45.2402953763687
17	1270.2	1249.29273383683	-16.2576915421857	1307.36495770536	-20.9072661631728
18	1276.66	1228.49469109470	5.19189777119832	1319.63341113410	-48.1653089052966
19	1303.82	1265.64824253952	10.0898928976459	1331.90186456284	-38.1717574604838
20	1335.85	1296.51671624677	28.3566089303243	1346.82667482290	-39.3332837532282
21	1377.94	1387.28019522295	6.84831969407701	1361.75148508297	9.34019522295353
22	1400.63	1416.55328502701	4.57487893124038	1380.13183604175	15.9232850270125
23	1418.3	1433.60336767690	4.48444532257202	1398.51218700053	15.3033676769028
24	1438.24	1485.53809836218	-24.8184940996659	1415.76039573748	47.2980983621812
25	1406.82	1418.69257378613	-38.0611782605698	1433.00860447444	11.8725737861255
26	1420.86	1412.31665859773	-16.9920843609289	1446.39542576320	-8.54334140226706
27	1482.37	1486.95236829495	18.0053846531078	1459.78224705195	4.58236829494513
28	1530.62	1575.61792315474	18.5780380729517	1467.04403877231	44.9979231547388
29	1503.35	1548.65186104951	-16.2576915421857	1474.30583049267	45.3018610495144
30	1455.27	1431.74627467583	5.19189777119832	1473.60182755297	-23.5237253241655
31	1473.99	1464.99228248909	10.0898928976459	1472.89782461326	-8.99771751090907
32	1526.75	1560.03054134258	28.3566089303243	1465.11284972710	33.2805413425779
33	1549.38	1634.58380546499	6.84831969407701	1457.32787484093	85.2038054649909
34	1481.14	1513.33443402742	4.57487893124038	1444.37068704134	32.1944340274160
35	1468.36	1500.82205543567	4.48444532257202	1431.41349924176	32.4620554356727
36	1378.55	1369.11020189526	-24.8184940996659	1412.80829220440	-9.4397981047373
37	1330.63	1305.11809309352	-38.0611782605698	1394.20308516705	-25.5119069064815
38	1322.7	1298.42940556296	-16.9920843609289	1363.96267879797	-24.2705944370377
39	1385.59	1419.45234291801	18.0053846531078	1333.72227242888	33.8623429180104
40	1400.38	1491.18708511077	18.5780380729517	1290.99487681628	90.807085110772
41	1280	1327.99021033851	-16.2576915421857	1248.26748120367	47.9902103385148
42	1267.38	1330.25647190506	5.19189777119832	1199.31163032374	62.8764719050621
43	1282.83	1405.21432765855	10.0898928976459	1150.35577944381	122.384327658546
44	1166.36	1203.07366846001	28.3566089303243	1101.28972260967	36.7136684600082
45	968.75	878.428014530397	6.84831969407701	1052.22366577553	-90.3219854696033
46	896.24	777.253445652208	4.57487893124038	1010.65167541655	-118.986554347792
47	903.25	832.93586961985	4.48444532257202	969.079685057578	-70.3141303801499
48	825.88	732.498732338044	-24.8184940996659	944.079761761622	-93.3812676619564
49	735.09	589.161339794903	-38.0611782605698	919.079838465667	-145.928660205097
50	797.87	697.964483179182	-16.9920843609289	914.767601181747	-99.9055168208182
51	872.81	817.159251449065	18.0053846531078	910.455363897828	-55.6507485509354
52	919.14	894.69564015219	18.5780380729517	925.006321774857	-24.4443598478092
53	919.32	915.340411890299	-16.2576915421857	939.557279651887	-3.97958810970147
54	987.48	1005.62714444735	5.19189777119832	964.14095778145	18.1471444473508
55	1020.62	1042.42547119134	10.0898928976459	988.724635911014	21.8054711913397
56	1057.08	1070.63476982128	28.3566089303243	1015.16862124839	13.5547698212820
57	1036.19	1023.91907372015	6.84831969407701	1041.61260658577	-12.2709262798501
58	1095.63	1126.75608995886	4.57487893124038	1059.9290311099	31.1260899588603
59	1115.1	1147.47009904340	4.48444532257202	1078.24545563403	32.3700990434024
60	1073.87	1085.19840840656	-24.8184940996659	1087.36008569311	11.3284084065579
61	1104.49	1150.56646250838	-38.0611782605698	1096.47471575219	46.0764625083791
62	1169.43	1255.48973238964	-16.9920843609289	1100.36235197129	86.0597323896407
63	1186.69	1251.12462715651	18.0053846531078	1104.24998819039	64.4346271565068
64	1089.41	1050.84793010717	18.5780380729517	1109.39403181988	-38.5620698928292
65	1030.71	963.139616092817	-16.2576915421857	1114.53807544937	-67.5703839071834
66	1101.6	1079.33088525056	5.19189777119832	1118.67721697824	-22.2691147494377
67	1049.33	965.753748595244	10.0898928976459	1122.81635850711	-83.5762514047556
68	1141.2	1127.74240322552	28.3566089303243	1126.30098784415	-13.4575967744786
69	1183.26	1229.88606312472	6.84831969407701	1129.7856171812	46.6260631247237
70	1180.55	1223.24962824369	4.57487893124038	1133.27549282507	42.6996282436924

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/13s5e1293630280.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/13s5e1293630280.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/2w2mh1293630280.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/2w2mh1293630280.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/3w2mh1293630280.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/3w2mh1293630280.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/46t321293630280.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630161r47sedpbeja5z8l/46t321293630280.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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