Home » date » 2010 » Dec » 20 »

Decomposition by 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: Mon, 20 Dec 2010 22:16:12 +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/t12928832744xy06y5a0ps8pdk.htm/, Retrieved Mon, 20 Dec 2010 23:14:34 +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/t12928832744xy06y5a0ps8pdk.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 «

1038.00 934.00 988.00 870.00 854.00 834.00 872.00 954.00 870.00 1238.00 1082.00 1053.00 934.00 787.00 1081.00 908.00 995.00 825.00 822.00 856.00 887.00 1094.00 990.00 936.00 1097.00 918.00 926.00 907.00 899.00 971.00 1087.00 1000.00 1071.00 1190.00 1116.00 1070.00 1314.00 1068.00 1185.00 1215.00 1145.00 1251.00 1363.00 1368.00 1535.00 1853.00 1866.00 2023.00 1373.00 1968.00 1424.00 1160.00 1243.00 1375.00 1539.00 1773.00 1906.00 2076.00 2004.00

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	591	0	60
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	1038	1049.90181044474	18.5822782767380	1007.51591127852	11.9018104447370
2	934	877.840663829668	-9.75089599791843	999.91023216825	-56.1593361703322
3	988	1019.77908573299	-36.0836387909675	992.304553057976	31.7790857329915
4	870	911.808447115832	-157.069828518108	985.261381402275	41.8084471158325
5	854	883.837906887489	-154.056116634063	978.218209746574	29.8379068874891
6	834	837.292577730278	-141.418452767651	972.125875037373	3.29257773027814
7	872	845.347237442496	-67.3807777706665	966.03354032817	-26.6527625575043
8	954	971.828934207828	-24.5655726533436	960.736638445516	17.8289342078281
9	870	756.310492321885	28.2497711152548	955.43973656286	-113.689507678115
10	1238	1268.67207264956	253.050264480702	954.277662869738	30.6720726495604
11	1082	1048.03358014752	162.850830675867	953.115589176615	-33.9664198524825
12	1053	1021.26444323776	127.592263689576	957.143293072666	-31.7355567622428
13	934	888.246724754544	18.5822782767380	961.170996968718	-45.7532752454558
14	787	623.035852420883	-9.75089599791843	960.715043577036	-163.964147579117
15	1081	1237.82454860561	-36.0836387909675	960.259090185354	156.824548605613
16	908	1018.23938155767	-157.069828518108	954.830446960433	110.239381557675
17	995	1194.65431289855	-154.056116634063	949.401803735511	199.654312898552
18	825	847.123955080673	-141.418452767651	944.294497686978	22.1239550806731
19	822	772.193586132223	-67.3807777706665	939.187191638444	-49.8064138677772
20	856	801.500603494358	-24.5655726533436	935.064969158985	-54.4993965056418
21	887	814.807482205218	28.2497711152548	930.942746679527	-72.192517794782
22	1094	1005.26738986077	253.050264480702	929.682345658524	-88.7326101392257
23	990	888.727224686612	162.850830675867	928.42194463752	-101.272775313388
24	936	805.402279608208	127.592263689576	939.005456702215	-130.597720391792
25	1097	1225.82875295635	18.5822782767380	949.58896876691	128.828752956353
26	918	877.948590627105	-9.75089599791843	967.802305370813	-40.0514093728949
27	926	902.06799681625	-36.0836387909675	986.015641974717	-23.9320031837497
28	907	971.273482781034	-157.069828518108	999.796345737074	64.2734827810339
29	899	938.479067134633	-154.056116634063	1013.57704949943	39.4790671346329
30	971	1059.30603971967	-141.418452767651	1024.11241304798	88.306039719672
31	1087	1206.73300117414	-67.3807777706665	1034.64777659653	119.733001174140
32	1000	977.434121083515	-24.5655726533436	1047.13145156983	-22.5658789164847
33	1071	1054.13510234162	28.2497711152548	1059.61512654313	-16.8648976583847
34	1190	1048.51422206814	253.050264480702	1078.43551345116	-141.485777931865
35	1116	971.893268964936	162.850830675867	1097.25590035920	-144.106731035064
36	1070	889.361052063019	127.592263689576	1123.04668424740	-180.638947936981
37	1314	1460.58025358765	18.5822782767380	1148.83746813561	146.580253587649
38	1068	959.543816839044	-9.75089599791843	1186.20707915887	-108.456183160956
39	1185	1182.50694860883	-36.0836387909675	1223.57669018214	-2.49305139116905
40	1215	1312.49714760927	-157.069828518108	1274.57268090884	97.4971476092699
41	1145	1118.48744499852	-154.056116634063	1325.56867163554	-26.5125550014759
42	1251	1265.13963890486	-141.418452767651	1378.27881386279	14.1396389048568
43	1363	1362.39182168062	-67.3807777706665	1430.98895609005	-0.60817831938175
44	1368	1289.67662688255	-24.5655726533436	1470.88894577079	-78.32337311745
45	1535	1530.96129343321	28.2497711152548	1510.78893545154	-4.03870656679396
46	1853	1922.71292352979	253.050264480702	1530.23681198951	69.7129235297889
47	1866	2019.46448079665	162.850830675867	1549.68468852748	153.464480796653
48	2023	2358.58153840987	127.592263689576	1559.82619790056	335.581538409866
49	1373	1157.45001444963	18.5822782767380	1569.96770727364	-215.549985550374
50	1968	2359.3522486222	-9.75089599791843	1586.39864737572	391.352248622199
51	1424	1281.25405131316	-36.0836387909675	1602.82958747780	-142.745948686836
52	1160	853.257764849069	-157.069828518108	1623.81206366904	-306.742235150931
53	1243	995.261576773788	-154.056116634063	1644.79453986028	-247.738423226212
54	1375	1227.52152900045	-141.418452767651	1663.8969237672	-147.478470999548
55	1539	1462.38147009654	-67.3807777706665	1682.99930767412	-76.6185299034555
56	1773	1866.70231895615	-24.5655726533436	1703.86325369720	93.7023189561473
57	1906	2059.02302916447	28.2497711152548	1724.72719972027	153.023029164474
58	2076	2149.81619918698	253.050264480702	1749.13353633232	73.8161991869765
59	2004	2071.60929637976	162.850830675867	1773.53987294437	67.6092963797598

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/1q1nx1292883368.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/1q1nx1292883368.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/2q1nx1292883368.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/2q1nx1292883368.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/3q1nx1292883368.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/3q1nx1292883368.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/41bm01292883368.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928832744xy06y5a0ps8pdk/41bm01292883368.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