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Paper Classical Decomposition

*The author of this computation has been verified*

R Software Module: /rwasp_decompose.wasp (opens new window with default values)

Title produced by software: Classical Decomposition

Date of computation: Tue, 07 Dec 2010 16:51:46 +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/07/t1291740610318nht9kgto4pga.htm/, Retrieved Tue, 07 Dec 2010 17:50:15 +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/07/t1291740610318nht9kgto4pga.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 «

17.848 19.592 21.092 20.899 25.890 24.965 22.225 20.977 22.897 22.785 22.769 19.637 20.203 20.450 23.083 21.738 26.766 25.280 22.574 22.729 21.378 22.902 24.989 21.116 15.169 15.846 20.927 18.273 22.538 15.596 14.034 11.366 14.861 15.149 13.577 13.026 13.190 13.196 15.826 14.733 16.307 15.703 14.589 12.043 15.057 14.053 12.698 10.888 10.045 11.549 13.767 12.434 13.116 14.211 12.266 12.602 15.714 13.742 12.745 10.491 10.057 10.900 11.771 11.992 11.933 14.504 11.727 11.477 13.578 11.555 11.846 11.397 10.066 10.269 14.279 13.870 13.695 14.420 11.424 9.704 12.464 14.301 13.464 9.893 11.572 12.380 16.692 16.052 16.459 14.761 13.654 13.480 18.068 16.560 14.530 10.650 11.651 13.735 13.360 17.818 20.613 16.231 13.862 12.004 17.734 15.034 12.609 12.320 10.833 11.350 13.648 14.890 16.325 18.045 15.616 11.926 16.855 15.083 12.520 12.355

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	'Gwilym Jenkins' @ 72.249.127.135

Classical Decomposition by Moving Averages
t	Observations	Fit	Trend	Seasonal	Random
1	17.848	NA	NA	-2.65356095679012	NA
2	19.592	NA	NA	-1.81561651234568	NA
3	21.092	NA	NA	0.88514737654321	NA
4	20.899	NA	NA	0.776221450617283	NA
5	25.89	NA	NA	2.63177237654321	NA
6	24.965	NA	NA	1.71282330246914	NA
7	22.225	21.4447492283951	21.896125	-0.451375771604937	0.78025077160494
8	20.977	20.5411473765432	22.03	-1.48885262345679	0.435852623456793
9	22.897	23.5512538580247	22.1487083333333	1.40254552469136	-0.654253858024692
10	22.785	23.1014529320988	22.266625	0.834827932098766	-0.316452932098759
11	22.769	22.4834575617284	22.3380833333333	0.145374228395062	0.285542438271605
12	19.637	20.4084020061728	22.3877083333333	-1.97930632716049	-0.771402006172835
13	20.203	19.7618140432099	22.415375	-2.65356095679012	0.441185956790122
14	20.45	20.687300154321	22.5029166666667	-1.81561651234568	-0.237300154320984
15	23.083	23.3977723765432	22.512625	0.88514737654321	-0.314772376543207
16	21.738	23.2304297839506	22.4542083333333	0.776221450617283	-1.49242978395061
17	26.766	25.1833557098765	22.5515833333333	2.63177237654321	1.58264429012346
18	25.28	24.4185316358025	22.7057083333333	1.71282330246914	0.861468364197531
19	22.574	22.1062075617284	22.5575833333333	-0.451375771604937	0.467792438271612
20	22.729	20.6671473765432	22.156	-1.48885262345679	2.06185262345679
21	21.378	23.2768788580247	21.8743333333333	1.40254552469136	-1.89887885802469
22	22.902	22.4749529320988	21.640125	0.834827932098766	0.427047067901238
23	24.989	21.4649575617284	21.3195833333333	0.145374228395062	3.52404243827161
24	21.116	18.7606103395062	20.7399166666667	-1.97930632716049	2.35538966049383
25	15.169	17.3270223765432	19.9805833333333	-2.65356095679012	-2.15802237654321
26	15.846	17.335675154321	19.1512916666667	-1.81561651234568	-1.48967515432099
27	20.927	19.2914390432099	18.4062916666667	0.88514737654321	1.63556095679012
28	18.273	18.5879297839506	17.8117083333333	0.776221450617283	-0.314929783950618
29	22.538	19.6449390432099	17.0131666666667	2.63177237654321	2.89306095679012
30	15.596	17.9134066358025	16.2005833333333	1.71282330246914	-2.31740663580247
31	14.034	15.3296658950617	15.7810416666667	-0.451375771604937	-1.29566589506173
32	11.366	14.0993140432099	15.5881666666667	-1.48885262345679	-2.73331404320988
33	14.861	16.6677538580247	15.2652083333333	1.40254552469136	-1.80675385802469
34	15.149	15.7399945987654	14.9051666666667	0.834827932098766	-0.590994598765432
35	13.577	14.6434158950617	14.4980416666667	0.145374228395062	-1.06641589506173
36	13.026	12.2635686728395	14.242875	-1.97930632716049	0.762431327160494
37	13.19	11.6168973765432	14.2704583333333	-2.65356095679012	1.57310262345679
38	13.196	12.5061751543210	14.3217916666667	-1.81561651234568	0.689824845679013
39	15.826	15.2433140432099	14.3581666666667	0.88514737654321	0.582685956790126
40	14.733	15.0968881172839	14.3206666666667	0.776221450617283	-0.363888117283949
41	16.307	16.8701473765432	14.238375	2.63177237654321	-0.56314737654321
42	15.703	15.8254899691358	14.1126666666667	1.71282330246914	-0.122489969135804
43	14.589	13.4411658950617	13.8925416666667	-0.451375771604937	1.14783410493827
44	12.043	12.2040223765432	13.692875	-1.48885262345679	-0.16102237654321
45	15.057	14.9410038580247	13.5384583333333	1.40254552469136	0.115996141975309
46	14.053	14.1917029320988	13.356875	0.834827932098766	-0.138702932098763
47	12.698	13.2734992283951	13.128125	0.145374228395062	-0.575499228395062
48	10.888	10.9536936728395	12.933	-1.97930632716049	-0.0656936728395063
49	10.045	10.1204807098765	12.7740416666667	-2.65356095679012	-0.0754807098765422
50	11.549	10.8849251543210	12.7005416666667	-1.81561651234568	0.664074845679012
51	13.767	13.6363557098765	12.7512083333333	0.88514737654321	0.130644290123456
52	12.434	13.5418464506173	12.765625	0.776221450617283	-1.10784645061728
53	13.116	15.3863973765432	12.754625	2.63177237654321	-2.27039737654321
54	14.211	14.4528649691358	12.7400416666667	1.71282330246914	-0.241864969135801
55	12.266	12.2726242283951	12.724	-0.451375771604937	-0.00662422839506149
56	12.602	11.2086057098765	12.6974583333333	-1.48885262345679	1.39339429012346
57	15.714	13.9897955246914	12.58725	1.40254552469136	1.72420447530864
58	13.742	13.3204945987654	12.4856666666667	0.834827932098766	0.421505401234567
59	12.745	12.5633325617284	12.4179583333333	0.145374228395062	0.181667438271601
60	10.491	10.4015686728395	12.380875	-1.97930632716049	0.0894313271604936
61	10.057	9.71706404320988	12.370625	-2.65356095679012	0.339935956790125
62	10.9	10.4856751543210	12.3012916666667	-1.81561651234568	0.414324845679014
63	11.771	13.0505640432099	12.1654166666667	0.88514737654321	-1.27956404320988
64	11.992	12.7615131172840	11.9852916666667	0.776221450617283	-0.769513117283951
65	11.933	14.4884807098765	11.8567083333333	2.63177237654321	-2.55548070987654
66	14.504	13.5698233024691	11.857	1.71282330246914	0.934176697530864
67	11.727	11.4437492283951	11.895125	-0.451375771604937	0.283250771604939
68	11.477	10.3803557098765	11.8692083333333	-1.48885262345679	1.09664429012346
69	13.578	13.3499621913580	11.9474166666667	1.40254552469136	0.228037808641975
70	11.555	12.9649945987654	12.1301666666667	0.834827932098766	-1.40999459876543
71	11.846	12.4272075617284	12.2818333333333	0.145374228395062	-0.581207561728393
72	11.397	10.3724436728395	12.35175	-1.97930632716049	1.02455632716050
73	10.066	9.68206404320988	12.335625	-2.65356095679012	0.383935956790125
74	10.269	10.4335084876543	12.249125	-1.81561651234568	-0.164508487654322
75	14.279	13.0139807098765	12.1288333333333	0.88514737654321	1.26501929012346
76	13.87	12.9730547839506	12.1968333333333	0.776221450617283	0.896945216049382
77	13.695	15.0104390432099	12.3786666666667	2.63177237654321	-1.31543904320988
78	14.42	14.0962399691358	12.3834166666667	1.71282330246914	0.323760030864198
79	11.424	11.9321242283951	12.3835	-0.451375771604937	-0.508124228395063
80	9.704	11.0453557098765	12.5342083333333	-1.48885262345679	-1.34135570987654
81	12.464	14.1252538580247	12.7227083333333	1.40254552469136	-1.66125385802469
82	14.301	13.7489945987654	12.9141666666667	0.834827932098766	0.552005401234567
83	13.464	13.2656242283951	13.12025	0.145374228395062	0.198375771604937
84	9.893	11.2703186728395	13.249625	-1.97930632716049	-1.37731867283951
85	11.572	10.7031890432099	13.35675	-2.65356095679012	0.868810956790121
86	12.38	11.7913834876543	13.607	-1.81561651234568	0.588616512345679
87	16.692	14.8829807098765	13.9978333333333	0.88514737654321	1.80901929012346
88	16.052	15.1016797839506	14.3254583333333	0.776221450617283	0.950320216049384
89	16.459	17.0957723765432	14.464	2.63177237654321	-0.636772376543206
90	14.761	16.2527816358025	14.5399583333333	1.71282330246914	-1.49178163580247
91	13.654	14.1234158950617	14.5747916666667	-0.451375771604937	-0.469415895061729
92	13.48	13.1456890432099	14.6345416666667	-1.48885262345679	0.334310956790123
93	18.068	15.9547121913580	14.5521666666667	1.40254552469136	2.11328780864197
94	16.56	15.3217445987654	14.4869166666667	0.834827932098766	1.23825540123457
95	14.53	14.8789575617284	14.7335833333333	0.145374228395062	-0.348957561728398
96	10.65	12.9886103395062	14.9679166666667	-1.97930632716049	-2.33861033950617
97	11.651	12.3842723765432	15.0378333333333	-2.65356095679012	-0.733272376543207
98	13.735	13.1693834876543	14.985	-1.81561651234568	0.565616512345679
99	13.36	15.7947307098765	14.9095833333333	0.88514737654321	-2.43473070987654
100	17.818	15.6083047839506	14.8320833333333	0.776221450617283	2.20969521604939
101	20.613	17.3202307098765	14.6884583333333	2.63177237654321	3.29276929012346
102	16.231	16.3908233024691	14.678	1.71282330246914	-0.159823302469134
103	13.862	14.2621242283951	14.7135	-0.451375771604937	-0.400124228395063
104	12.004	13.0911890432099	14.5800416666667	-1.48885262345679	-1.08718904320988
105	17.734	15.8952121913580	14.4926666666667	1.40254552469136	1.83878780864198
106	15.034	15.2174945987654	14.3826666666667	0.834827932098766	-0.183494598765433
107	12.609	14.2273742283951	14.082	0.145374228395062	-1.61837422839506
108	12.32	11.9996103395062	13.9789166666667	-1.97930632716049	0.320389660493831
109	10.833	11.4740223765432	14.1275833333333	-2.65356095679012	-0.641022376543209
110	11.35	12.3818001543210	14.1974166666667	-1.81561651234568	-1.03180015432099
111	13.648	15.0426890432099	14.1575416666667	0.88514737654321	-1.39468904320987
112	14.89	14.8991797839506	14.1229583333333	0.776221450617283	-0.00917978395061603
113	16.325	16.7530640432099	14.1212916666667	2.63177237654321	-0.428064043209876
114	18.045	15.8318649691358	14.1190416666667	1.71282330246914	2.2131350308642
115	15.616	NA	NA	-0.451375771604937	NA
116	11.926	NA	NA	-1.48885262345679	NA
117	16.855	NA	NA	1.40254552469136	NA
118	15.083	NA	NA	0.834827932098766	NA
119	12.52	NA	NA	0.145374228395062	NA
120	12.355	NA	NA	-1.97930632716049	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/1giev1291740702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/1giev1291740702.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/2giev1291740702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/2giev1291740702.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/38rdx1291740702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/38rdx1291740702.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/48rdx1291740702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291740610318nht9kgto4pga/48rdx1291740702.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = additive ; par2 = 12 ;

R code (references can be found in the software module):

par2 <- as.numeric(par2)

x <- ts(x,freq=par2)

m <- decompose(x,type=par1)

m$figure

bitmap(file='test1.png')

plot(m)

dev.off()

mylagmax <- length(x)/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(as.numeric(m$trend),na.action=na.pass,lag.max = mylagmax,main='Trend')

acf(as.numeric(m$seasonal),na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(as.numeric(m$random),na.action=na.pass,lag.max = mylagmax,main='Random')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')

spectrum(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')

spectrum(as.numeric(m$random[!is.na(m$random)]),main='Random')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')

cpgram(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')

cpgram(as.numeric(m$random[!is.na(m$random)]),main='Random')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Classical Decomposition by Moving Averages',6,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observations',header=TRUE)

a<-table.element(a,'Fit',header=TRUE)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,'Random',header=TRUE)

a<-table.row.end(a)

for (i in 1:length(m$trend)) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,m$trend[i]+m$seasonal[i])

a<-table.element(a,m$trend[i])

a<-table.element(a,m$seasonal[i])

a<-table.element(a,m$random[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.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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