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CD

*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: Sat, 18 Dec 2010 14:47:46 +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/18/t1292683554od4uff0rv0m56ql.htm/, Retrieved Sat, 18 Dec 2010 15:46:00 +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/18/t1292683554od4uff0rv0m56ql.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 «

14.458 13.594 17.814 20.235 21.811 21.439 21.393 19.831 20.468 21.080 21.600 17.390 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 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	'George Udny Yule' @ 72.249.76.132

Classical Decomposition by Moving Averages
t	Observations	Fit	Trend	Seasonal	Random
1	14.458	NA	NA	-2.73059479166667	NA
2	13.594	NA	NA	-1.81028645833333	NA
3	17.814	NA	NA	0.755505208333333	NA
4	20.235	NA	NA	0.620946874999999	NA
5	21.811	NA	NA	2.77806770833333	NA
6	21.439	NA	NA	1.84428020833333	NA
7	21.393	19.1703385416667	19.4006666666667	-0.230328124999999	2.22266145833333
8	19.831	18.432459375	19.7918333333333	-1.35937395833333	1.39854062500000
9	20.468	21.4462677083333	20.1783333333333	1.267934375	-0.978267708333327
10	21.08	21.144346875	20.3425833333333	0.801763541666667	-0.0643468749999982
11	21.6	20.7537010416667	20.5402083333333	0.213492708333334	0.846298958333339
12	17.39	18.7056760416667	20.8570833333333	-2.15140729166667	-1.31567604166667
13	17.848	18.308071875	21.0386666666667	-2.73059479166667	-0.460071875000001
14	19.592	19.310796875	21.1210833333333	-1.81028645833333	0.281203124999998
15	21.092	22.025546875	21.2700416666667	0.755505208333333	-0.933546875000001
16	20.899	22.0632385416667	21.4422916666667	0.620946874999999	-1.16423854166667
17	25.89	24.340109375	21.5620416666667	2.77806770833333	1.54989062500001
18	24.965	23.5486552083333	21.704375	1.84428020833333	1.41634479166667
19	22.225	21.665796875	21.896125	-0.230328124999999	0.559203125000003
20	20.977	20.6706260416667	22.03	-1.35937395833333	0.306373958333335
21	22.897	23.4166427083333	22.1487083333333	1.267934375	-0.519642708333333
22	22.785	23.0683885416667	22.266625	0.801763541666667	-0.283388541666660
23	22.769	22.5515760416667	22.3380833333333	0.213492708333334	0.217423958333335
24	19.637	20.2363010416667	22.3877083333333	-2.15140729166667	-0.599301041666664
25	20.203	19.6847802083333	22.415375	-2.73059479166667	0.518219791666667
26	20.45	20.6926302083333	22.5029166666667	-1.81028645833333	-0.242630208333331
27	23.083	23.2681302083333	22.512625	0.755505208333333	-0.185130208333330
28	21.738	23.0751552083333	22.4542083333333	0.620946874999999	-1.33715520833333
29	26.766	25.3296510416667	22.5515833333333	2.77806770833333	1.43634895833334
30	25.28	24.5499885416667	22.7057083333333	1.84428020833333	0.730011458333333
31	22.574	22.3272552083333	22.5575833333333	-0.230328124999999	0.246744791666675
32	22.729	20.7966260416667	22.156	-1.35937395833333	1.93237395833334
33	21.378	23.1422677083333	21.8743333333333	1.267934375	-1.76426770833333
34	22.902	22.4418885416667	21.640125	0.801763541666667	0.460111458333337
35	24.989	21.5330760416667	21.3195833333333	0.213492708333334	3.45592395833334
36	21.116	18.588509375	20.7399166666667	-2.15140729166667	2.527490625
37	15.169	17.2499885416667	19.9805833333333	-2.73059479166667	-2.08098854166667
38	15.846	17.3410052083333	19.1512916666667	-1.81028645833333	-1.49500520833334
39	20.927	19.161796875	18.4062916666667	0.755505208333333	1.765203125
40	18.273	18.4326552083333	17.8117083333333	0.620946874999999	-0.159655208333334
41	22.538	19.791234375	17.0131666666667	2.77806770833333	2.746765625
42	15.596	18.0448635416667	16.2005833333333	1.84428020833333	-2.44886354166667
43	14.034	15.5507135416667	15.7810416666667	-0.230328124999999	-1.51671354166667
44	11.366	14.2287927083333	15.5881666666667	-1.35937395833333	-2.86279270833333
45	14.861	16.5331427083333	15.2652083333333	1.267934375	-1.67214270833333
46	15.149	15.7069302083333	14.9051666666667	0.801763541666667	-0.557930208333332
47	13.577	14.711534375	14.4980416666667	0.213492708333334	-1.13453437500000
48	13.026	12.0914677083333	14.242875	-2.15140729166667	0.934532291666667
49	13.19	11.5398635416667	14.2704583333333	-2.73059479166667	1.65013645833333
50	13.196	12.5115052083333	14.3217916666667	-1.81028645833333	0.684494791666669
51	15.826	15.113671875	14.3581666666667	0.755505208333333	0.712328125000003
52	14.733	14.9416135416667	14.3206666666667	0.620946874999999	-0.208613541666665
53	16.307	17.0164427083333	14.238375	2.77806770833333	-0.709442708333334
54	15.703	15.956946875	14.1126666666667	1.84428020833333	-0.253946875000000
55	14.589	13.6622135416667	13.8925416666667	-0.230328124999999	0.926786458333334
56	12.043	12.3335010416667	13.692875	-1.35937395833333	-0.290501041666666
57	15.057	14.8063927083333	13.5384583333333	1.267934375	0.250607291666666
58	14.053	14.1586385416667	13.356875	0.801763541666667	-0.105638541666664
59	12.698	13.3416177083333	13.128125	0.213492708333334	-0.643617708333332
60	10.888	10.7815927083333	12.933	-2.15140729166667	0.106407291666667
61	10.045	10.043446875	12.7740416666667	-2.73059479166667	0.00155312500000093
62	11.549	10.8902552083333	12.7005416666667	-1.81028645833333	0.658744791666667
63	13.767	13.5067135416667	12.7512083333333	0.755505208333333	0.260286458333333
64	12.434	13.386571875	12.765625	0.620946874999999	-0.952571875
65	13.116	15.5326927083333	12.754625	2.77806770833333	-2.41669270833333
66	14.211	14.584321875	12.7400416666667	1.84428020833333	-0.373321874999998
67	12.266	12.493671875	12.724	-0.230328124999999	-0.227671874999999
68	12.602	11.338084375	12.6974583333333	-1.35937395833333	1.263915625
69	15.714	13.855184375	12.58725	1.267934375	1.858815625
70	13.742	13.2874302083333	12.4856666666667	0.801763541666667	0.454569791666666
71	12.745	12.6314510416667	12.4179583333333	0.213492708333334	0.113548958333331
72	10.491	10.2294677083333	12.380875	-2.15140729166667	0.261532291666667
73	10.057	9.64003020833333	12.370625	-2.73059479166667	0.416969791666668
74	10.9	10.4910052083333	12.3012916666667	-1.81028645833333	0.40899479166667
75	11.771	12.920921875	12.1654166666667	0.755505208333333	-1.14992187500000
76	11.992	12.6062385416667	11.9852916666667	0.620946874999999	-0.614238541666667
77	11.933	14.6347760416667	11.8567083333333	2.77806770833333	-2.70177604166667
78	14.504	13.7012802083333	11.857	1.84428020833333	0.802719791666666
79	11.727	11.664796875	11.895125	-0.230328124999999	0.0622031250000017
80	11.477	10.509834375	11.8692083333333	-1.35937395833333	0.967165625000002
81	13.578	13.2153510416667	11.9474166666667	1.267934375	0.362648958333333
82	11.555	12.9319302083333	12.1301666666667	0.801763541666667	-1.37693020833333
83	11.846	12.4953260416667	12.2818333333333	0.213492708333334	-0.649326041666663
84	11.397	10.2003427083333	12.35175	-2.15140729166667	1.19665729166667
85	10.066	9.60503020833333	12.335625	-2.73059479166667	0.460969791666669
86	10.269	10.4388385416667	12.249125	-1.81028645833333	-0.169838541666666
87	14.279	12.8843385416667	12.1288333333333	0.755505208333333	1.39466145833333
88	13.87	12.8177802083333	12.1968333333333	0.620946874999999	1.05221979166667
89	13.695	15.156734375	12.3786666666667	2.77806770833333	-1.461734375
90	14.42	14.227696875	12.3834166666667	1.84428020833333	0.192303125000000
91	11.424	12.153171875	12.3835	-0.230328124999999	-0.729171875
92	9.704	11.174834375	12.5342083333333	-1.35937395833333	-1.470834375
93	12.464	13.9906427083333	12.7227083333333	1.267934375	-1.52664270833333
94	14.301	13.7159302083333	12.9141666666667	0.801763541666667	0.585069791666667
95	13.464	13.3337427083333	13.12025	0.213492708333334	0.130257291666666
96	9.893	11.0982177083333	13.249625	-2.15140729166667	-1.20521770833333
97	11.572	10.6261552083333	13.35675	-2.73059479166667	0.945844791666666
98	12.38	11.7967135416667	13.607	-1.81028645833333	0.583286458333335
99	16.692	14.7533385416667	13.9978333333333	0.755505208333333	1.93866145833334
100	16.052	14.9464052083333	14.3254583333333	0.620946874999999	1.10559479166667
101	16.459	17.2420677083333	14.464	2.77806770833333	-0.78306770833333
102	14.761	16.3842385416667	14.5399583333333	1.84428020833333	-1.62323854166667
103	13.654	14.3444635416667	14.5747916666667	-0.230328124999999	-0.690463541666666
104	13.48	13.2751677083333	14.6345416666667	-1.35937395833333	0.204832291666667
105	18.068	15.8201010416667	14.5521666666667	1.267934375	2.24789895833333
106	16.56	15.2886802083333	14.4869166666667	0.801763541666667	1.27131979166667
107	14.53	14.9470760416667	14.7335833333333	0.213492708333334	-0.417076041666668
108	10.65	12.816509375	14.9679166666667	-2.15140729166667	-2.166509375
109	11.651	12.3072385416667	15.0378333333333	-2.73059479166667	-0.656238541666662
110	13.735	13.1747135416667	14.985	-1.81028645833333	0.560286458333334
111	13.36	15.6650885416667	14.9095833333333	0.755505208333333	-2.30508854166666
112	17.818	15.4530302083333	14.8320833333333	0.620946874999999	2.36496979166667
113	20.613	17.4665260416667	14.6884583333333	2.77806770833333	3.14647395833333
114	16.231	16.5222802083333	14.678	1.84428020833333	-0.291280208333330
115	13.862	14.483171875	14.7135	-0.230328124999999	-0.621171875
116	12.004	13.2206677083333	14.5800416666667	-1.35937395833333	-1.21666770833333
117	17.734	15.7606010416667	14.4926666666667	1.267934375	1.97339895833334
118	15.034	15.1844302083333	14.3826666666667	0.801763541666667	-0.150430208333333
119	12.609	14.2954927083333	14.082	0.213492708333334	-1.68649270833333
120	12.32	11.827509375	13.9789166666667	-2.15140729166667	0.492490625000004
121	10.833	11.3969885416667	14.1275833333333	-2.73059479166667	-0.563988541666665
122	11.35	12.3871302083333	14.1974166666667	-1.81028645833333	-1.03713020833333
123	13.648	14.913046875	14.1575416666667	0.755505208333333	-1.26504687500000
124	14.89	14.7439052083333	14.1229583333333	0.620946874999999	0.146094791666668
125	16.325	16.899359375	14.1212916666667	2.77806770833333	-0.574359375
126	18.045	15.963321875	14.1190416666667	1.84428020833333	2.08167812500000
127	15.616	NA	NA	-0.230328124999999	NA
128	11.926	NA	NA	-1.35937395833333	NA
129	16.855	NA	NA	1.267934375	NA
130	15.083	NA	NA	0.801763541666667	NA
131	12.52	NA	NA	0.213492708333334	NA
132	12.355	NA	NA	-2.15140729166667	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/1ahf71292683662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/1ahf71292683662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/2ahf71292683662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/2ahf71292683662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/3l8ws1292683662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/3l8ws1292683662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/4l8ws1292683662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292683554od4uff0rv0m56ql/4l8ws1292683662.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = additive ; par2 = 12 ; par3 = No Linear Trend ;

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])

if (par1 == 'additive') a<-table.element(a,m$trend[i]+m$seasonal[i]) else 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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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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