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Decomposition

*Unverified author*

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

Title produced by software: Classical Decomposition

Date of computation: Mon, 16 Aug 2010 13:18:35 +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/Aug/16/t12819647614j5bacx30ged4ir.htm/, Retrieved Mon, 16 Aug 2010 15:19:27 +0200

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/Aug/16/t12819647614j5bacx30ged4ir.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 «

244 243 242 240 260 259 244 234 235 235 236 238 240 233 233 233 247 251 233 226 233 233 227 225 223 212 206 202 223 221 212 205 204 200 195 193 196 180 174 164 192 189 181 167 166 164 167 164 161 141 134 111 147 144 142 140 143 137 140 130 129 112 101 74 104 103 100 98 99 91 92 94 93 76 64 32 62 69 69 68 68 59 66 73 70 57 48 22 64 74 67 61 61 52 54 69 69 53 50 22 69 78 74 63 67 59 60 80 77 58 54 32 78 86 84 78 72 64 62 72

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	'Gwilym Jenkins' @ 72.249.127.135

Classical Decomposition by Moving Averages
t	Observations	Fit	Trend	Seasonal	Random
1	244	NA	NA	8.14621913580246	NA
2	243	NA	NA	-5.50192901234568	NA
3	242	NA	NA	-10.4695216049383	NA
4	240	NA	NA	-28.0343364197531	NA
5	260	NA	NA	6.2295524691358	NA
6	259	NA	NA	11.0258487654321	NA
7	244	247.410108024691	242.333333333333	5.07677469135803	-3.41010802469134
8	234	241.789737654321	241.75	0.0397376543209901	-7.78973765432096
9	235	244.280478395062	240.958333333333	3.32214506172839	-9.28047839506175
10	235	240.336033950617	240.291666666667	0.0443672839506155	-5.33603395061726
11	236	242.086033950617	239.458333333333	2.62770061728395	-6.08603395061732
12	238	246.076774691358	238.583333333333	7.49344135802469	-8.07677469135803
13	240	245.937885802469	237.791666666667	8.14621913580246	-5.93788580246911
14	233	231.498070987654	237	-5.50192901234568	1.50192901234567
15	233	226.113811728395	236.583333333333	-10.4695216049383	6.88618827160496
16	233	208.382330246914	236.416666666667	-28.0343364197531	24.6176697530865
17	247	242.187885802469	235.958333333333	6.2295524691358	4.81211419753089
18	251	246.067515432099	235.041666666667	11.0258487654321	4.93248456790127
19	233	238.868441358025	233.791666666667	5.07677469135803	-5.86844135802465
20	226	232.248070987654	232.208333333333	0.0397376543209901	-6.2480709876543
21	233	233.530478395062	230.208333333333	3.32214506172839	-0.530478395061721
22	233	227.836033950617	227.791666666667	0.0443672839506155	5.16396604938274
23	227	228.127700617284	225.5	2.62770061728395	-1.12770061728389
24	225	230.743441358025	223.25	7.49344135802469	-5.74344135802465
25	223	229.271219135802	221.125	8.14621913580246	-6.27121913580243
26	212	213.873070987654	219.375	-5.50192901234568	-1.87307098765427
27	206	206.822145061728	217.291666666667	-10.4695216049383	-0.822145061728378
28	202	186.67399691358	214.708333333333	-28.0343364197531	15.3260030864198
29	223	218.229552469136	212	6.2295524691358	4.77044753086423
30	221	220.359182098765	209.333333333333	11.0258487654321	0.640817901234584
31	212	211.951774691358	206.875	5.07677469135803	0.048225308642003
32	205	204.456404320988	204.416666666667	0.0397376543209901	0.543595679012356
33	204	205.072145061728	201.75	3.32214506172839	-1.07214506172841
34	200	198.877700617284	198.833333333333	0.0443672839506155	1.12229938271608
35	195	198.586033950617	195.958333333333	2.62770061728395	-3.58603395061726
36	193	200.826774691358	193.333333333333	7.49344135802469	-7.826774691358
37	196	198.854552469136	190.708333333333	8.14621913580246	-2.85455246913580
38	180	182.331404320988	187.833333333333	-5.50192901234568	-2.33140432098764
39	174	174.197145061728	184.666666666667	-10.4695216049383	-0.197145061728378
40	164	153.548996913580	181.583333333333	-28.0343364197531	10.4510030864197
41	192	185.146219135802	178.916666666667	6.2295524691358	6.85378086419752
42	189	187.567515432099	176.541666666667	11.0258487654321	1.43248456790121
43	181	178.951774691358	173.875	5.07677469135803	2.04822530864200
44	167	170.831404320988	170.791666666667	0.0397376543209901	-3.83140432098764
45	166	170.822145061728	167.5	3.32214506172839	-4.82214506172838
46	164	163.669367283951	163.625	0.0443672839506155	0.330632716049394
47	167	162.169367283951	159.541666666667	2.62770061728395	4.83063271604937
48	164	163.285108024691	155.791666666667	7.49344135802469	0.714891975308632
49	161	160.437885802469	152.291666666667	8.14621913580246	0.562114197530889
50	141	144.039737654321	149.541666666667	-5.50192901234568	-3.03973765432102
51	134	136.988811728395	147.458333333333	-10.4695216049383	-2.98881172839506
52	111	117.340663580247	145.375	-28.0343364197531	-6.34066358024694
53	147	149.354552469136	143.125	6.2295524691358	-2.35455246913580
54	144	151.609182098765	140.583333333333	11.0258487654321	-7.60918209876544
55	142	142.910108024691	137.833333333333	5.07677469135803	-0.910108024691368
56	140	135.331404320988	135.291666666667	0.0397376543209901	4.66859567901236
57	143	136.030478395062	132.708333333333	3.32214506172839	6.96952160493825
58	137	129.836033950617	129.791666666667	0.0443672839506155	7.1639660493827
59	140	129.086033950617	126.458333333333	2.62770061728395	10.9139660493827
60	130	130.451774691358	122.958333333333	7.49344135802469	-0.451774691358025
61	129	127.646219135802	119.5	8.14621913580246	1.35378086419752
62	112	110.498070987654	116	-5.50192901234568	1.50192901234567
63	101	101.947145061728	112.416666666667	-10.4695216049383	-0.947145061728378
64	74	80.6323302469136	108.666666666667	-28.0343364197531	-6.63233024691357
65	104	110.979552469136	104.75	6.2295524691358	-6.97955246913578
66	103	112.275848765432	101.25	11.0258487654321	-9.27584876543209
67	100	103.326774691358	98.25	5.07677469135803	-3.32677469135803
68	98	95.289737654321	95.25	0.0397376543209901	2.710262345679
69	99	95.5304783950617	92.2083333333333	3.32214506172839	3.46952160493828
70	91	88.9610339506173	88.9166666666667	0.0443672839506155	2.03896604938272
71	92	88.0443672839506	85.4166666666667	2.62770061728395	3.95563271604939
72	94	89.7434413580247	82.25	7.49344135802469	4.25655864197532
73	93	87.6878858024692	79.5416666666667	8.14621913580246	5.31211419753085
74	76	71.4980709876543	77	-5.50192901234568	4.50192901234567
75	64	63.9888117283951	74.4583333333333	-10.4695216049383	0.0111882716049507
76	32	43.7989969135803	71.8333333333333	-28.0343364197531	-11.7989969135803
77	62	75.6462191358025	69.4166666666667	6.2295524691358	-13.6462191358025
78	69	78.4841820987654	67.4583333333333	11.0258487654321	-9.48418209876543
79	69	70.701774691358	65.625	5.07677469135803	-1.70177469135803
80	68	63.914737654321	63.875	0.0397376543209901	4.08526234567903
81	68	65.7388117283950	62.4166666666667	3.32214506172839	2.26118827160496
82	59	61.377700617284	61.3333333333333	0.0443672839506155	-2.37770061728394
83	66	63.627700617284	61	2.62770061728395	2.37229938271606
84	73	68.7851080246913	61.2916666666667	7.49344135802469	4.21489197530866
85	70	69.5628858024691	61.4166666666667	8.14621913580246	0.437114197530875
86	57	55.539737654321	61.0416666666667	-5.50192901234568	1.46026234567901
87	48	49.9888117283951	60.4583333333333	-10.4695216049383	-1.98881172839506
88	22	31.8406635802469	59.875	-28.0343364197531	-9.8406635802469
89	64	65.3128858024692	59.0833333333333	6.2295524691358	-1.31288580246915
90	74	69.4425154320988	58.4166666666667	11.0258487654321	4.55748456790123
91	67	63.2851080246914	58.2083333333333	5.07677469135803	3.71489197530864
92	61	58.039737654321	58	0.0397376543209901	2.96026234567901
93	61	61.2388117283951	57.9166666666667	3.32214506172839	-0.238811728395063
94	52	58.0443672839506	58	0.0443672839506155	-6.04436728395061
95	54	60.8360339506173	58.2083333333333	2.62770061728395	-6.83603395061728
96	69	66.076774691358	58.5833333333333	7.49344135802469	2.92322530864197
97	69	67.1878858024691	59.0416666666667	8.14621913580246	1.81211419753087
98	53	53.914737654321	59.4166666666667	-5.50192901234568	-0.914737654320987
99	50	49.2804783950617	59.75	-10.4695216049383	0.71952160493828
100	22	32.2573302469136	60.2916666666667	-28.0343364197531	-10.2573302469136
101	69	67.0628858024691	60.8333333333333	6.2295524691358	1.93711419753087
102	78	72.5675154320988	61.5416666666667	11.0258487654321	5.43248456790123
103	74	67.4101080246914	62.3333333333333	5.07677469135803	6.58989197530865
104	63	62.914737654321	62.875	0.0397376543209901	0.0852623456790127
105	67	66.5721450617284	63.25	3.32214506172839	0.427854938271608
106	59	63.877700617284	63.8333333333333	0.0443672839506155	-4.87770061728394
107	60	67.252700617284	64.625	2.62770061728395	-7.25270061728395
108	80	72.826774691358	65.3333333333333	7.49344135802469	7.17322530864199
109	77	74.2295524691358	66.0833333333333	8.14621913580246	2.77044753086420
110	58	61.6230709876543	67.125	-5.50192901234568	-3.62307098765431
111	54	57.488811728395	67.9583333333333	-10.4695216049383	-3.48881172839505
112	32	40.3406635802469	68.375	-28.0343364197531	-8.3406635802469
113	78	74.8962191358025	68.6666666666667	6.2295524691358	3.10378086419753
114	86	79.4425154320988	68.4166666666667	11.0258487654321	6.55748456790124
115	84	NA	NA	5.07677469135803	NA
116	78	NA	NA	0.0397376543209901	NA
117	72	NA	NA	3.32214506172839	NA
118	64	NA	NA	0.0443672839506155	NA
119	62	NA	NA	2.62770061728395	NA
120	72	NA	NA	7.49344135802469	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/1nkqi1281964712.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/1nkqi1281964712.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/2gtpl1281964712.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/2gtpl1281964712.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/39lo61281964712.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/39lo61281964712.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/49lo61281964712.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819647614j5bacx30ged4ir/49lo61281964712.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])

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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