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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: Sun, 19 Dec 2010 19:44:23 +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/19/t1292787740d201uv7u3g0vmr1.htm/, Retrieved Sun, 19 Dec 2010 20:42:24 +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/19/t1292787740d201uv7u3g0vmr1.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	'George Udny Yule' @ 72.249.76.132

Classical Decomposition by Moving Averages
t	Observations	Fit	Trend	Seasonal	Random
1	1038	NA	NA	83.3981481481482	NA
2	934	NA	NA	-119.837962962963	NA
3	988	NA	NA	4.84259259259255	NA
4	870	NA	NA	-66.9351851851852	NA
5	854	NA	NA	-83.3657407407408	NA
6	834	NA	NA	-105.060185185185	NA
7	872	911.62037037037	961.25	-49.6296296296296	-39.6203703703703
8	954	862.662037037037	950.791666666667	-88.1296296296296	91.337962962963
9	870	928.912037037037	948.541666666667	-19.6296296296296	-58.9120370370370
10	1238	1140.77314814815	954	186.773148148148	97.226851851852
11	1082	1086.28703703704	961.458333333333	124.828703703704	-4.28703703703695
12	1053	1099.70370370370	966.958333333333	132.745370370370	-46.7037037037036
13	934	1047.89814814815	964.5	83.3981481481482	-113.898148148148
14	787	838.49537037037	958.333333333333	-119.837962962963	-51.4953703703703
15	1081	959.800925925926	954.958333333333	4.84259259259255	121.199074074074
16	908	882.731481481482	949.666666666667	-66.9351851851852	25.2685185185185
17	995	856.467592592593	939.833333333333	-83.3657407407408	138.532407407408
18	825	826.064814814815	931.125	-105.060185185185	-1.06481481481478
19	822	883.412037037037	933.041666666667	-49.6296296296296	-61.4120370370370
20	856	857.162037037037	945.291666666667	-88.1296296296296	-1.16203703703695
21	887	924.662037037037	944.291666666667	-19.6296296296296	-37.6620370370370
22	1094	1124.56481481481	937.791666666667	186.773148148148	-30.5648148148148
23	990	1058.57870370370	933.75	124.828703703704	-68.5787037037037
24	936	1068.57870370370	935.833333333333	132.745370370370	-132.578703703704
25	1097	1036.35648148148	952.958333333333	83.3981481481482	60.6435185185185
26	918	850.162037037037	970	-119.837962962963	67.8379629629633
27	926	988.50925925926	983.666666666667	4.84259259259255	-62.5092592592591
28	907	928.398148148148	995.333333333333	-66.9351851851852	-21.3981481481480
29	899	921.217592592592	1004.58333333333	-83.3657407407408	-22.2175925925925
30	971	910.356481481481	1015.41666666667	-105.060185185185	60.6435185185187
31	1087	980.412037037037	1030.04166666667	-49.6296296296296	106.587962962963
32	1000	957.203703703704	1045.33333333333	-88.1296296296296	42.7962962962963
33	1071	1042.74537037037	1062.375	-19.6296296296296	28.2546296296296
34	1190	1272.77314814815	1086	186.773148148148	-82.7731481481482
35	1116	1233.91203703704	1109.08333333333	124.828703703704	-117.912037037037
36	1070	1263.74537037037	1131	132.745370370370	-193.74537037037
37	1314	1237.56481481481	1154.16666666667	83.3981481481482	76.4351851851852
38	1068	1061.16203703704	1181	-119.837962962963	6.83796296296305
39	1185	1220.50925925926	1215.66666666667	4.84259259259255	-35.5092592592594
40	1215	1195.68981481481	1262.625	-66.9351851851852	19.3101851851852
41	1145	1238.13425925926	1321.5	-83.3657407407408	-93.1342592592591
42	1251	1287.39814814815	1392.45833333333	-105.060185185185	-36.3981481481480
43	1363	1384.99537037037	1434.625	-49.6296296296296	-21.9953703703704
44	1368	1386.45370370370	1474.58333333333	-88.1296296296296	-18.4537037037037
45	1535	1502.41203703704	1522.04166666667	-19.6296296296296	32.5879629629630
46	1853	1716.48148148148	1529.70833333333	186.773148148148	136.518518518519
47	1866	1656.32870370370	1531.5	124.828703703704	209.671296296296
48	2023	1673.49537037037	1540.75	132.745370370370	349.504629629630
49	1373	NA	1553.25	NA	NA
50	1968	NA	1577.45833333333	NA	NA
51	1424	NA	1609.79166666667	NA	NA
52	1160	NA	1634.54166666667	NA	NA
53	1243	NA	1649.58333333333	NA	NA
54	1375	NA	NA	NA	NA
55	1539	NA	NA	NA	NA
56	1773	NA	NA	NA	NA
57	1906	NA	NA	NA	NA
58	2076	NA	NA	NA	NA
59	2004	NA	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/1rpyf1292787860.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/1rpyf1292787860.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/2rpyf1292787860.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/2rpyf1292787860.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/32gxi1292787860.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/32gxi1292787860.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/42gxi1292787860.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292787740d201uv7u3g0vmr1/42gxi1292787860.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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