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paper classical decomposition paper

*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, 21 Dec 2010 13:31:40 +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/21/t12929382370ghwtp3w794hwzt.htm/, Retrieved Tue, 21 Dec 2010 14:30:42 +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/21/t12929382370ghwtp3w794hwzt.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 «
180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211547 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171397 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 214126 206903 204442 220375 214320 212588 205816 202196 195722 198563 229139 229527 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132


Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
1180144NANA0.995692256096594NA
2173666NANA0.976032046752195NA
3165688NANA0.956856540722797NA
4161570NANA0.939354498381057NA
5156145NANA0.914931013610114NA
6153730NANA0.929435372126363NA
7182698185349.209468992168936.7083333331.09715177534580.985696138243115
8200765189673.753412293167617.0833333331.131589630605231.05847538938926
9176512176541.900212255166583.7916666671.059778376071030.999830633904931
10166618168704.604961205165833.7083333331.017311900317040.98763160637088
11158644161825.795970228165275.3333333330.9791285408806430.980338141078485
12159585165364.330986005164912.7916666671.002738049091130.965050921492287
13163095163944.7127353291646540.9956922560965940.994817077530885
14159044160335.021060090164272.2916666670.9760320467521950.991947978354608
15155511157477.256675919164577.7083333330.9568565407227970.987514027628984
16153745155806.816669389165865.8333333330.9393544983810570.986766839131536
17150569153059.609831473167290.8750.9149310136101140.983727844111094
18150605156906.233907579168818.8750.9294353721263630.959840767631383
19179612186958.273976852170403.2916666671.09715177534580.96070634468009
20194690194565.332487992171939.8333333331.131589630605231.00064074884469
21189917183912.084771209173538.251.059778376071031.03265100950958
22184128178029.370615503174999.7916666671.017311900317041.03425631042458
23175335172613.956624719176293.4583333330.9791285408806431.01576375067514
24179566178107.62748288177621.2916666671.002738049091131.00818815307200
25181140178644.366435147179417.250.9956922560965941.01396984195278
26177876177058.964169172181406.9166666670.9760320467521951.00461448441576
27175041174904.325376013182790.5416666670.9568565407227971.00078142506592
28169292172623.884555052183768.6250.9393544983810570.980698588937217
29166070169243.405187841184979.4166666670.9149310136101140.981249460300572
30166972173220.187003301186371.4166666670.9294353721263630.963929221464345
31206348205998.29160086187757.3333333331.09715177534581.00169762766682
32215706214063.423365975189170.5416666671.131589630605231.00767331759997
33202108201877.138700338190489.9583333331.059778376071031.00114357327010
34195411195306.039514621191982.4583333331.017311900317041.00053741546160
35193111189623.704013078193665.7916666670.9791285408806431.01839061210766
36195198196056.053631083195520.7083333331.002738049091130.995623426998602
37198770196785.257033566197636.6250.9956922560965941.01008583161337
38194163195095.507709127199886.3750.9760320467521950.99522025022474
39190420193372.055302188202090.9583333330.9568565407227970.98473380604258
40189733191697.595063991204073.750.9393544983810570.989751592536488
41186029188162.653664275205657.750.9149310136101140.988660589002521
42191531192445.1704109962070560.9294353721263630.995249709779446
43232571228792.625456130208533.251.09715177534581.01651440703710
44243477237713.269449081210070.2083333331.131589630605231.02424656631191
45227247224326.512355516211673.0416666671.059778376071031.01301891432189
46217859216751.440641258213062.9166666671.017311900317041.00510981313649
47208679209779.513794354214251.250.9791285408806430.994753950114344
48213188215938.510791470215348.8751.002738049091130.98726252773816
49216234215294.097407791216225.5416666670.9956922560965941.00436566818842
50213586212089.649023151217297.8333333330.9760320467521951.00705527584086
51209465209234.823034291218668.9583333330.9568565407227971.00110008918387
52204045207078.076803463220447.2083333330.9393544983810570.985352979657324
53200237203657.162868265222592.9166666670.9149310136101140.983206272639292
54203666208780.423067329224631.4583333330.9294353721263630.97550333986209
55241476248422.270730072226424.7083333331.09715177534580.972038454082004
56260307257906.722155071227915.4166666671.131589630605231.00930676728731
57243324243062.687525534229352.3751.059778376071031.00107508263455
58244460234821.400882644230825.3751.017311900317041.04104651058688
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60237217234266.264387493233626.5833333331.002738049091131.01259564888791
61235243233896.159469493234908.0833333330.9956922560965941.00575828407598
62230354230111.836758418235762.5833333330.9760320467521951.00105237194658
63227184226023.070386385236214.1666666670.9568565407227971.00513633237364
64221678221965.319151743236295.5833333330.9393544983810570.998705567370432
65217142215901.532134907235975.750.9149310136101141.00574552599431
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68265845264287.048838535233553.7916666671.131589630605231.00589492057334
69248624246384.165428438232486.51.059778376071031.00909082191896
70241114235600.746574278231591.4583333331.017311900317041.02340083172862
71229245226231.239508456231053.6666666670.9791285408806431.01332159297758
72231805231105.341591493230474.2916666671.002738049091131.00302744369164
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74219313222269.866610786227728.0416666670.9760320467521950.98669695242152
75212610216178.611343249225925.8333333330.9568565407227970.98349230147666
76214771210253.251567074223827.3750.9393544983810571.02148717510552
77211142202360.438767101221175.6250.9149310136101141.04339564238149
78211547202914.446622049218320.1250.9294353721263631.04254282295647
79240048236700.346876935215740.751.09715177534581.01414300049508
80240636241380.091347921213310.6251.131589630605230.996917345818513
81230580223053.497738693210471.8333333331.059778376071031.03374303625637
82208795210865.740253978207277.3751.017311900317040.99017981654353
83197922199442.527412097203693.9166666670.9791285408806430.99237611239776
84194596200602.7604109262000551.002738049091130.970056441902287
85194581195822.713032162196669.9166666670.9956922560965940.99365899382694
86185686188865.535822709193503.4166666670.9760320467521950.9831650819253
87178106181713.834817089189907.0833333330.9568565407227970.980145513847523
88172608175126.481497822186432.7916666670.9393544983810570.98561907099211
89167302168026.699428242183649.5833333330.9149310136101140.99568699837164
90168053168572.971416195181371.3750.9294353721263630.996915452033462
91202300196794.011069540179368.0833333331.09715177534581.02797843745618
92202388200784.077602119177435.4166666671.131589630605231.00798829477435
93182516186377.659163138175864.751.059778376071030.97928046107845
94173476177672.082198513174648.5833333331.017311900317040.97638299643596
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97169701170525.574753290171263.3333333330.9956922560965940.995164509754724
98164182165894.174254375169967.9583333330.9760320467521950.989679117653946
99161914161697.831269980168988.5833333330.9568565407227971.00133686845595
100159612158258.766748788168476.0833333330.9393544983810571.00855076327847
101151001154001.760042738168320.6250.9149310136101140.9805147678708
102158114156715.118759185168613.250.9294353721263631.00892626858143
103186530186061.855261737169586.251.09715177534581.00251607046272
104187069193870.819352208171326.0833333331.131589630605230.964915713592508
105174330183982.780820379173604.9583333331.059778376071030.947534324802912
106169362179108.865705727176060.9166666671.017311900317040.945581333077387
107166827175009.4353970061787400.9791285408806430.953245747131037
108178037182245.927411479181748.2916666671.002738049091130.976905232005673
109186413184043.590668185184839.8333333330.9956922560965941.01287417466271
110189226183534.204775337188041.1666666670.9760320467521951.03101217689438
111191563183103.031038129191358.9166666670.9568565407227971.04620332560257
112188906182780.811627880194581.2916666670.9393544983810571.03351111266860
113186005180893.564883269197712.7916666670.9149310136101141.02825658900597
114195309186857.559859668201044.1666666670.9294353721263631.04522931877457
115223532223787.190483716203971.0416666671.09715177534580.998859673410422
116226899233228.826892560206107.251.131589630605230.972860014875107
117214126220088.988518796207674.5416666671.059778376071030.972906465884883
118206903212437.275199989208822.1666666671.017311900317040.973948662282649
119204442205402.360449369209780.7916666670.9791285408806430.99532449165984
120220375210897.119907408210321.251.002738049091131.04494077537310
121214320NA210690.458333333NANA
122212588NA211033.583333333NANA
123205816NA211049NANA
124202196NA210815.416666667NANA
125195722NA210314.583333333NANA
126198563NANANANA
127229139NANANANA
128229527NANANANA
129211868NANANANA
130203555NANANANA
131195770NANANANA
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/184vl1292938296.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/184vl1292938296.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/284vl1292938296.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/284vl1292938296.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/384vl1292938296.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/384vl1292938296.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/40dc61292938296.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929382370ghwtp3w794hwzt/40dc61292938296.ps (open in new window)


 
Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
 
Parameters (R input):
par1 = multiplicative ; 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')
 




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