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: Thu, 16 Dec 2010 15:47:36 +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/16/t1292514372t8o1qzv9aud9lod.htm/, Retrieved Thu, 16 Dec 2010 16:46:13 +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/16/t1292514372t8o1qzv9aud9lod.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 «

15561600 14917500 14805920 16958000 17605000 17131200 18474600 17286700 18574400 18056000 19701600 19061700 19681900 34521200 19922700 20177900 19759900 23076700 22532000 22029400 22587000 23256600 22680300 21916400 19640200 18813100 18730000 18154700 17848800 18077500 17133100 16602600 15878900 15789100 15422000 14661400 15879200 14339300 13169600 14528900 13375800 12309900 11933900 10061900 12609600 11156500 12187200 11284300 10177000 10970720 10820680 11492390 14573750 13992820 14727070 15685360 16736210 17950180 17002730 17415160 17929810 17865790 19202360 19085000 18188880 18466410 18520400 20025500 20636100 20672000 22589100 21864800 22750100 22548746 21325495 21556563 21415269 20401054 19062253 19085706 19279967 18552045 17800733 17142490 17593173 17633859 17336613 17008347 17951965 14520929 16941217 15436824 14744261 14248004 11540953 12881661 15185757 13554339 13575106 12238400 13303614 14151478 1417 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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Classical Decomposition by Moving Averages t Observations Fit Trend Seasonal Random 1 15561600 NA NA 0.900288132417252 NA 2 14917500 NA NA 0.863765434895422 NA 3 14805920 NA NA 0.907841152495603 NA 4 16958000 NA NA 0.965843848011875 NA 5 17605000 NA NA 1.02986775797667 NA 6 17131200 NA NA 1.10379595379534 NA 7 18474600 NA NA 1.04416963049344 NA 8 17286700 NA NA 1.06729684004503 NA 9 18574400 NA NA 1.09645404680177 NA 10 18056000 NA NA 1.08985937772229 NA 11 19701600 NA NA 1.16842145088156 NA 12 19061700 NA NA 1.15977935690514 NA 13 19681900 NA NA 1.10282328990127 NA 14 34521200 NA NA 1.1166612212153 NA 15 19922700 NA NA 1.1184734102911 NA 16 20177900 NA NA 1.2070943792417 NA 17 19759900 NA NA 1.2428079398952 NA 18 23076700 NA NA 1.24325565288817 NA 19 22532000 NA NA 1.35440701915374 NA 20 22029400 NA NA 1.30730071355346 NA 21 22587000 NA NA 1.35733431410796 NA 22 23256600 NA NA 1.3435497453056 NA 23 22680300 NA NA 1.26775501927876 NA 24 21916400 NA NA 1.27697403913775 NA 25 19640200 NA NA 1.26398949541412 NA 26 18813100 NA NA 1.2001969497807 NA 27 18730000 19088645.9165184 16977511.25 1.12434888927071 0.981211558007471 28 18154700 18502329.9530495 16959121.5384615 1.09099577540547 0.981211558007472 29 17848800 18190572.5165379 16949472.2115385 1.07322353696385 0.981211558007472 30 18077500 18423651.7114715 16936477.1153846 1.08780896912357 0.981211558007471 31 17133100 17461168.1448106 16915886.4423077 1.03223488785897 0.981211558007472 32 16602600 16920510.0210138 16915407.5 1.00030164931077 0.981211558007472 33 15878900 16182952.4636308 16909129.7115385 0.95705413227671 0.981211558007472 34 15789100 16091432.954645 16896212.3076923 0.95236924475192 0.981211558007472 35 15422000 15717303.6478669 16891249.5192308 0.93049976142811 0.981211558007472 36 14661400 14942139.5216467 16883222.5961538 0.885028876243727 0.981211558007472 37 15879200 16183258.2080929 16876593.2692308 0.95891735671547 0.981211558007472 38 14339300 14613871.8841822 16872016.9230769 0.866160338198445 0.981211558007472 39 13169600 13421774.2264912 16857885 0.796171893834324 0.981211558007472 40 14528900 14807102.3842234 16689156.0576923 0.887228948727972 0.981211558007472 41 13375800 13631922.5867681 16521299.4230769 0.825112010725203 0.981211558007472 42 12309900 12545612.5129605 16506350.3846154 0.76004763140455 0.981211558007472 43 11933900 12162412.7871404 16513310 0.736521798908903 0.981211558007472 44 10061900 10254567.3436955 16498612.8846154 0.621541181395781 0.981211558007471 45 12609600 12851051.2305889 16476039.8076923 0.779984230469573 0.981211558007472 46 11156500 11370126.9710431 16475006.1538462 0.690144019666343 0.981211558007472 47 12187200 12420563.0279655 16474991.7307692 0.753904052332143 0.981211558007472 48 11284300 11500374.1118937 16469753.7115385 0.698272379376062 0.981211558007471 49 10177000 10371871.3023176 16449920.4519231 0.630511942755628 0.981211558007472 50 10970720 11180789.6171525 16433433.5096154 0.680368445864373 0.981211558007472 51 10820680 11027876.620179 16447041.5096154 0.670508225672793 0.981211558007472 52 11492390 11712448.6622817 16479378.2692308 0.710733649712409 0.981211558007471 53 14573750 14852811.1813059 16497841.7980769 0.900288132417252 0.981211558007472 54 13992820 14260757.4134318 16509988.5192308 0.863765434895422 0.981211558007472 55 14727070 15009066.9843983 16532701.7211538 0.907841152495603 0.981211558007472 56 15685360 15985706.5196541 16551025.875 0.965843848011875 0.981211558007472 57 16736210 17056678.4129469 16562008.3557692 1.02986775797667 0.981211558007471 58 17950180 18293893.7617603 16573619.1538462 1.10379595379534 0.981211558007471 59 17002730 17328301.7930681 16595293.7980769 1.04416963049344 0.981211558007471 60 17415160 17748629.0880681 16629515.2596154 1.06729684004503 0.981211558007471 61 17929810 18273133.7127844 16665663.0673077 1.09645404680177 0.981211558007472 62 17865790 18207887.8445742 16706639.6057692 1.08985937772229 0.981211558007472 63 19202360 19570050.763562 16749136.8365385 1.16842145088156 0.981211558007472 64 19085000 19450443.5299922 16770813.7019231 1.15977935690514 0.981211558007472 65 18188880 18537164.4387637 16808825.6826923 1.10282328990127 0.981211558007472 66 18466410 18820008.6406436 16853821.2692308 1.1166612212153 0.981211558007471 67 18520400 18875032.4523378 16875709.5865385 1.1184734102911 0.981211558007471 68 20025500 20408952.418646 16907503.4807692 1.2070943792417 0.981211558007472 69 20636100 21031244.3138209 16922360.7596154 1.2428079398952 0.981211558007472 70 20672000 21067831.7344511 16945695.5096154 1.24325565288817 0.981211558007472 71 22589100 23021640.7620302 16997579.3365385 1.35440701915374 0.981211558007472 72 21864800 22283471.715723 17045406.2211538 1.30730071355346 0.981211558007472 73 22750100 23185723.6233521 17081807.6153846 1.35733431410796 0.981211558007472 74 22548746 22980514.0552862 17104326.9038462 1.3435497453056 0.981211558007472 75 21325495 21733839.9919639 17143564.5384615 1.26775501927876 0.981211558007471 76 21556563 21969332.5298517 17204212.3461538 1.27697403913775 0.981211558007472 77 21415269 21825333.0030963 17267020.875 1.26398949541412 0.981211558007472 78 20401054 20791697.6043658 17323571.4423077 1.2001969497807 0.981211558007471 79 19062253 NA NA 1.12434888927071 NA 80 19085706 NA NA 1.09099577540547 NA 81 19279967 NA NA 1.07322353696385 NA 82 18552045 NA NA 1.08780896912357 NA 83 17800733 NA NA 1.03223488785897 NA 84 17142490 NA NA 1.00030164931077 NA 85 17593173 NA NA 0.95705413227671 NA 86 17633859 NA NA 0.95236924475192 NA 87 17336613 NA NA 0.93049976142811 NA 88 17008347 NA NA 0.885028876243727 NA 89 17951965 NA NA 0.95891735671547 NA 90 14520929 NA NA 0.866160338198445 NA 91 16941217 NA NA 0.796171893834324 NA 92 15436824 NA NA 0.887228948727972 NA 93 14744261 NA NA 0.825112010725203 NA 94 14248004 NA NA 0.76004763140455 NA 95 11540953 NA NA 0.736521798908903 NA 96 12881661 NA NA 0.621541181395781 NA 97 15185757 NA NA 0.779984230469573 NA 98 13554339 NA NA 0.690144019666343 NA 99 13575106 NA NA 0.753904052332143 NA 100 12238400 NA NA 0.698272379376062 NA 101 13303614 NA NA 0.630511942755628 NA 102 14151478 NA NA 0.680368445864373 NA 103 14172009 NA NA 0.670508225672793 NA 104 14022320 NA NA 0.710733649712409 NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/111fc1292514452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/111fc1292514452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/2usfx1292514452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/2usfx1292514452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/3usfx1292514452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/3usfx1292514452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/4mkei1292514452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292514372t8o1qzv9aud9lod/4mkei1292514452.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 1 ;

Parameters (R input):

par1 = multiplicative ; par2 = 4 ;

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

par2 = 52 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')

Copyright

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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