Classical Decomp of Time Series By Moving Averages : BRU Passengers

*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: Fri, 17 Dec 2010 15:38:24 +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/17/t1292600201y2i7du2lttagquk.htm/, Retrieved Fri, 17 Dec 2010 16:36:42 +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/17/t1292600201y2i7du2lttagquk.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 «

989236 1008380 1207763 1368839 1469798 1498721 1761769 1653214 1599104 1421179 1163995 1037735 1015407 1039210 1258049 1469445 1552346 1549144 1785895 1662335 1629440 1467430 1202209 1076982 1039367 1063449 1335135 1491602 1591972 1641248 1898849 1798580 1762444 1622044 1368955 1262973 1195650 1269530 1479279 1607819 1712466 1721766 1949843 1821326 1757802 1590367 1260647 1149235 1016367 1027885 1262159 1520854 1544144 1564709 1821776 1741365 1623386 1498658 1241822 1136029

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Classical Decomposition by Moving Averages t Observations Fit Trend Seasonal Random 1 989236 NA NA 0.733744074532938 NA 2 1008380 NA NA 0.755235166348185 NA 3 1207763 NA NA 0.915662813815028 NA 4 1368839 NA NA 1.04597623431699 NA 5 1469798 NA NA 1.09772359962096 NA 6 1498721 NA NA 1.10914781047047 NA 7 1761769 1349402.82282745 1349401.54166667 1.28116078359081 1.01907025513798 8 1653214 1351777.78401665 1351776.58333333 1.20068331985177 1.01858125150116 9 1599104 1355157.58430571 1355156.41666667 1.16763904526397 1.01059855901928 10 1421179 1361444.63671823 1361443.58333333 1.05338490037458 0.990973505518608 11 1163995 1369075.86087193 1369075 0.860871927897658 0.987609658442794 12 1037735 1374616.23710366 1374615.45833333 0.778770323916639 0.969384000015323 13 1015407 1377722.40041074 1377721.66666667 0.733744074532938 1.00446326298971 14 1039210 1379107.7135685 1379106.95833333 0.755235166348185 0.997753278359556 15 1258049 1380751.91566281 1380751 0.915662813815028 0.995053915814916 16 1469445 1383943.17097623 1383942.125 1.04597623431699 1.01511113032871 17 1552346 1387462.5977236 1387461.5 1.09772359962096 1.01923560136255 18 1549144 1390690.15081448 1390689.04166667 1.10914781047047 1.00432050701601 19 1785895 1393323.94782745 1393322.66666667 1.28116078359081 1.00046196530806 20 1662335 1395332.15901665 1395330.95833333 1.20068331985177 0.992231114319257 21 1629440 1399554.00097238 1399552.83333333 1.16763904526397 0.997104018081911 22 1467430 1403689.01171823 1403687.95833333 1.05338490037458 0.992429649176563 23 1202209 1406263.11087193 1406262.25 0.860871927897658 0.993059133389468 24 1076982 1411751.77877032 1411751 0.778770323916639 0.97958233995903 25 1039367 1420295.81707741 1420295.08333333 0.733744074532938 0.99734573109696 26 1063449 1430679.13023517 1430678.375 0.755235166348185 0.984220599443754 27 1335135 1441897.99899615 1441897.08333333 0.915662813815028 1.01124256195496 28 1491602 1453882.2126429 1453881.16666667 1.04597623431699 0.98084917061082 29 1591972 1467272.26439027 1467271.16666667 1.09772359962096 0.988398415723614 30 1641248 1481969.65081448 1481968.54166667 1.10914781047047 0.998494780181753 31 1898849 1496231.23949412 1496229.95833333 1.28116078359081 0.990577473614528 32 1798580 1511329.65901665 1511328.45833333 1.20068331985177 0.991156930938869 33 1762444 1525922.33430571 1525921.16666667 1.16763904526397 0.989178390187852 34 1622044 1536770.59505157 1536769.54166667 1.05338490037458 1.00199786867595 35 1368955 1546633.36087193 1546632.5 0.860871927897658 1.02816660595764 36 1262973 1555008.77877032 1555008 0.778770323916639 1.0429225186482 37 1195650 1560488.40041074 1560487.66666667 0.733744074532938 1.04423710399253 38 1269530 1563560.92190183 1563560.16666667 0.755235166348185 1.07509332702272 39 1479279 1564315.41566281 1564314.5 0.915662813815028 1.03273868114025 40 1607819 1562802.25430957 1562801.20833333 1.04597623431699 0.983584330041577 41 1712466 1556969.5977236 1556968.5 1.09772359962096 1.00195710751537 42 1721766 1547717.69248114 1547716.58333333 1.10914781047047 1.00298229162928 43 1949843 1535508.65616078 1535507.375 1.28116078359081 0.991160761287156 44 1821326 1517969.90901665 1517968.70833333 1.20068331985177 0.999301158588433 45 1757802 1498854.66763905 1498853.5 1.16763904526397 1.00438948805868 46 1590367 1486184.34505157 1486183.29166667 1.05338490037458 1.0158694319766 47 1260647 1475547.19420526 1475546.33333333 0.860871927897658 0.99243505755782 48 1149235 1461989.65377032 1461988.875 0.778770323916639 1.00938159672517 49 1016367 1450109.44207741 1450108.70833333 0.733744074532938 0.955224357268524 50 1027885 1441441.63023517 1441440.875 0.755235166348185 0.944203250521692 51 1262159 1432509.41566281 1432508.5 0.915662813815028 0.962235296437596 52 1520854 1423087.67097623 1423086.625 1.04597623431699 1.02172582436661 53 1544144 1418482.13939027 1418481.04166667 1.09772359962096 0.991679330746192 54 1564709 1417147.52581448 1417146.41666667 1.10914781047047 0.99547287652068 55 1821776 NA NA 1.28116078359081 NA 56 1741365 NA NA 1.20068331985177 NA 57 1623386 NA NA 1.16763904526397 NA 58 1498658 NA NA 1.05338490037458 NA 59 1241822 NA NA 0.860871927897658 NA 60 1136029 NA NA 0.778770323916639 NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/10kzt1292600300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/10kzt1292600300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/20kzt1292600300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/20kzt1292600300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/3sbye1292600300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/3sbye1292600300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/4sbye1292600300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292600201y2i7du2lttagquk/4sbye1292600300.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$trend)) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,m$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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