Paper

*The author of this computation has been verified*

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

Title produced by software: Decomposition by Loess

Date of computation: Tue, 28 Dec 2010 19:23:24 +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/28/t1293564106f0hj7ezoj41fcln.htm/, Retrieved Tue, 28 Dec 2010 20:21:47 +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/28/t1293564106f0hj7ezoj41fcln.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:

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961 935 956 951 986 980 1031 1059 1036 1023 1030 1075 1151 1220 1290 1330 1419 1443 1516 1546 1579 1591 1603 1606 1616 1628 1594 1596 1526 1535 1581 1611 1571 1535 1498 1493 1480 1448 1462 1428 1315 1186 1230 1271 1243 1220 1214 1227 1262 1274 1272 1249 1266 1307 1345 1369 1374 1400 1425 1465 1510 1508 1512 1539 1569 1571 1650 1736 1700 1731 1752

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 Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 711 0 72 Trend 19 1 2 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 961 993.563096169051 10.146251441526 918.290652389423 32.5630961690513 2 935 931.62797872193 3.9310079154315 934.441013362638 -3.37202127806961 3 956 957.026209883083 4.38241578106375 950.591374335854 1.02620988308274 4 951 939.42566243381 -5.03494916108284 967.609286727273 -11.5743375661901 5 986 1004.99182176169 -17.6190208803822 984.627199118693 18.9918217616896 6 980 994.568313682935 -37.3926362951399 1002.8243226122 14.5683136829349 7 1031 1033.14479373586 7.83376015842168 1021.02144610572 2.14479373586107 8 1059 1039.86370334354 37.5764665500332 1040.55983010643 -19.1362966564618 9 1036 999.249263518768 12.6525223740924 1060.09821410714 -36.750736481232 10 1023 959.120312920057 0.174587862703851 1086.70509921724 -63.8796870799433 11 1030 954.82469494038 -8.13667926772009 1113.31198432734 -75.1753050596192 12 1075 1006.57162279473 -8.51371840574718 1151.94209561101 -68.4283772052663 13 1151 1101.28154166379 10.146251441526 1190.57220689469 -49.7184583362136 14 1220 1200.2804968716 3.9310079154315 1235.78849521297 -19.7195031284032 15 1290 1294.61280068768 4.38241578106375 1281.00478353126 4.61280068768087 16 1330 1336.27269511379 -5.03494916108284 1328.76225404729 6.27269511379359 17 1419 1479.09929631706 -17.6190208803822 1376.51972456332 60.099296317059 18 1443 1503.497298035 -37.3926362951399 1419.89533826014 60.4972980349987 19 1516 1560.89528788462 7.83376015842168 1463.27095195696 44.8952878846187 20 1546 1558.60714298897 37.5764665500332 1495.816390461 12.6071429889685 21 1579 1616.98564866087 12.6525223740924 1528.36182896504 37.985648660871 22 1591 1634.1960225333 0.174587862703851 1547.629389604 43.1960225332959 23 1603 1647.23972902476 -8.13667926772009 1566.89695024296 44.2397290247566 24 1606 1645.07549137118 -8.51371840574718 1575.43822703457 39.0754913711762 25 1616 1637.8742447323 10.146251441526 1583.97950382618 21.8742447322957 26 1628 1666.44583059988 3.9310079154315 1585.62316148469 38.4458305998769 27 1594 1596.35076507573 4.38241578106375 1587.2668191432 2.35076507573126 28 1596 1614.26133892942 -5.03494916108284 1582.77361023167 18.2613389294156 29 1526 1491.33861956025 -17.6190208803822 1578.28040132013 -34.6613804397473 30 1535 1538.51841233463 -37.3926362951399 1568.87422396051 3.51841233463324 31 1581 1594.69819324069 7.83376015842168 1559.46804660088 13.6981932406945 32 1611 1637.01941742519 37.5764665500332 1547.40411602478 26.0194174251865 33 1571 1594.00729217723 12.6525223740924 1535.34018544868 23.0072921772307 34 1535 1550.35366275221 0.174587862703851 1519.47174938508 15.3536627522114 35 1498 1500.53336594623 -8.13667926772009 1503.60331332149 2.53336594622783 36 1493 1514.43786986119 -8.51371840574718 1480.07584854456 21.4378698611856 37 1480 1493.30536479084 10.146251441526 1456.54838376763 13.3053647908434 38 1448 1464.16953696276 3.9310079154315 1427.8994551218 16.1695369627637 39 1462 1520.36705774296 4.38241578106375 1399.25052647598 58.3670577429573 40 1428 1489.52735159265 -5.03494916108284 1371.50759756843 61.5273515926528 41 1315 1303.8543522195 -17.6190208803822 1343.76466866088 -11.1456477804986 42 1186 1088.98831148918 -37.3926362951399 1320.40432480596 -97.011688510817 43 1230 1155.12225889055 7.83376015842168 1297.04398095103 -74.877741109455 44 1271 1224.30370083936 37.5764665500332 1280.11983261061 -46.6962991606399 45 1243 1210.15179335573 12.6525223740924 1263.19568427018 -32.8482066442723 46 1220 1184.07104987085 0.174587862703851 1255.75436226645 -35.9289501291496 47 1214 1187.82363900501 -8.13667926772009 1248.31304026271 -26.1763609949912 48 1227 1210.33509690024 -8.51371840574718 1252.1786215055 -16.6649030997564 49 1262 1257.80954581018 10.146251441526 1256.0442027483 -4.19045418982182 50 1274 1277.73478193414 3.9310079154315 1266.33421015043 3.73478193414303 51 1272 1262.99336666638 4.38241578106375 1276.62421755256 -9.006633333619 52 1249 1212.09746785192 -5.03494916108284 1290.93748130916 -36.9025321480822 53 1266 1244.36827581461 -17.6190208803822 1305.25074506577 -21.6317241853928 54 1307 1327.67132325972 -37.3926362951399 1323.72131303542 20.6713232597181 55 1345 1339.97435883651 7.83376015842168 1342.19188100507 -5.02564116349049 56 1369 1337.0933118965 37.5764665500332 1363.33022155347 -31.9066881035021 57 1374 1350.87891552404 12.6525223740924 1384.46856210187 -23.1210844759612 58 1400 1392.32427766019 0.174587862703851 1407.5011344771 -7.67572233980786 59 1425 1427.60297241538 -8.13667926772009 1430.53370685234 2.60297241538115 60 1465 1483.10095158686 -8.51371840574718 1455.41276681889 18.1009515868559 61 1510 1529.56192177303 10.146251441526 1480.29182678544 19.5619217730309 62 1508 1504.73341156624 3.9310079154315 1507.33558051833 -3.2665884337589 63 1512 1485.23824996772 4.38241578106375 1534.37933425121 -26.7617500322754 64 1539 1521.17014681437 -5.03494916108284 1561.86480234671 -17.8298531856256 65 1569 1566.26875043818 -17.6190208803822 1589.35027044221 -2.73124956182301 66 1571 1562.60185362193 -37.3926362951399 1616.79078267321 -8.39814637807308 67 1650 1647.93494493736 7.83376015842168 1644.23129490422 -2.06505506264284 68 1736 1762.59184832044 37.5764665500332 1671.83168512953 26.5918483204396 69 1700 1687.91540227107 12.6525223740924 1699.43207535483 -12.0845977289257 70 1731 1734.59825582557 0.174587862703851 1727.22715631173 3.59825582556527 71 1752 1757.11444199909 -8.13667926772009 1755.02223726863 5.11444199909192

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/1gj0h1293564200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/1gj0h1293564200.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/2rbzk1293564200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/2rbzk1293564200.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/3rbzk1293564200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/3rbzk1293564200.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/422y51293564200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564106f0hj7ezoj41fcln/422y51293564200.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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

par1 <- as.numeric(par1) #seasonal period if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window par3 <- as.numeric(par3) #s.degree if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window par5 <- as.numeric(par5)#t.degree if (par6 != '') par6 <- as.numeric(par6)#l.window par7 <- as.numeric(par7)#l.degree if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust nx <- length(x) x <- ts(x,frequency=par1) if (par6 != '') { m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8) } else { m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8) } m$time.series m$win m$deg m$jump m$inner m$outer bitmap(file='test1.png') plot(m,main=main) dev.off() mylagmax <- nx/2 bitmap(file='test2.png') op <- par(mfrow = c(2,2)) acf(as.numeric(x),lag.max = mylagmax,main='Observed') acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend') acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal') acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder') par(op) dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) spectrum(as.numeric(x),main='Observed') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal') spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder') par(op) dev.off() bitmap(file='test4.png') op <- par(mfrow = c(2,2)) cpgram(as.numeric(x),main='Observed') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal') cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder') par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Component',header=TRUE) a<-table.element(a,'Window',header=TRUE) a<-table.element(a,'Degree',header=TRUE) a<-table.element(a,'Jump',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Seasonal',header=TRUE) a<-table.element(a,m$win['s']) a<-table.element(a,m$deg['s']) a<-table.element(a,m$jump['s']) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Trend',header=TRUE) a<-table.element(a,m$win['t']) a<-table.element(a,m$deg['t']) a<-table.element(a,m$jump['t']) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Low-pass',header=TRUE) a<-table.element(a,m$win['l']) a<-table.element(a,m$deg['l']) a<-table.element(a,m$jump['l']) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Seasonal Decomposition by Loess - Time Series Components',6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Seasonal',header=TRUE) a<-table.element(a,'Trend',header=TRUE) a<-table.element(a,'Remainder',header=TRUE) a<-table.row.end(a) for (i in 1:nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]+m$time.series[i,'remainder']) a<-table.element(a,m$time.series[i,'seasonal']) a<-table.element(a,m$time.series[i,'trend']) a<-table.element(a,m$time.series[i,'remainder']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')

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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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