| | | *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: Sun, 26 Dec 2010 20:54:45 +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/26/t129339677033gntbcoe6eazao.htm/, Retrieved Sun, 26 Dec 2010 21:52:55 +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/26/t129339677033gntbcoe6eazao.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 « | | 6
6
8
4
8
10
9
12
9
11
11
11
11
11
9
8
6
7
8
6
5
2
3
3
7
8
7
7
6
6
7
5
5
5
4
4
4
1
-1
3
4
3
2
1
4
3
5
6
6
6
6
6
5
6
5
6
5
7
4
5
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
2 | | | | Output produced by software: |
| Seasonal Decomposition by Loess - Parameters | | Component | Window | Degree | Jump | | Seasonal | 1311 | 0 | 132 | | Trend | 19 | 1 | 2 | | Low-pass | 13 | 1 | 2 |
| Seasonal Decomposition by Loess - Time Series Components | | t | Observed | Fitted | Seasonal | Trend | Remainder | | 1 | 6 | 5.3203773933325 | 0.787033171394304 | 5.89258943527319 | -0.679622606667494 | | 2 | 6 | 4.97159118934293 | 0.62721519021123 | 6.40119362044584 | -1.02840881065707 | | 3 | 8 | 9.25916973161067 | -0.168967537229158 | 6.90979780561848 | 1.25916973161067 | | 4 | 4 | 0.679209855869273 | -0.0585336279596937 | 7.37932377209042 | -3.32079014413073 | | 5 | 8 | 8.462887837853 | -0.311737576415358 | 7.84884973856236 | 0.462887837852999 | | 6 | 10 | 11.7323731233649 | -0.0118871955187904 | 8.2795140721539 | 1.73237312336490 | | 7 | 9 | 9.6382210634115 | -0.348399469156933 | 8.71017840574543 | 0.638221063411505 | | 8 | 12 | 14.9278488578223 | -0.0484221477745754 | 9.1205732899523 | 2.92784885782227 | | 9 | 9 | 8.7629296466815 | -0.293897820840682 | 9.53096817415919 | -0.237070353318504 | | 10 | 11 | 12.0754381192109 | 0.190998934148415 | 9.7335629466407 | 1.07543811921089 | | 11 | 11 | 12.2061289506423 | -0.142286669764515 | 9.9361577191222 | 1.20612895064231 | | 12 | 11 | 12.4612008872695 | -0.221114980894888 | 9.75991409362541 | 1.46120088726948 | | 13 | 11 | 11.6292963604771 | 0.787033171394304 | 9.58367046812862 | 0.629296360477079 | | 14 | 11 | 12.1812073724796 | 0.62721519021123 | 9.19157743730914 | 1.18120737247963 | | 15 | 9 | 9.3694831307395 | -0.168967537229158 | 8.79948440648967 | 0.369483130739491 | | 16 | 8 | 7.83818162519734 | -0.0585336279596937 | 8.22035200276235 | -0.161818374802660 | | 17 | 6 | 4.67051797738032 | -0.311737576415358 | 7.64121959903504 | -1.32948202261968 | | 18 | 7 | 6.95367905017171 | -0.0118871955187904 | 7.05820814534708 | -0.0463209498282913 | | 19 | 8 | 9.87320277749781 | -0.348399469156933 | 6.47519669165912 | 1.87320277749781 | | 20 | 6 | 5.9123655193109 | -0.0484221477745754 | 6.13605662846367 | -0.0876344806890952 | | 21 | 5 | 4.49698125557246 | -0.293897820840682 | 5.79691656526822 | -0.503018744427536 | | 22 | 2 | -1.87266546519159 | 0.190998934148415 | 5.68166653104318 | -3.87266546519159 | | 23 | 3 | 0.57587017294638 | -0.142286669764515 | 5.56641649681814 | -2.42412982705362 | | 24 | 3 | 0.658578748793659 | -0.221114980894888 | 5.56253623210123 | -2.34142125120634 | | 25 | 7 | 7.65431086122137 | 0.787033171394304 | 5.55865596738432 | 0.654310861221373 | | 26 | 8 | 9.74191055895315 | 0.62721519021123 | 5.63087425083562 | 1.74191055895315 | | 27 | 7 | 8.46587500294224 | -0.168967537229158 | 5.70309253428692 | 1.46587500294224 | | 28 | 7 | 8.25809326485338 | -0.0585336279596937 | 5.80044036310632 | 1.25809326485338 | | 29 | 6 | 6.41394938448964 | -0.311737576415358 | 5.89778819192572 | 0.41394938448964 | | 30 | 6 | 6.21860969585519 | -0.0118871955187904 | 5.7932774996636 | 0.218609695855195 | | 31 | 7 | 8.65963266175546 | -0.348399469156933 | 5.68876680740147 | 1.65963266175546 | | 32 | 5 | 4.76250798747698 | -0.0484221477745754 | 5.2859141602976 | -0.237492012523020 | | 33 | 5 | 5.41083630764696 | -0.293897820840682 | 4.88306151319372 | 0.410836307646964 | | 34 | 5 | 5.36263290574962 | 0.190998934148415 | 4.44636816010196 | 0.362632905749623 | | 35 | 4 | 4.13261186275431 | -0.142286669764515 | 4.00967480701020 | 0.132611862754310 | | 36 | 4 | 4.55521203934419 | -0.221114980894888 | 3.66590294155070 | 0.555212039344192 | | 37 | 4 | 3.89083575251451 | 0.787033171394304 | 3.32213107609119 | -0.109164247485491 | | 38 | 1 | -1.70068752837947 | 0.62721519021123 | 3.07347233816824 | -2.70068752837947 | | 39 | -1 | -4.65584606301614 | -0.168967537229158 | 2.82481360024529 | -3.65584606301614 | | 40 | 3 | 3.30472629673109 | -0.0585336279596937 | 2.7538073312286 | 0.304726296731094 | | 41 | 4 | 5.62893651420345 | -0.311737576415358 | 2.68280106221190 | 1.62893651420345 | | 42 | 3 | 3.15283437420992 | -0.0118871955187904 | 2.85905282130887 | 0.152834374209924 | | 43 | 2 | 1.31309488875110 | -0.348399469156933 | 3.03530458040583 | -0.686905111248896 | | 44 | 1 | -1.32677038601085 | -0.0484221477745754 | 3.37519253378542 | -2.32677038601085 | | 45 | 4 | 4.57881733367567 | -0.293897820840682 | 3.71508048716501 | 0.57881733367567 | | 46 | 3 | 1.76660427501527 | 0.190998934148415 | 4.04239679083631 | -1.23339572498473 | | 47 | 5 | 5.7725735752569 | -0.142286669764515 | 4.36971309450761 | 0.772573575256904 | | 48 | 6 | 7.5778430607591 | -0.221114980894888 | 4.64327192013579 | 1.57784306075909 | | 49 | 6 | 6.29613608284172 | 0.787033171394304 | 4.91683074576398 | 0.29613608284172 | | 50 | 6 | 6.20964488956545 | 0.62721519021123 | 5.16313992022332 | 0.209644889565453 | | 51 | 6 | 6.7595184425465 | -0.168967537229158 | 5.40944909468266 | 0.7595184425465 | | 52 | 6 | 6.53387606775289 | -0.0585336279596937 | 5.5246575602068 | 0.533876067752887 | | 53 | 5 | 4.6718715506844 | -0.311737576415358 | 5.63986602573096 | -0.328128449315598 | | 54 | 6 | 6.37922525442707 | -0.0118871955187904 | 5.63266194109172 | 0.379225254427070 | | 55 | 5 | 4.72294161270445 | -0.348399469156933 | 5.62545785645248 | -0.277058387295551 | | 56 | 6 | 6.48949103082872 | -0.0484221477745754 | 5.55893111694586 | 0.48949103082872 | | 57 | 5 | 4.80149344340145 | -0.293897820840682 | 5.49240437743923 | -0.198506556598545 | | 58 | 7 | 8.47596959375359 | 0.190998934148415 | 5.333031472098 | 1.47596959375359 | | 59 | 4 | 2.96862810300775 | -0.142286669764515 | 5.17365856675676 | -1.03137189699225 | | 60 | 5 | 5.28743801725568 | -0.221114980894888 | 4.93367696363921 | 0.287438017255681 | | 61 | 6 | 6.51927146808405 | 0.787033171394304 | 4.69369536052165 | 0.519271468084048 | | 62 | 6 | 6.98165989322633 | 0.62721519021123 | 4.39112491656244 | 0.98165989322633 | | 63 | 5 | 6.08041306462593 | -0.168967537229158 | 4.08855447260323 | 1.08041306462593 | | 64 | 3 | 2.21441588640866 | -0.0585336279596937 | 3.84411774155104 | -0.785584113591345 | | 65 | 2 | 0.712056565916512 | -0.311737576415358 | 3.59968101049885 | -1.28794343408349 | | 66 | 3 | 2.50362652219531 | -0.0118871955187904 | 3.50826067332348 | -0.496373477804689 | | 67 | 3 | 2.93155913300882 | -0.348399469156933 | 3.41684033614811 | -0.0684408669911809 | | 68 | 2 | 0.58247061926342 | -0.0484221477745754 | 3.46595152851116 | -1.41752938073658 | | 69 | 0 | -3.22116490003352 | -0.293897820840682 | 3.5150627208742 | -3.22116490003352 | | 70 | 4 | 4.15128681600825 | 0.190998934148415 | 3.65771424984333 | 0.151286816008254 | | 71 | 4 | 4.34192089095205 | -0.142286669764515 | 3.80036577881246 | 0.34192089095205 | | 72 | 5 | 6.21733177139415 | -0.221114980894888 | 4.00378320950074 | 1.21733177139415 | | 73 | 6 | 7.00576618841669 | 0.787033171394304 | 4.207200640189 | 1.00576618841669 | | 74 | 6 | 6.97193017348004 | 0.62721519021123 | 4.40085463630873 | 0.971930173480045 | | 75 | 5 | 5.57445890480071 | -0.168967537229158 | 4.59450863242845 | 0.574458904800712 | | 76 | 5 | 5.33812989599521 | -0.0585336279596937 | 4.72040373196448 | 0.338129895995211 | | 77 | 3 | 1.46543874491484 | -0.311737576415358 | 4.84629883150052 | -1.53456125508516 | | 78 | 5 | 5.15080063825786 | -0.0118871955187904 | 4.86108655726093 | 0.150800638257863 | | 79 | 5 | 5.4725251861356 | -0.348399469156933 | 4.87587428302134 | 0.472525186135597 | | 80 | 5 | 5.19167169001523 | -0.0484221477745754 | 4.85675045775934 | 0.191671690015230 | | 81 | 3 | 1.45627118834333 | -0.293897820840682 | 4.83762663249736 | -1.54372881165667 | | 82 | 6 | 6.97526627956659 | 0.190998934148415 | 4.833734786285 | 0.975266279566588 | | 83 | 6 | 7.31244372969188 | -0.142286669764515 | 4.82984294007264 | 1.31244372969188 | | 84 | 4 | 3.43507239525282 | -0.221114980894888 | 4.78604258564206 | -0.564927604747177 | | 85 | 6 | 6.4707245973942 | 0.787033171394304 | 4.74224223121149 | 0.470724597394206 | | 86 | 5 | 4.78365153842848 | 0.62721519021123 | 4.5891332713603 | -0.216348461571524 | | 87 | 4 | 3.73294322572006 | -0.168967537229158 | 4.4360243115091 | -0.267056774279941 | | 88 | 5 | 5.92073912685493 | -0.0585336279596937 | 4.13779450110476 | 0.920739126854934 | | 89 | 5 | 6.47217288571494 | -0.311737576415358 | 3.83956469070042 | 1.47217288571494 | | 90 | 4 | 4.62261443137574 | -0.0118871955187904 | 3.38927276414305 | 0.622614431375742 | | 91 | 3 | 3.40941863157126 | -0.348399469156933 | 2.93898083758568 | 0.409418631571257 | | 92 | 2 | 1.63800961297636 | -0.0484221477745754 | 2.41041253479822 | -0.361990387023642 | | 93 | 3 | 4.41205358882992 | -0.293897820840682 | 1.88184423201076 | 1.41205358882992 | | 94 | 2 | 2.51837830345609 | 0.190998934148415 | 1.29062276239550 | 0.518378303456086 | | 95 | -1 | -2.55711462301572 | -0.142286669764515 | 0.699401292780238 | -1.55711462301572 | | 96 | 0 | 0.139731634696662 | -0.221114980894888 | 0.0813833461982257 | 0.139731634696662 | | 97 | -2 | -4.25039857101052 | 0.787033171394304 | -0.536634600383787 | -2.25039857101052 | | 98 | 1 | 2.39033138549862 | 0.62721519021123 | -1.01754657570985 | 1.39033138549862 | | 99 | -2 | -2.33257391173494 | -0.168967537229158 | -1.49845855103591 | -0.332573911734936 | | 100 | -2 | -2.08503515215598 | -0.0585336279596937 | -1.85643121988432 | -0.0850351521559838 | | 101 | -2 | -1.47385853485190 | -0.311737576415358 | -2.21440388873274 | 0.526141465148097 | | 102 | -6 | -9.5282449279866 | -0.0118871955187904 | -2.45986787649461 | -3.5282449279866 | | 103 | -4 | -4.94626866658659 | -0.348399469156933 | -2.70533186425648 | -0.946268666586587 | | 104 | -2 | -1.10913900044847 | -0.0484221477745754 | -2.84243885177695 | 0.890860999551529 | | 105 | 0 | 3.27344366013811 | -0.293897820840682 | -2.97954583929743 | 3.27344366013811 | | 106 | -5 | -7.29448259656839 | 0.190998934148415 | -2.89651633758002 | -2.29448259656839 | | 107 | -4 | -5.04422649437286 | -0.142286669764515 | -2.81348683586262 | -1.04422649437286 | | 108 | -5 | -7.2206826225404 | -0.221114980894888 | -2.55820239656472 | -2.22068262254040 | | 109 | -1 | -0.484115214127492 | 0.787033171394304 | -2.30291795726681 | 0.515884785872508 | | 110 | -2 | -2.65579234788854 | 0.62721519021123 | -1.97142284232268 | -0.655792347888545 | | 111 | -4 | -6.19110473539228 | -0.168967537229158 | -1.63992772737856 | -2.19110473539228 | | 112 | -1 | -0.754141021805861 | -0.0585336279596937 | -1.18732535023445 | 0.245858978194139 | | 113 | 1 | 3.04646054950569 | -0.311737576415358 | -0.734722973090333 | 2.04646054950569 | | 114 | 1 | 2.28944779257329 | -0.0118871955187904 | -0.277560597054501 | 1.28944779257329 | | 115 | -2 | -3.8312023098244 | -0.348399469156933 | 0.179601778981332 | -1.8312023098244 | | 116 | 1 | 1.56937560537044 | -0.0484221477745754 | 0.47904654240414 | 0.569375605370436 | | 117 | 1 | 1.51540651501373 | -0.293897820840682 | 0.778491305826948 | 0.515406515013735 | | 118 | 3 | 4.87895549602602 | 0.190998934148415 | 0.930045569825564 | 1.87895549602602 | | 119 | 3 | 5.06068683594033 | -0.142286669764515 | 1.08159983382418 | 2.06068683594033 | | 120 | 1 | 1.11183656491032 | -0.221114980894888 | 1.10927841598457 | 0.111836564910319 | | 121 | 1 | 0.0760098304607387 | 0.787033171394304 | 1.13695699814496 | -0.923990169539261 | | 122 | 0 | -1.7603366331818 | 0.62721519021123 | 1.13312144297057 | -1.7603366331818 | | 123 | 2 | 3.03968164943298 | -0.168967537229158 | 1.12928588779618 | 1.03968164943298 | | 124 | 2 | 2.88683379696071 | -0.0585336279596937 | 1.17169983099898 | 0.886833796960713 | | 125 | -1 | -2.90237619778642 | -0.311737576415358 | 1.21411377420178 | -1.90237619778642 | | 126 | 1 | 0.752080378101334 | -0.0118871955187904 | 1.25980681741746 | -0.247919621898666 | | 127 | 0 | -0.9571003914762 | -0.348399469156933 | 1.30549986063313 | -0.9571003914762 | | 128 | 1 | 0.689055714269325 | -0.0484221477745754 | 1.35936643350525 | -0.310944285730675 | | 129 | 1 | 0.880664814463312 | -0.293897820840682 | 1.41323300637737 | -0.119335185536688 | | 130 | 3 | 4.32487694557783 | 0.190998934148415 | 1.48412412027375 | 1.32487694557783 | | 131 | 2 | 2.58727143559438 | -0.142286669764515 | 1.55501523417013 | 0.58727143559438 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/1tqf61293396881.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/1tqf61293396881.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/2tqf61293396881.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/2tqf61293396881.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/34hwr1293396881.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/34hwr1293396881.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/4w9wc1293396881.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t129339677033gntbcoe6eazao/4w9wc1293396881.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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