| | | *The author of this computation has been verified* | | R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values) | | Title produced by software: Structural Time Series Models | | Date of computation: Fri, 24 Dec 2010 11:10:31 +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/24/t1293188893qoxsjx76i8i2w2u.htm/, Retrieved Fri, 24 Dec 2010 12:08:13 +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/24/t1293188893qoxsjx76i8i2w2u.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 « | | 6.4
7.7
9.2
8.6
7.4
8.6
6.2
6
6.6
5.1
4.7
5
3.6
1.9
-0.1
-5.7
-5.6
-6.4
-7.7
-8
-11.9
-15.4
-15.5
-13.4
-10.9
-10.8
-7.3
-6.5
-5.1
-5.3
-6.8
-8.4
-8.4
-9.7
-8.8
-9.6
-11.5
-11
-14.9
-16.2
-14.4
-17.3
-15.7
-12.6
-9.4
-8.1
-5.4
-4.6
-4.9
-4
-3.1
-1.3
0
-0.4
3
0.4
1.2
0.6
-1.3
-3.2
-1.8
-3.6
-4.2
-6.9
-8
-7.5
-8.2
-7.6
-3.7
-1.7
-0.7
0.2
0.6
2.2
3.3
5.3
5.5
6.3
7.7
6.5
5.5
6.9
5.7
6.9
6.1
4.8
3.7
5.8
6.8
8.5
7.2
5
4.7
2.3
2.4
0.1
1.9
1.7
2
-1.9
0.5
-1.3
-3.3
-2.8
-8
-13.9
-21.9
-28.8
-27.6
-31.4
-31.8
-29.4
-27.6
-23.6
-22.8
-18.2
-17.8
-14.2
-8.8
-7.9
-7
-7
-3.6
-2.4
-4.9
-7.7
-6.5
-5.1
-3.4
-2.8
0.8 | | | | Output produced by software: |
| Structural Time Series Model | | t | Observed | Level | Slope | Seasonal | Stand. Residuals | | 1 | 6.4 | 6.4 | 0 | 0 | 0 | | 2 | 7.7 | 7.60380275726153 | 0.188796934020855 | 0.0604662721890126 | 0.466507988564282 | | 3 | 9.2 | 9.07312203221113 | 0.662406615863685 | 0.0561872798148749 | 0.667912037000793 | | 4 | 8.6 | 8.59632043777291 | 0.193158021104694 | 0.0613129984471699 | -0.567268451881281 | | 5 | 7.4 | 7.40350209897595 | -0.394641487846067 | 0.065088302310559 | -0.682808893518477 | | 6 | 8.6 | 8.46547351097807 | 0.228867476765928 | 0.0628637481529474 | 0.715807502377138 | | 7 | 6.2 | 6.2549116996384 | -0.818608545794043 | 0.0649266987924918 | -1.19824534535687 | | 8 | 6 | 5.91193627672651 | -0.614145308883627 | 0.064704503489117 | 0.233638492231172 | | 9 | 6.6 | 6.4776540500291 | -0.106729542556945 | 0.0644001998515175 | 0.579627784896738 | | 10 | 5.1 | 5.09794107320545 | -0.654293973707885 | 0.0645814307154015 | -0.625427000041763 | | 11 | 4.7 | 4.62645397989651 | -0.575654275133032 | 0.0645670657666765 | 0.0898193447160561 | | 12 | 5 | 4.894050215296 | -0.212890439243395 | 0.0645304932017087 | 0.41433150710664 | | 13 | 3.6 | 4.41941638597563 | -0.321731944507249 | -0.806996822707501 | -0.146992399363553 | | 14 | 1.9 | 1.94423572821245 | -1.16695000592684 | 0.0252698381774235 | -0.859979170687236 | | 15 | -0.1 | -0.0842640279499554 | -1.53870162797755 | 0.0264650527868505 | -0.422438482659356 | | 16 | -5.7 | -5.54233803705323 | -3.22735552338509 | 0.0339688449372715 | -1.91944138627479 | | 17 | -5.6 | -5.77719360453071 | -1.93996450343460 | 0.0305148566060218 | 1.46797129717789 | | 18 | -6.4 | -6.48994660682633 | -1.41215420673273 | 0.0297227273200824 | 0.602529673355523 | | 19 | -7.7 | -7.73773419040903 | -1.34145863651139 | 0.0296640448916183 | 0.0807321861188502 | | 20 | -8 | -8.0786051773133 | -0.911059861189304 | 0.0294667976624250 | 0.491555539518069 | | 21 | -11.9 | -11.7921291628312 | -2.11660789304596 | 0.0297717431203848 | -1.37689374777000 | | 22 | -15.4 | -15.3586430154831 | -2.74034629560583 | 0.0298588226819208 | -0.712398115841548 | | 23 | -15.5 | -15.6500661745556 | -1.68681223255642 | 0.0297776454177358 | 1.20328967775168 | | 24 | -13.4 | -13.6126428638747 | -0.0846121785294146 | 0.0297095098589694 | 1.82994803291517 | | 25 | -10.9 | -11.1447879855162 | 0.99611928006535 | 0.121425764516836 | 1.34374156542834 | | 26 | -10.8 | -10.7569175628409 | 0.74932618665675 | -0.0198529805423151 | -0.263981665850402 | | 27 | -7.3 | -7.40538703139535 | 1.87099634543777 | -0.0222013877781709 | 1.27687557708577 | | 28 | -6.5 | -6.43482493121306 | 1.48324423571604 | -0.0210785320077307 | -0.441486069015543 | | 29 | -5.1 | -5.0730542582074 | 1.43098513410308 | -0.0209872059809898 | -0.0596236445878037 | | 30 | -5.3 | -5.20304078063969 | 0.759558706338779 | -0.0203309687623448 | -0.766613257124456 | | 31 | -6.8 | -6.67081129725204 | -0.198519468904899 | -0.0198130799609372 | -1.09415555439157 | | 32 | -8.4 | -8.30963366552282 | -0.818095593866202 | -0.0196281757747800 | -0.707625438290224 | | 33 | -8.4 | -8.41531298878417 | -0.511621850147074 | -0.0196786582706016 | 0.350034921944936 | | 34 | -9.7 | -9.64507536418977 | -0.820566533582286 | -0.0196505713794382 | -0.352859384354870 | | 35 | -8.8 | -8.85922137387733 | -0.129471846451820 | -0.0196852476486485 | 0.789331377077581 | | 36 | -9.6 | -9.55262130986432 | -0.372080371855951 | -0.0196785291527574 | -0.277094646228957 | | 37 | -11.5 | -11.4645305222624 | -1.02767283239963 | 0.0393711461505852 | -0.792636157370212 | | 38 | -11 | -11.0700274898158 | -0.441588479291659 | 0.0116737740860523 | 0.639489607250994 | | 39 | -14.9 | -14.7547535956884 | -1.83883417978183 | 0.0138428778402815 | -1.59194703226260 | | 40 | -16.2 | -16.2312655516052 | -1.68284661778230 | 0.0135078481509548 | 0.177747857925857 | | 41 | -14.4 | -14.5754730317516 | -0.246525565999561 | 0.0116465930783660 | 1.63918703337121 | | 42 | -17.3 | -17.1958359423766 | -1.26764394040584 | 0.0123865771590610 | -1.16598052847565 | | 43 | -15.7 | -15.8407370743436 | -0.139432325226527 | 0.0119344109217928 | 1.28848712795872 | | 44 | -12.6 | -12.7693299922675 | 1.24181506114254 | 0.0116287837944068 | 1.57755207633975 | | 45 | -9.4 | -9.51058979842697 | 2.10948880720251 | 0.0115228166440622 | 0.991004475837045 | | 46 | -8.1 | -8.07828000986263 | 1.81816300123435 | 0.0115424533582531 | -0.332736332175885 | | 47 | -5.4 | -5.45126039225042 | 2.16614133926418 | 0.0115295080070992 | 0.397442330178966 | | 48 | -4.6 | -4.54943714757656 | 1.62221511041974 | 0.0115406759396499 | -0.621243858109478 | | 49 | -4.9 | -4.55459618418016 | 0.927487517029764 | -0.266092189475626 | -0.828188779853126 | | 50 | -4 | -4.00484529482508 | 0.770409395452861 | 0.0209746348785859 | -0.173226027416277 | | 51 | -3.1 | -3.12622673071045 | 0.817015632354533 | 0.0209171448859901 | 0.0531274699942224 | | 52 | -1.3 | -1.36645114180379 | 1.22283518530608 | 0.0202244542649359 | 0.462652015815929 | | 53 | 0 | -0.0259475255823856 | 1.27345762981466 | 0.0201723287310314 | 0.0577817943494162 | | 54 | -0.4 | -0.342492828404964 | 0.589489517228566 | 0.0205661624114972 | -0.781039579130078 | | 55 | 3 | 2.85186032028830 | 1.71003800151936 | 0.0202093319359584 | 1.27975514218800 | | 56 | 0.4 | 0.575296522978114 | -0.00495692385774981 | 0.0205108441102944 | -1.95874147957381 | | 57 | 1.2 | 1.15099264622019 | 0.244840324955692 | 0.0204866046257279 | 0.285303719235541 | | 58 | 0.6 | 0.61771612671021 | -0.0899113337150898 | 0.0205045326871962 | -0.382335122732968 | | 59 | -1.3 | -1.23398772886313 | -0.847854807761657 | 0.0205269363545627 | -0.86568279589298 | | 60 | -3.2 | -3.16722049849946 | -1.3147994787559 | 0.0205345539667284 | -0.533319603492941 | | 61 | -1.8 | -1.87838109882391 | -0.201540844111999 | -0.0487142006451782 | 1.31588969490328 | | 62 | -3.6 | -3.53065180587113 | -0.808379388946135 | -0.00580922992567405 | -0.673673904938567 | | 63 | -4.2 | -4.20090852513943 | -0.74890075762594 | -0.00587009471375314 | 0.0678235527845756 | | 64 | -6.9 | -6.8043007852979 | -1.54710687156649 | -0.00473969329204041 | -0.910275862911133 | | 65 | -8 | -8.01180559335525 | -1.40100553141641 | -0.00486449868849522 | 0.166781878100931 | | 66 | -7.5 | -7.58453842785194 | -0.614526156320503 | -0.0052401815511236 | 0.898129607462122 | | 67 | -8.2 | -8.19496089869986 | -0.612760822486348 | -0.0052406478996085 | 0.00201617163498521 | | 68 | -7.6 | -7.65147812230554 | -0.115351409309629 | -0.00531319282561275 | 0.568106331057676 | | 69 | -3.7 | -3.88521266367572 | 1.55453302835629 | -0.0054476155664953 | 1.90724555060352 | | 70 | -1.7 | -1.72432472722433 | 1.81539239647266 | -0.0054592051412537 | 0.297939456533914 | | 71 | -0.7 | -0.65776592410732 | 1.49323486413477 | -0.00545130561555192 | -0.367951261981779 | | 72 | 0.2 | 0.234945706662705 | 1.23488112582282 | -0.00544780923576579 | -0.295078037120003 | | 73 | 0.6 | 0.628706766246988 | 0.874860369536394 | 0.0123957376526022 | -0.423138823595452 | | 74 | 2.2 | 2.16752929938767 | 1.15375051900022 | 0.00287444291452112 | 0.311009825169212 | | 75 | 3.3 | 3.29824739102486 | 1.14383361291613 | 0.00288311403698353 | -0.0113109255236458 | | 76 | 5.3 | 5.25753634487212 | 1.49479623614618 | 0.00245842175312193 | 0.400327640454205 | | 77 | 5.5 | 5.55590112092705 | 0.980074842135397 | 0.00283410273423844 | -0.587624661311565 | | 78 | 6.3 | 6.30830629847808 | 0.882135425986709 | 0.00287407409679779 | -0.111845741912317 | | 79 | 7.7 | 7.67345006824516 | 1.08991959519774 | 0.0028271765300132 | 0.237310113945621 | | 80 | 6.5 | 6.603161273121 | 0.160603150815246 | 0.00294297685934762 | -1.06140274669048 | | 81 | 5.5 | 5.55632935643467 | -0.358841797525406 | 0.00297870238945125 | -0.593280414062778 | | 82 | 6.9 | 6.81747435924532 | 0.338093025128486 | 0.00295224749940295 | 0.796001409494349 | | 83 | 5.7 | 5.76532419435288 | -0.260007792455636 | 0.00296477775202967 | -0.683119102364486 | | 84 | 6.9 | 6.83188050306628 | 0.310699653546261 | 0.0029581788742391 | 0.651832008419736 | | 85 | 6.1 | 6.22203474826827 | -0.0836096247457896 | -0.0770170873189704 | -0.461557479171838 | | 86 | 4.8 | 4.85757010912065 | -0.623280085559336 | 0.000266148029649547 | -0.603802782043617 | | 87 | 3.7 | 3.72458667079312 | -0.842716956034724 | 0.000433622957724666 | -0.250327105928739 | | 88 | 5.8 | 5.66430652858494 | 0.354751222629176 | -0.00083131812947201 | 1.36612622875762 | | 89 | 6.8 | 6.76444057503678 | 0.675425527135285 | -0.00103562504019138 | 0.366114277832437 | | 90 | 8.5 | 8.45150937723033 | 1.11062083145818 | -0.00119066361602316 | 0.496997040758866 | | 91 | 7.2 | 7.3115385220949 | 0.142435951647924 | -0.000999916560964622 | -1.10576904094341 | | 92 | 5 | 5.11573987125026 | -0.863472666927765 | -0.000890504386909045 | -1.14888306271052 | | 93 | 4.7 | 4.67989671006126 | -0.679503564105113 | -0.000901548853962455 | 0.210119128910024 | | 94 | 2.3 | 2.38044988431253 | -1.37642103009318 | -0.000878457159913245 | -0.795981706860443 | | 95 | 2.4 | 2.33548739493846 | -0.803609500005544 | -0.000888932251069489 | 0.654235046842367 | | 96 | 0.1 | 0.167882985706366 | -1.39042059718936 | -0.000883009609001514 | -0.670224760732735 | | 97 | 1.9 | 1.6303092091751 | -0.167746499462456 | 0.130098796410866 | 1.42683113296707 | | 98 | 1.7 | 1.69989710663353 | -0.0675107301982554 | -0.0107201924221256 | 0.112427027807016 | | 99 | 2 | 1.99311651020288 | 0.0877780811394915 | -0.0108253432404314 | 0.177173005894065 | | 100 | -1.9 | -1.70492141531801 | -1.54144713198587 | -0.0092983155039725 | -1.85893342897724 | | 101 | 0.5 | 0.334360818407338 | -0.000965313993765508 | -0.0101691161899185 | 1.75884763074481 | | 102 | -1.3 | -1.21404532145824 | -0.666658797649266 | -0.0099587058193209 | -0.760238463763401 | | 103 | -3.3 | -3.22415734074427 | -1.24460451343108 | -0.00985768242098883 | -0.660077593260864 | | 104 | -2.8 | -2.86866966417225 | -0.556241754926039 | -0.00992411166147253 | 0.786203940181916 | | 105 | -8 | -7.77643154268564 | -2.42830007254806 | -0.00982439818146275 | -2.13816020857631 | | 106 | -13.9 | -13.7176648624865 | -3.93960502580483 | -0.00977996973532293 | -1.72613156774375 | | 107 | -21.9 | -21.6920583157117 | -5.67542725072353 | -0.00975180628492066 | -1.98256444882152 | | 108 | -28.8 | -28.7236386049055 | -6.25886493865877 | -0.00974658176728158 | -0.66637183746955 | | 109 | -27.6 | -28.2858563707992 | -3.38758187279346 | 0.358041381407861 | 3.34275537022097 | | 110 | -31.4 | -31.3820633686062 | -3.26428959234133 | -0.0313281963214016 | 0.138558280510251 | | 111 | -31.8 | -31.9026538566709 | -2.08324356300299 | -0.0320468874016483 | 1.34763206552816 | | 112 | -29.4 | -29.5824666239146 | -0.188287265384134 | -0.03364305372854 | 2.16235231560535 | | 113 | -27.6 | -27.6690907721545 | 0.715879249778494 | -0.0341023689462983 | 1.03236986409788 | | 114 | -23.6 | -23.7240908065754 | 2.10502331968948 | -0.034496949384607 | 1.58645424436042 | | 115 | -22.8 | -22.7119008386324 | 1.63489029055794 | -0.0344230995358375 | -0.536945429063395 | | 116 | -18.2 | -18.3017881672465 | 2.82880052969295 | -0.0345266392732215 | 1.3636093379913 | | 117 | -17.8 | -17.6581826224820 | 1.88871040748318 | -0.0344816408484821 | -1.07371864079225 | | 118 | -14.2 | -14.2405992730086 | 2.54645022223412 | -0.0344990171133864 | 0.751235256601043 | | 119 | -8.8 | -8.90260495802585 | 3.74741223008509 | -0.0345165277989882 | 1.37167540268165 | | 120 | -7.9 | -7.73859456992647 | 2.63599299167445 | -0.0345075839822455 | -1.26940460288320 | | 121 | -7 | -7.2057754635848 | 1.73391851037215 | 0.308766062995488 | -1.04819861025028 | | 122 | -7 | -6.90042272603732 | 1.12850359708754 | -0.0335042709891022 | -0.681448877892028 | | 123 | -3.6 | -3.66923125854014 | 2.03357490008093 | -0.0340043515244278 | 1.03282265515809 | | 124 | -2.4 | -2.33204503049557 | 1.73390120246519 | -0.033775148349878 | -0.341989071353872 | | 125 | -4.9 | -4.66722987456049 | -0.0166804985108977 | -0.0329676766363624 | -1.99885703693101 | | 126 | -7.7 | -7.5276828892239 | -1.24005692541326 | -0.0326521565820421 | -1.39715383747115 | | 127 | -6.5 | -6.57491771303776 | -0.296708522388085 | -0.0327867049197032 | 1.07741417012446 | | 128 | -5.1 | -5.15163860280477 | 0.443238211371043 | -0.0328449706018695 | 0.84512141448727 | | 129 | -3.4 | -3.42992915193602 | 0.993248742588917 | -0.0328688748840918 | 0.628191590146622 | | 130 | -2.8 | -2.75166243123423 | 0.857739494663727 | -0.0328656243997475 | -0.154771431141281 | | 131 | 0.8 | 0.705210152945384 | 1.97592417743159 | -0.0328804278945758 | 1.27713154190420 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/153hk1293189026.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/153hk1293189026.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/2fuhn1293189026.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/2fuhn1293189026.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/3fuhn1293189026.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/3fuhn1293189026.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/48myq1293189026.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/48myq1293189026.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/58myq1293189026.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/24/t1293188893qoxsjx76i8i2w2u/58myq1293189026.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 12 ; | | | | Parameters (R input): | | par1 = 12 ; | | | | R code (references can be found in the software module): | par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',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,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
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