*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: Mon, 13 Dec 2010 10:45:57 +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/13/t1292237040e1i0yy4r12ubkaa.htm/, Retrieved Mon, 13 Dec 2010 11:44:02 +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/13/t1292237040e1i0yy4r12ubkaa.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 «

10 10 10 10 10 9,94 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 10,06 9,94 9,94 9,94 9,94 9,94 9,94 10,06 10,06 9,94 10,06 10,06 10,06 10,18 10,28 10,28 10,18 10,28 10,28 10,28 10,18 10,28 10,28 10,18 10,18 10,18 10,28 10,28 10,18 10,18 10,18 10,18 10,18 10,18 10,28 10,28 10,28 10,18 10,18 10,18 10,28 10,18 10,18 10,28 10,18 10,18 10,18 10,28 10,28 10,28 10,28 10,28 10,28 10,18 10,18 10,18 10,18 10,18 10,18 10,18 10,18 10,18 10,28 10,28 10,28 10,28 10,28 10,28 10,28 10,28 10,18 10,28 10,28 10,28 10,28 10,18 10,28 10,28 10,28 10,18 10,18 10,28 10,28 10,28 10,28 10,28 10,28 10,28 10,18 10,28 10,28 10,28 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,34 10,34 10,34 10,42 10,42 10,42 10,42 10,34 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,42 10,34 10,34 10,34 10,3 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 10 10 0 0 0 2 10 10 0 0 0 3 10 10 0 0 0 4 10 10 0 0 0 5 10 10 0 0 0 6 9.94 9.96033376827986 -0.000439872949836983 -0.000439872949836979 -1.37147104487248 7 10.06 10.0263673463267 0.000258887158578052 0.000258887158578049 2.29951404088319 8 10.06 10.0485203718453 0.000483325437433103 0.000483325437433101 0.75750592761294 9 10.06 10.0559547746182 0.000553508651002014 0.000553508651002014 0.240510182781962 10 10.06 10.0584510934905 0.000572896150599928 0.000572896150599928 0.0672232633429626 11 10.06 10.059290550871 0.000575528429474178 0.000575528429474178 0.0092233568338851 12 10.06 10.0595740501603 0.00057267339363835 0.00057267339363835 -0.0101046053433722 13 10.06 10.0628269292646 0.000384384483148751 -0.00422822930606574 0.116559846759196 14 10.06 10.060650322408 0.000305633343610417 0.000305633337032108 -0.0735972547388267 15 10.06 10.0601129318859 0.000293920789957197 0.000293920789957198 -0.0284399386396052 16 10.06 10.0599419139381 0.000290228927683805 0.000290228927683806 -0.01601096834448 17 10.06 10.0598858431347 0.00028817483319575 0.000288174833195751 -0.01196845273466 18 10.06 10.0598676381287 0.000286567778753758 0.000286567778753768 -0.0105977384650291 19 10.06 10.059862024348 0.000285106763261678 0.000285106763261677 -0.0101090697003643 20 10.06 10.0598606049069 0.00028370197200987 0.000283701972009869 -0.00991416243012074 21 9.94 9.98031286846234 -0.000103852284037064 -0.000103852284037066 -2.76233648703172 22 9.94 9.95362309474005 -0.000232078918597237 -0.000232078918597235 -0.919936843750012 23 9.94 9.94466778882357 -0.000273926397035301 -0.0002739263970353 -0.301845519145338 24 9.94 9.9416626734602 -0.000286963565243233 -0.000286963565243233 -0.0945060845445728 25 9.94 9.93897135731364 -0.00020575957275545 0.00226335529647749 -0.0939061003734024 26 9.94 9.93976661873987 -0.000185554332093692 -0.00018555432879502 0.0308340362842609 27 10.06 10.0200139495117 0.000541851334498573 0.000541851334498566 2.73794306662051 28 10.06 10.0463799599874 0.000675588873434804 0.000675588873434807 0.890801275123412 29 9.94 9.97557883325968 0.000398470950320232 0.00039847095032023 -2.47136012953554 30 10.06 10.031456602714 0.000589044093196123 0.000589044093196125 1.9192956547063 31 10.06 10.050200723671 0.000648600114002564 0.000648600114002564 0.62817099112397 32 10.06 10.0564899125109 0.000666773495197392 0.000666773495197383 0.195175818243442 33 10.18 10.1382134694213 0.00092579570832808 0.000925795708328083 2.80477547876306 34 10.28 10.2319781373427 0.00122102708320596 0.00122102708320595 3.2124841135102 35 10.28 10.2634389245864 0.00131683184948386 0.00131683184948386 1.0463820743332 36 10.18 10.207650925046 0.0011365194258104 0.0011365194258104 -1.97599158861176 37 10.28 10.2564844686971 7.61863259791146e-05 -0.000838049591668815 1.79238896970685 38 10.28 10.2726108670245 0.00031730638558028 0.000317306384838519 0.510249612880247 39 10.28 10.2774286063447 0.00034747541962797 0.000347475419627966 0.153853635905734 40 10.18 10.2126228277362 9.7132021113173e-05 9.71320211131764e-05 -2.24928312954998 41 10.28 10.2573115129638 0.000225538843204645 0.000225538843204645 1.542104772106 42 10.28 10.272296133054 0.000263229035048086 0.000263229035048093 0.51062054428307 43 10.18 10.2109527188502 0.000112857213115462 0.000112857213115464 -2.13165861131433 44 10.18 10.1903723121265 6.32079882584806e-05 6.3207988258487e-05 -0.716036724597112 45 10.18 10.1834674495357 4.66125888957483e-05 4.66125888957445e-05 -0.241114964566128 46 10.28 10.2475216125226 0.000198437692441336 0.000198437692441323 2.21485148551728 47 10.28 10.2690128647441 0.000248796035573339 0.000248796035573335 0.736795691916197 48 10.18 10.2098525282372 0.00010864916733827 0.00010864916733827 -2.0557364120503 49 10.18 10.1929538755831 0.000390426139390517 -0.00429468752918502 -0.62651244654893 50 10.18 10.1839733305575 0.000278316844444597 0.000278316843547046 -0.303347034028454 51 10.18 10.1812350796734 0.000262251858946248 0.000262251858946241 -0.103384986626091 52 10.18 10.1803288038283 0.000258682911810125 0.000258682911810127 -0.040360363121712 53 10.18 10.180025725234 0.000257396258378532 0.000257396258378532 -0.0194297067341698 54 10.28 10.2463107427278 0.000391582172171479 0.000391582172171471 2.28444736584929 55 10.28 10.2685474509672 0.00043403695065689 0.000434036950656891 0.755876319146383 56 10.28 10.2760081333462 0.000447467028813392 0.000447467028813398 0.243140389408743 57 10.18 10.2121250968892 0.000325357351922054 0.000325357351922041 -2.22602612008501 58 10.18 10.1906917196779 0.00028420323173694 0.000284203231736928 -0.752919169958811 59 10.18 10.1835006991568 0.000270099368546637 0.000270099368546632 -0.25866602884882 60 10.28 10.2474749709244 0.000390044010231276 0.000390044010231276 2.20436365828707 61 10.18 10.2094174274908 0.000897726402192297 -0.00987499040942788 -1.39920724945556 62 10.18 10.1891152005854 0.00068701307122452 0.00068701306281248 -0.69435266846231 63 10.28 10.2493868861919 0.000950229113043338 0.000950229113043329 2.04548099998014 64 10.18 10.2029908907818 0.000830236135310885 0.000830236135310886 -1.63583114810244 65 10.18 10.187452886628 0.000799114589511965 0.000799114589511964 -0.566175684872796 66 10.18 10.1822423324208 0.000788972237293642 0.000788972237293635 -0.207929906256347 67 10.28 10.2468915834417 0.00089207153989053 0.00089207153989053 2.20968821049648 68 10.28 10.2685819905223 0.000925104958799112 0.000925104958799107 0.719680055883865 69 10.28 10.2758598215131 0.000935128643428837 0.000935128643428826 0.219823709218034 70 10.28 10.2783021101506 0.000937498990434778 0.000937498990434766 0.05215247669635 71 10.28 10.2791220144802 0.000937314441096997 0.000937314441096992 -0.00406914888281937 72 10.28 10.2793975858417 0.000936277746191528 0.00093627774619153 -0.0228984202166926 73 10.18 10.2250454910829 0.00154313648975891 -0.0169745013626545 -1.99565373121464 74 10.18 10.1940017314475 0.00126611474765802 0.00126611473152511 -1.07610805172462 75 10.18 10.1842645330444 0.00122458821158438 0.00122458821158437 -0.378173392471801 76 10.18 10.1810298233075 0.00121493050516431 0.00121493050516431 -0.154105001546692 77 10.18 10.179947310851 0.00121119655297951 0.00121119655297951 -0.0794728425316655 78 10.18 10.17958491779 0.00120892587190517 0.00120892587190517 -0.0544459576767499 79 10.18 10.1794639181146 0.00120708961912965 0.00120708961912965 -0.0460182770574289 80 10.18 10.1794238693947 0.00120539520179449 0.00120539520179448 -0.043154570927683 81 10.18 10.1794109697064 0.00120375045204474 0.00120375045204473 -0.0421567966974484 82 10.28 10.24581163562 0.0012915027440251 0.00129150274402508 2.25602149935534 83 10.28 10.2680905252035 0.00131969698547596 0.00131969698547595 0.726231179539443 84 10.28 10.275565980328 0.00132795390882726 0.00132795390882727 0.213009114609302 85 10.28 10.2878919011895 0.00122466730833558 -0.0134713403766126 0.394638351810466 86 10.28 10.2821318628546 0.00117279641131098 0.00117279639789329 -0.232060202330946 87 10.28 10.2803254990967 0.00116298264675905 0.00116298264675904 -0.102479856208765 88 10.28 10.2797272646261 0.00115965264904126 0.00115965264904126 -0.0608745214250034 89 10.28 10.2795277588076 0.00115772373436134 0.00115772373436134 -0.0470178316437762 90 10.18 10.2130513346435 0.00107248579188601 0.00107248579188602 -2.34016219588342 91 10.28 10.2571599069467 0.00112439180185492 0.00112439180185492 1.48914817376726 92 10.28 10.2719589760705 0.00114062401528992 0.00114062401528991 0.473184180343956 93 10.28 10.2769246664029 0.00114513649774498 0.00114513649774497 0.132359380547876 94 10.28 10.2785911618747 0.00114574979530967 0.00114574979530965 0.0180407042493486 95 10.18 10.212740661516 0.00106707618892212 0.00106707618892211 -2.31828819769601 96 10.28 10.2570574513717 0.00111779508515656 0.00111779508515656 1.49658113429995 97 10.28 10.2795368052545 0.000942491058864225 -0.0103674016386234 0.763106195052214 98 10.28 10.2795207592709 0.000936171513546158 0.000936171504872611 -0.0319958486362645 99 10.18 10.2130032077412 0.000739035514268154 0.000739035514268148 -2.32189344332764 100 10.18 10.1908373433709 0.000700607962785358 0.000700607962785357 -0.791784757082682 101 10.28 10.2498253354392 0.000774021249080552 0.000774021249080553 2.01642183772999 102 10.28 10.2696115585842 0.000795288979468202 0.000795288979468213 0.657834776012721 103 10.28 10.2762498848475 0.000801545103992838 0.000801545103992838 0.202183372774933 104 10.28 10.2784773612404 0.000803047897829865 0.000803047897829859 0.049341513666958 105 10.28 10.2792249817178 0.000802989834895836 0.000802989834895823 -0.00191796584492423 106 10.28 10.2794760939357 0.000802413291228861 0.000802413291228834 -0.0190967630724289 107 10.28 10.2795606204919 0.000801664524349817 0.000801664524349814 -0.0248412342448785 108 10.18 10.2131748321803 0.000731673263893693 0.000731673263893696 -2.32490658479398 109 10.28 10.2606266285494 0.000391218586614733 -0.00430340445152096 1.66319910374375 110 10.28 10.2735330196785 0.000465404221900307 0.000465404218117286 0.419309179524872 111 10.28 10.2776810296703 0.000475075758818388 0.000475075758818383 0.126830565475181 112 10.42 10.3720663489938 0.000616674501777516 0.000616674501777517 3.24665701554703 113 10.42 10.4037009169221 0.000651790373837415 0.000651790373837415 1.07307617221195 114 10.42 10.4143124004267 0.000661805981332506 0.000661805981332518 0.344614809545411 115 10.42 10.4178726686058 0.000664596114342473 0.000664596114342472 0.100294178658602 116 10.42 10.4190673708109 0.000665098457711405 0.0006650984577114 0.0183432908900091 117 10.42 10.4194684136251 0.000664849713588041 0.000664849713588025 -0.00913717639951302 118 10.42 10.4196031741741 0.000664351670214248 0.000664351670214221 -0.0183428232737376 119 10.42 10.4196485929946 0.00066377102794112 0.000663771027941115 -0.0214171176968864 120 10.42 10.4196640359958 0.000663163494267178 0.00066316349426718 -0.0224342919007193 121 10.42 10.4247407754341 0.00063424152260963 -0.0069766567452943 0.156681257599661 122 10.34 10.3675441148048 0.000322859538973722 0.000322859546580644 -1.94342870981942 123 10.34 10.3491172071071 0.000278149776499278 0.000278149776499277 -0.646031958471749 124 10.34 10.3429691464059 0.000269351250614702 0.000269351250614701 -0.222185065878707 125 10.42 10.3940459328751 0.000321587871867984 0.000321587871867984 1.75774085814405 126 10.42 10.4111791906139 0.000336942557391159 0.000336942557391168 0.581703591191031 127 10.42 10.4169273675199 0.000341673977161303 0.000341673977161302 0.187242958174161 128 10.42 10.4188560182094 0.000343040082878805 0.0003430400828788 0.0549143052415347 129 10.34 10.3663667170163 0.000297826317408062 0.00029782631740804 -1.82817051589808 130 10.42 10.4018924692878 0.000327897889804651 0.000327897889804619 1.21900237990263 131 10.42 10.4138119228353 0.00033777875411022 0.000337778754110214 0.401106238807845 132 10.42 10.4178111542475 0.000340896597258579 0.000340896597258581 0.126698416771718 133 10.42 10.4217131720261 0.000319696561577743 -0.00351666218473014 0.126129634116454 134 10.42 10.4204526269483 0.000311902364886063 0.000311902372545633 -0.0532376659322874 135 10.42 10.4200486255138 0.000310339137380198 0.000310339137380197 -0.0246757397072978 136 10.42 10.4199143292867 0.000309781624119558 0.000309781624119557 -0.0153742608558138 137 10.42 10.419869477996 0.000309447688237092 0.000309447688237092 -0.0122691470341138 138 10.42 10.4198545332183 0.00030917631183475 0.00030917631183476 -0.0112244242398007 139 10.42 10.4198496048594 0.000308924733440389 0.000308924733440386 -0.0108688709280258 140 10.42 10.4198480326899 0.000308679879859159 0.000308679879859151 -0.0107441635682406 141 10.42 10.41984758515 0.000308437511987789 0.000308437511987764 -0.0106968181260944 142 10.42 10.4198475143984 0.000308196225125785 0.000308196225125754 -0.0106754075953617 143 10.42 10.4198475698035 0.000307955549958277 0.000307955549958271 -0.0106626976362645 144 10.42 10.4198476673666 0.000307715328904468 0.000307715328904469 -0.010652912293055 145 10.42 10.4222172317835 0.000296469986947599 -0.00326116986433358 0.0728878553867881 146 10.42 10.4206276692121 0.000287888081765991 0.000287888089998967 -0.0636737315160314 147 10.34 10.3669131703805 0.000179135987933434 0.000179135987933436 -1.86192130217501 148 10.34 10.3489748582603 0.000158183524152381 0.000158183524152379 -0.626488177434008 149 10.34 10.342961258265 0.000152822899476047 0.000152822899476048 -0.213526884374736 150 10.34 10.3409440391134 0.000151148266189549 0.000151148266189558 -0.075086784981142 151 10.42 10.393407254779 0.000189800855467781 0.000189800855467778 1.81014209894196 152 10.42 10.4110091180369 0.000202468733972886 0.000202468733972876 0.602512263127179 153 10.34 10.3637748401915 0.000168153787237153 0.000168153787237124 -1.6414670904742 154 10.34 10.3479271736034 0.000156596037735477 0.000156596037735449 -0.554200623976319 155 10.34 10.3426101086105 0.000152651070566811 0.000152651070566806 -0.189406945548136 156 10.42 10.39396619366 0.000189520749715515 0.000189520749715517 1.77181000847946 157 10.42 10.4120410809292 9.95204578181402e-05 -0.00109472504441041 0.631234335116518 158 10.42 10.4173448555469 0.000121498708298702 0.000121498715858001 0.176015737423047 159 10.34 10.3658714486733 2.50890100033602e-05 2.5089010003364e-05 -1.77938048155902 160 10.34 10.3486755447697 6.60862870915618e-06 6.60862870915407e-06 -0.595519458922765 161 10.34 10.3429104195661 1.95646909108144e-06 1.95646909108182e-06 -0.199688833136391 162 10.34 10.3409764801959 5.70024649640367e-07 5.70024649655946e-07 -0.0669852368215796 163 10.34 10.3403276499619 1.24694975048295e-07 1.24694975043976e-07 -0.0224710767231532 164 10.42 10.3932512709753 3.58616508058868e-05 3.58616508058685e-05 1.83132106719266 165 10.42 10.4110077731879 4.77599759864094e-05 4.77599759863818e-05 0.613192555402628 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Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/1wa3d1292237147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/1wa3d1292237147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/2pjkh1292237147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/2pjkh1292237147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/30aj21292237147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/30aj21292237147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/40aj21292237147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/40aj21292237147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/5sjjm1292237147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292237040e1i0yy4r12ubkaa/5sjjm1292237147.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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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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