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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationSun, 18 Dec 2016 18:33:50 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482082479xo8vi43058ew7fc.htm/, Retrieved Fri, 01 Nov 2024 03:37:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301200, Retrieved Fri, 01 Nov 2024 03:37:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [structural time s...] [2016-12-18 17:33:50] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataseries X:
2119.9
2108.7
2092
2104.2
2110.1
2114
2138.8
2165.5
2155.1
2135.2
2163.1
2175.2
2183.3
2201.5
2212.3
2223.8
2241.9
2269.2
2261.4
2273.4
2299.3
2315.5
2338.7
2333
2311
2303.6
2310.5
2295.8
2265.5
2271.1
2231.9
2245
2249.7
2300.5
2280.4
2290.7
2261.5
2259.1
2249.8
2271.2
2259
2259.4
2250.2
2243.3
2234.3
2216.5
2197.6
2211.7
2206.7
2214.6
2229.8
2219.5
2213.8
2214.1
2224.1
2229.6
2251.7
2262.9
2268.9
2293.7
2312.4
2342
2327.4
2366.2
2371.8
2364.4
2370.5
2412.8
2447.3
2443.5
2459.3
2480.7
2504.4
2505.5
2534
2538.7
2538.1
2522
2566.4
2572.8
2557.3
2541
2540.7
2508.5
2567.1
2553.6
2522.4
2520.6
2499.4
2470.8
2479.3
2481.8
2470.3
2491
2479.1
2456.6
2456.1
2482.2
2444.7
2425.3
2389.3
2367.7
2339.3
2342.4
2343.6
2346.3
2363.5
2338.7
2369.4
2356
2348.6
2349.7
2371.9
2364.9
2394.1
2399.2




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301200&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301200&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
12119.92119.9000
22108.72110.0279752091-0.707250916295394-0.570591932414039-0.41196358187324
320922095.23102559922-1.80894957391344-0.771047769930013-0.908220477971867
42104.22103.19183507849-0.792885279732673-0.6608044378714630.619782096177108
52110.12109.581314310620.117481218137906-0.6695046270089830.447037206068277
621142113.975493107930.732788859469574-0.6655866540259050.26236626859254
72138.82136.011824620754.05805975050061-0.5874400259095381.29326503070542
82165.52162.55063641647.75747608575763-0.567234470270421.35461119985305
92155.12157.716032902735.61271742022658-0.663782324758044-0.75484088934367
102135.22139.548897248741.47014113500555-0.684527318259551-1.42044971724949
112163.12160.648734705544.94054073701393-0.5611133924339521.16971629293666
122175.22174.456546217436.52343729785254-0.6135359435227020.527527019003593
132183.32178.304810568096.076181767388085.38651737995945-0.187149609622243
142201.52199.842708329518.82577580592963-0.042469925090070.77309961198664
152212.32211.951309351039.41795876996284-0.1491626029392630.194743488461929
162223.82223.540092988689.81109606695416-0.06998195504443130.128722044980108
172241.92240.8251068368311.1663293648552-0.05984062218882670.442860066748364
182269.22267.0069933934713.8910157298243-0.08630810448806330.889645698415558
192261.42264.1566337442710.8517157588958-0.215434563799124-0.991911591928025
202273.42273.6407329971210.6033512118381-0.0331399637708015-0.0810327301732154
212299.32297.3400808295312.9821792728377-0.02797546161776870.775978718740828
222315.52314.9826400297913.8288519838186-0.1900724971621770.276151338771876
232338.72337.4246562144115.3938292107964-0.03214586539034080.510392187738888
2423332335.7748587647312.2969978131147-0.187777531172401-1.0099056674519
2523112320.950891017287.45992613836058-5.9327302801285-1.75314110471905
262303.62306.21284242933.493283770553390.155556386652649-1.18622148503997
272310.52310.240342392073.590129694393140.178851922419740.0316573657076356
282295.82298.097501112930.731081732294160.0856727581061134-0.93204971921255
292265.52269.88810583958-4.52838885535942-0.00609091702494724-1.71388285780337
302271.12270.00958655709-3.683441976194080.3863127030808630.275383537670679
312231.92236.51329560895-9.10046592170624-0.0984437279989058-1.76579290324947
3222452242.35323849099-6.385878250288120.3839880427454650.88497753621253
332249.72247.62840525323-4.267162706950980.3053689354970630.690770785290845
342300.52292.681076425224.693840018763440.3483371847753012.92172985896659
352280.42282.549818465252.000208391588930.0958955226171737-0.878289893995652
362290.72289.653034017982.927308209332710.2740622460186630.302284130445473
372261.52270.69815488851-1.00356739949062-5.93365671376412-1.37562216139352
382259.12260.06256648583-2.731388736795430.305648124931859-0.529879346582519
392249.82250.41855541737-3.984807098376840.425119115861769-0.409501904716866
402271.22267.34424915617-0.1857367690593030.6945873833764911.2385299405313
4122592260.06682599476-1.474226974917450.00492642740956051-0.419926104192948
422259.42258.5674886067-1.478788871479690.836306481705146-0.00148695019982057
432250.22251.11719480113-2.56358774228233-0.0146089468717951-0.353636733507104
442243.32243.50242210972-3.481170377470060.561111535060136-0.299152701583375
452234.32234.92851387827-4.406289483353440.141342677743515-0.301628099143173
462216.52217.8488143544-6.708470916210410.567080919146243-0.750640112749196
472197.62199.22576459562-8.872836555442660.175504894469541-0.705727349551415
482211.72208.20592194399-5.630175105833310.7956178452853651.05727504071943
492206.72209.36618296698-4.40680380463882-3.682171004180070.42060331023624
502214.62213.0553326582-2.950796922514780.4457156959936740.452826809952015
512229.82226.859578343410.08736977318475070.4154931824287080.992259535881776
522219.52219.91566065091-1.189786376118640.645301478075312-0.4163841691435
532213.82214.45045294454-1.96640063521392-0.00550171437503547-0.253126298639038
542214.12213.08667625146-1.856944627955010.9224130046072610.0356797736557719
552224.12222.280012381490.1500450663644450.152844924128420.654296949413813
562229.62228.122680219041.183932436737660.6184316881275710.337081829323051
572251.72248.385346044014.648953415949220.4359760159195761.12976876837919
582262.92260.961019086526.08858086456590.7429174711135930.469406375047131
592268.92268.617013691166.373254088236840.04646806041591170.0928234846010845
602293.72290.443353361669.179315884293490.925517135099140.914920607108833
612312.42313.5648042269611.695299009555-3.253413563852190.855583236651448
6223422339.650014412914.28760530609350.3582577286161370.813614332364
632327.42330.8129969617210.09468971645090.0654281706989805-1.36908041534213
642366.22362.0248442024413.92953208203330.9943950252639561.25030016663251
652371.82372.4907820964213.3005235763209-0.169207374242545-0.205028529015853
662364.42366.727635698049.838681937505240.54324916704985-1.12852245343061
672370.52371.207744736688.865639966987140.0992771190465357-0.317230938975759
682412.82407.8546612209613.91022327921840.7611667053983151.64473862591387
692447.32443.5450503647117.86507817137340.4744862111695691.28949776553003
702443.52445.4767931778514.97188848824930.423125493017191-0.943366276506526
712459.32459.5200019858914.8032554845712-0.0801158784431939-0.0549866234863027
722480.72479.1488521245615.67930465503270.8245444626201040.285638637047674
732504.42505.9791884940317.6937414660926-3.250384989833370.679904696229089
742505.52507.4514504421414.76805404619060.324207429834018-0.924197916057099
7525342532.624558317416.6544934688799-0.1869729901552570.615856475858866
762538.72539.5449802363714.887170878490.618794675905235-0.576231400048928
772538.12540.4651014275712.3511973164735-0.265273036445513-0.826646812036516
7825222525.851634153457.455560336324260.202454991631498-1.59597558774809
792566.42561.9247880110812.65110636613660.1723649522602881.69388929464341
802572.82572.9183263829112.3501792755740.130910862461761-0.0981159234532809
812557.32560.825784883177.912700214895830.149627184178221-1.44687441218168
8225412544.587262450983.528127592839510.0444443342312502-1.42966434485416
832540.72541.905605135492.40074659461792-0.271781045496277-0.367609935430232
842508.52513.04953896669-3.27239305929580.148771325096195-1.84976792556492
852567.12558.227085087895.48645157926751.611840099405872.94006873734885
862553.62555.139483078373.93872600349097-0.324816964604739-0.491279338789482
872522.42528.04302018134-1.68730110454502-0.990392154431384-1.83643767495332
882520.62520.97289686461-2.664418200038940.435324991054683-0.318596566705055
892499.42502.2228068133-5.58451129487483-0.408120089534752-0.951884685118144
902470.82474.92293586848-9.52636740514243-0.863012404817024-1.28507288981117
912479.32477.45756570253-7.337081872501480.03173369975683650.713778370919629
922481.82480.17096040849-5.512772211166020.1201161427266850.594814582425995
932470.32470.90863700111-6.19336678135286-0.0456821693403476-0.221914834804166
9424912487.51062123486-2.055682272526120.06678389190616921.34917049792189
952479.12480.1924585532-3.01090943132788-0.302300601287815-0.311475823693473
962456.62460.15129740665-6.10125648167838-0.995498486169947-1.00764949100196
972456.12453.71734759708-6.161432411810322.432499434825-0.020114486387768
982482.22477.32291823324-0.7846637671162080.6287178846446471.71311886690676
992444.72450.11052472929-5.57486317177258-1.45459926709322-1.56341372861246
1002425.32427.30361262367-8.702343677308590.580166599827987-1.01976991777142
1012389.32393.32968373756-13.2891876479713-0.241323985982174-1.49523928222274
1022367.72370.11257836805-15.0910327931577-0.924261739980083-0.587424004836978
1032339.32341.48887984445-17.5470377316461-0.160063654610066-0.800747436805128
1042342.42339.36964877298-14.7471317757920.7173306755735670.912914620770784
1052343.62341.20041727363-11.7385178830024-0.0859401371084990.980995259656445
1062346.32343.76906470385-9.141990421322080.3857895601977610.846651218070855
1072363.52359.32558371874-4.659558282607010.471151667279211.4616110178508
1082338.72341.87781670717-6.97967560351426-1.26142974034204-0.756525714467698
1092369.42362.74922173045-1.94018513964552.479565307622871.67891457914711
11023562355.9541006742-2.817558702299960.742800586069899-0.280386822749344
1112348.62350.46532386189-3.30167533028218-1.46602697948677-0.15798702584049
1122349.72348.63528716229-3.034629620330390.8443321459703040.0870775693068053
1132371.92368.334048206021.090863560459980.1623836647949321.34486765517628
1142364.92366.328349761130.528948762624683-0.964723588326429-0.183193478996922
1152394.12390.593464081684.83608579284691-0.04748906575158761.40429739421019
1162399.22398.461681121385.386285077759150.2843008808195420.179394697456704

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 2119.9 & 2119.9 & 0 & 0 & 0 \tabularnewline
2 & 2108.7 & 2110.0279752091 & -0.707250916295394 & -0.570591932414039 & -0.41196358187324 \tabularnewline
3 & 2092 & 2095.23102559922 & -1.80894957391344 & -0.771047769930013 & -0.908220477971867 \tabularnewline
4 & 2104.2 & 2103.19183507849 & -0.792885279732673 & -0.660804437871463 & 0.619782096177108 \tabularnewline
5 & 2110.1 & 2109.58131431062 & 0.117481218137906 & -0.669504627008983 & 0.447037206068277 \tabularnewline
6 & 2114 & 2113.97549310793 & 0.732788859469574 & -0.665586654025905 & 0.26236626859254 \tabularnewline
7 & 2138.8 & 2136.01182462075 & 4.05805975050061 & -0.587440025909538 & 1.29326503070542 \tabularnewline
8 & 2165.5 & 2162.5506364164 & 7.75747608575763 & -0.56723447027042 & 1.35461119985305 \tabularnewline
9 & 2155.1 & 2157.71603290273 & 5.61271742022658 & -0.663782324758044 & -0.75484088934367 \tabularnewline
10 & 2135.2 & 2139.54889724874 & 1.47014113500555 & -0.684527318259551 & -1.42044971724949 \tabularnewline
11 & 2163.1 & 2160.64873470554 & 4.94054073701393 & -0.561113392433952 & 1.16971629293666 \tabularnewline
12 & 2175.2 & 2174.45654621743 & 6.52343729785254 & -0.613535943522702 & 0.527527019003593 \tabularnewline
13 & 2183.3 & 2178.30481056809 & 6.07618176738808 & 5.38651737995945 & -0.187149609622243 \tabularnewline
14 & 2201.5 & 2199.84270832951 & 8.82577580592963 & -0.04246992509007 & 0.77309961198664 \tabularnewline
15 & 2212.3 & 2211.95130935103 & 9.41795876996284 & -0.149162602939263 & 0.194743488461929 \tabularnewline
16 & 2223.8 & 2223.54009298868 & 9.81109606695416 & -0.0699819550444313 & 0.128722044980108 \tabularnewline
17 & 2241.9 & 2240.82510683683 & 11.1663293648552 & -0.0598406221888267 & 0.442860066748364 \tabularnewline
18 & 2269.2 & 2267.00699339347 & 13.8910157298243 & -0.0863081044880633 & 0.889645698415558 \tabularnewline
19 & 2261.4 & 2264.15663374427 & 10.8517157588958 & -0.215434563799124 & -0.991911591928025 \tabularnewline
20 & 2273.4 & 2273.64073299712 & 10.6033512118381 & -0.0331399637708015 & -0.0810327301732154 \tabularnewline
21 & 2299.3 & 2297.34008082953 & 12.9821792728377 & -0.0279754616177687 & 0.775978718740828 \tabularnewline
22 & 2315.5 & 2314.98264002979 & 13.8288519838186 & -0.190072497162177 & 0.276151338771876 \tabularnewline
23 & 2338.7 & 2337.42465621441 & 15.3938292107964 & -0.0321458653903408 & 0.510392187738888 \tabularnewline
24 & 2333 & 2335.77485876473 & 12.2969978131147 & -0.187777531172401 & -1.0099056674519 \tabularnewline
25 & 2311 & 2320.95089101728 & 7.45992613836058 & -5.9327302801285 & -1.75314110471905 \tabularnewline
26 & 2303.6 & 2306.2128424293 & 3.49328377055339 & 0.155556386652649 & -1.18622148503997 \tabularnewline
27 & 2310.5 & 2310.24034239207 & 3.59012969439314 & 0.17885192241974 & 0.0316573657076356 \tabularnewline
28 & 2295.8 & 2298.09750111293 & 0.73108173229416 & 0.0856727581061134 & -0.93204971921255 \tabularnewline
29 & 2265.5 & 2269.88810583958 & -4.52838885535942 & -0.00609091702494724 & -1.71388285780337 \tabularnewline
30 & 2271.1 & 2270.00958655709 & -3.68344197619408 & 0.386312703080863 & 0.275383537670679 \tabularnewline
31 & 2231.9 & 2236.51329560895 & -9.10046592170624 & -0.0984437279989058 & -1.76579290324947 \tabularnewline
32 & 2245 & 2242.35323849099 & -6.38587825028812 & 0.383988042745465 & 0.88497753621253 \tabularnewline
33 & 2249.7 & 2247.62840525323 & -4.26716270695098 & 0.305368935497063 & 0.690770785290845 \tabularnewline
34 & 2300.5 & 2292.68107642522 & 4.69384001876344 & 0.348337184775301 & 2.92172985896659 \tabularnewline
35 & 2280.4 & 2282.54981846525 & 2.00020839158893 & 0.0958955226171737 & -0.878289893995652 \tabularnewline
36 & 2290.7 & 2289.65303401798 & 2.92730820933271 & 0.274062246018663 & 0.302284130445473 \tabularnewline
37 & 2261.5 & 2270.69815488851 & -1.00356739949062 & -5.93365671376412 & -1.37562216139352 \tabularnewline
38 & 2259.1 & 2260.06256648583 & -2.73138873679543 & 0.305648124931859 & -0.529879346582519 \tabularnewline
39 & 2249.8 & 2250.41855541737 & -3.98480709837684 & 0.425119115861769 & -0.409501904716866 \tabularnewline
40 & 2271.2 & 2267.34424915617 & -0.185736769059303 & 0.694587383376491 & 1.2385299405313 \tabularnewline
41 & 2259 & 2260.06682599476 & -1.47422697491745 & 0.00492642740956051 & -0.419926104192948 \tabularnewline
42 & 2259.4 & 2258.5674886067 & -1.47878887147969 & 0.836306481705146 & -0.00148695019982057 \tabularnewline
43 & 2250.2 & 2251.11719480113 & -2.56358774228233 & -0.0146089468717951 & -0.353636733507104 \tabularnewline
44 & 2243.3 & 2243.50242210972 & -3.48117037747006 & 0.561111535060136 & -0.299152701583375 \tabularnewline
45 & 2234.3 & 2234.92851387827 & -4.40628948335344 & 0.141342677743515 & -0.301628099143173 \tabularnewline
46 & 2216.5 & 2217.8488143544 & -6.70847091621041 & 0.567080919146243 & -0.750640112749196 \tabularnewline
47 & 2197.6 & 2199.22576459562 & -8.87283655544266 & 0.175504894469541 & -0.705727349551415 \tabularnewline
48 & 2211.7 & 2208.20592194399 & -5.63017510583331 & 0.795617845285365 & 1.05727504071943 \tabularnewline
49 & 2206.7 & 2209.36618296698 & -4.40680380463882 & -3.68217100418007 & 0.42060331023624 \tabularnewline
50 & 2214.6 & 2213.0553326582 & -2.95079692251478 & 0.445715695993674 & 0.452826809952015 \tabularnewline
51 & 2229.8 & 2226.85957834341 & 0.0873697731847507 & 0.415493182428708 & 0.992259535881776 \tabularnewline
52 & 2219.5 & 2219.91566065091 & -1.18978637611864 & 0.645301478075312 & -0.4163841691435 \tabularnewline
53 & 2213.8 & 2214.45045294454 & -1.96640063521392 & -0.00550171437503547 & -0.253126298639038 \tabularnewline
54 & 2214.1 & 2213.08667625146 & -1.85694462795501 & 0.922413004607261 & 0.0356797736557719 \tabularnewline
55 & 2224.1 & 2222.28001238149 & 0.150045066364445 & 0.15284492412842 & 0.654296949413813 \tabularnewline
56 & 2229.6 & 2228.12268021904 & 1.18393243673766 & 0.618431688127571 & 0.337081829323051 \tabularnewline
57 & 2251.7 & 2248.38534604401 & 4.64895341594922 & 0.435976015919576 & 1.12976876837919 \tabularnewline
58 & 2262.9 & 2260.96101908652 & 6.0885808645659 & 0.742917471113593 & 0.469406375047131 \tabularnewline
59 & 2268.9 & 2268.61701369116 & 6.37325408823684 & 0.0464680604159117 & 0.0928234846010845 \tabularnewline
60 & 2293.7 & 2290.44335336166 & 9.17931588429349 & 0.92551713509914 & 0.914920607108833 \tabularnewline
61 & 2312.4 & 2313.56480422696 & 11.695299009555 & -3.25341356385219 & 0.855583236651448 \tabularnewline
62 & 2342 & 2339.6500144129 & 14.2876053060935 & 0.358257728616137 & 0.813614332364 \tabularnewline
63 & 2327.4 & 2330.81299696172 & 10.0946897164509 & 0.0654281706989805 & -1.36908041534213 \tabularnewline
64 & 2366.2 & 2362.02484420244 & 13.9295320820333 & 0.994395025263956 & 1.25030016663251 \tabularnewline
65 & 2371.8 & 2372.49078209642 & 13.3005235763209 & -0.169207374242545 & -0.205028529015853 \tabularnewline
66 & 2364.4 & 2366.72763569804 & 9.83868193750524 & 0.54324916704985 & -1.12852245343061 \tabularnewline
67 & 2370.5 & 2371.20774473668 & 8.86563996698714 & 0.0992771190465357 & -0.317230938975759 \tabularnewline
68 & 2412.8 & 2407.85466122096 & 13.9102232792184 & 0.761166705398315 & 1.64473862591387 \tabularnewline
69 & 2447.3 & 2443.54505036471 & 17.8650781713734 & 0.474486211169569 & 1.28949776553003 \tabularnewline
70 & 2443.5 & 2445.47679317785 & 14.9718884882493 & 0.423125493017191 & -0.943366276506526 \tabularnewline
71 & 2459.3 & 2459.52000198589 & 14.8032554845712 & -0.0801158784431939 & -0.0549866234863027 \tabularnewline
72 & 2480.7 & 2479.14885212456 & 15.6793046550327 & 0.824544462620104 & 0.285638637047674 \tabularnewline
73 & 2504.4 & 2505.97918849403 & 17.6937414660926 & -3.25038498983337 & 0.679904696229089 \tabularnewline
74 & 2505.5 & 2507.45145044214 & 14.7680540461906 & 0.324207429834018 & -0.924197916057099 \tabularnewline
75 & 2534 & 2532.6245583174 & 16.6544934688799 & -0.186972990155257 & 0.615856475858866 \tabularnewline
76 & 2538.7 & 2539.54498023637 & 14.88717087849 & 0.618794675905235 & -0.576231400048928 \tabularnewline
77 & 2538.1 & 2540.46510142757 & 12.3511973164735 & -0.265273036445513 & -0.826646812036516 \tabularnewline
78 & 2522 & 2525.85163415345 & 7.45556033632426 & 0.202454991631498 & -1.59597558774809 \tabularnewline
79 & 2566.4 & 2561.92478801108 & 12.6511063661366 & 0.172364952260288 & 1.69388929464341 \tabularnewline
80 & 2572.8 & 2572.91832638291 & 12.350179275574 & 0.130910862461761 & -0.0981159234532809 \tabularnewline
81 & 2557.3 & 2560.82578488317 & 7.91270021489583 & 0.149627184178221 & -1.44687441218168 \tabularnewline
82 & 2541 & 2544.58726245098 & 3.52812759283951 & 0.0444443342312502 & -1.42966434485416 \tabularnewline
83 & 2540.7 & 2541.90560513549 & 2.40074659461792 & -0.271781045496277 & -0.367609935430232 \tabularnewline
84 & 2508.5 & 2513.04953896669 & -3.2723930592958 & 0.148771325096195 & -1.84976792556492 \tabularnewline
85 & 2567.1 & 2558.22708508789 & 5.4864515792675 & 1.61184009940587 & 2.94006873734885 \tabularnewline
86 & 2553.6 & 2555.13948307837 & 3.93872600349097 & -0.324816964604739 & -0.491279338789482 \tabularnewline
87 & 2522.4 & 2528.04302018134 & -1.68730110454502 & -0.990392154431384 & -1.83643767495332 \tabularnewline
88 & 2520.6 & 2520.97289686461 & -2.66441820003894 & 0.435324991054683 & -0.318596566705055 \tabularnewline
89 & 2499.4 & 2502.2228068133 & -5.58451129487483 & -0.408120089534752 & -0.951884685118144 \tabularnewline
90 & 2470.8 & 2474.92293586848 & -9.52636740514243 & -0.863012404817024 & -1.28507288981117 \tabularnewline
91 & 2479.3 & 2477.45756570253 & -7.33708187250148 & 0.0317336997568365 & 0.713778370919629 \tabularnewline
92 & 2481.8 & 2480.17096040849 & -5.51277221116602 & 0.120116142726685 & 0.594814582425995 \tabularnewline
93 & 2470.3 & 2470.90863700111 & -6.19336678135286 & -0.0456821693403476 & -0.221914834804166 \tabularnewline
94 & 2491 & 2487.51062123486 & -2.05568227252612 & 0.0667838919061692 & 1.34917049792189 \tabularnewline
95 & 2479.1 & 2480.1924585532 & -3.01090943132788 & -0.302300601287815 & -0.311475823693473 \tabularnewline
96 & 2456.6 & 2460.15129740665 & -6.10125648167838 & -0.995498486169947 & -1.00764949100196 \tabularnewline
97 & 2456.1 & 2453.71734759708 & -6.16143241181032 & 2.432499434825 & -0.020114486387768 \tabularnewline
98 & 2482.2 & 2477.32291823324 & -0.784663767116208 & 0.628717884644647 & 1.71311886690676 \tabularnewline
99 & 2444.7 & 2450.11052472929 & -5.57486317177258 & -1.45459926709322 & -1.56341372861246 \tabularnewline
100 & 2425.3 & 2427.30361262367 & -8.70234367730859 & 0.580166599827987 & -1.01976991777142 \tabularnewline
101 & 2389.3 & 2393.32968373756 & -13.2891876479713 & -0.241323985982174 & -1.49523928222274 \tabularnewline
102 & 2367.7 & 2370.11257836805 & -15.0910327931577 & -0.924261739980083 & -0.587424004836978 \tabularnewline
103 & 2339.3 & 2341.48887984445 & -17.5470377316461 & -0.160063654610066 & -0.800747436805128 \tabularnewline
104 & 2342.4 & 2339.36964877298 & -14.747131775792 & 0.717330675573567 & 0.912914620770784 \tabularnewline
105 & 2343.6 & 2341.20041727363 & -11.7385178830024 & -0.085940137108499 & 0.980995259656445 \tabularnewline
106 & 2346.3 & 2343.76906470385 & -9.14199042132208 & 0.385789560197761 & 0.846651218070855 \tabularnewline
107 & 2363.5 & 2359.32558371874 & -4.65955828260701 & 0.47115166727921 & 1.4616110178508 \tabularnewline
108 & 2338.7 & 2341.87781670717 & -6.97967560351426 & -1.26142974034204 & -0.756525714467698 \tabularnewline
109 & 2369.4 & 2362.74922173045 & -1.9401851396455 & 2.47956530762287 & 1.67891457914711 \tabularnewline
110 & 2356 & 2355.9541006742 & -2.81755870229996 & 0.742800586069899 & -0.280386822749344 \tabularnewline
111 & 2348.6 & 2350.46532386189 & -3.30167533028218 & -1.46602697948677 & -0.15798702584049 \tabularnewline
112 & 2349.7 & 2348.63528716229 & -3.03462962033039 & 0.844332145970304 & 0.0870775693068053 \tabularnewline
113 & 2371.9 & 2368.33404820602 & 1.09086356045998 & 0.162383664794932 & 1.34486765517628 \tabularnewline
114 & 2364.9 & 2366.32834976113 & 0.528948762624683 & -0.964723588326429 & -0.183193478996922 \tabularnewline
115 & 2394.1 & 2390.59346408168 & 4.83608579284691 & -0.0474890657515876 & 1.40429739421019 \tabularnewline
116 & 2399.2 & 2398.46168112138 & 5.38628507775915 & 0.284300880819542 & 0.179394697456704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301200&T=1

[TABLE]
[ROW][C]Structural Time Series Model -- Interpolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]2119.9[/C][C]2119.9[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2108.7[/C][C]2110.0279752091[/C][C]-0.707250916295394[/C][C]-0.570591932414039[/C][C]-0.41196358187324[/C][/ROW]
[ROW][C]3[/C][C]2092[/C][C]2095.23102559922[/C][C]-1.80894957391344[/C][C]-0.771047769930013[/C][C]-0.908220477971867[/C][/ROW]
[ROW][C]4[/C][C]2104.2[/C][C]2103.19183507849[/C][C]-0.792885279732673[/C][C]-0.660804437871463[/C][C]0.619782096177108[/C][/ROW]
[ROW][C]5[/C][C]2110.1[/C][C]2109.58131431062[/C][C]0.117481218137906[/C][C]-0.669504627008983[/C][C]0.447037206068277[/C][/ROW]
[ROW][C]6[/C][C]2114[/C][C]2113.97549310793[/C][C]0.732788859469574[/C][C]-0.665586654025905[/C][C]0.26236626859254[/C][/ROW]
[ROW][C]7[/C][C]2138.8[/C][C]2136.01182462075[/C][C]4.05805975050061[/C][C]-0.587440025909538[/C][C]1.29326503070542[/C][/ROW]
[ROW][C]8[/C][C]2165.5[/C][C]2162.5506364164[/C][C]7.75747608575763[/C][C]-0.56723447027042[/C][C]1.35461119985305[/C][/ROW]
[ROW][C]9[/C][C]2155.1[/C][C]2157.71603290273[/C][C]5.61271742022658[/C][C]-0.663782324758044[/C][C]-0.75484088934367[/C][/ROW]
[ROW][C]10[/C][C]2135.2[/C][C]2139.54889724874[/C][C]1.47014113500555[/C][C]-0.684527318259551[/C][C]-1.42044971724949[/C][/ROW]
[ROW][C]11[/C][C]2163.1[/C][C]2160.64873470554[/C][C]4.94054073701393[/C][C]-0.561113392433952[/C][C]1.16971629293666[/C][/ROW]
[ROW][C]12[/C][C]2175.2[/C][C]2174.45654621743[/C][C]6.52343729785254[/C][C]-0.613535943522702[/C][C]0.527527019003593[/C][/ROW]
[ROW][C]13[/C][C]2183.3[/C][C]2178.30481056809[/C][C]6.07618176738808[/C][C]5.38651737995945[/C][C]-0.187149609622243[/C][/ROW]
[ROW][C]14[/C][C]2201.5[/C][C]2199.84270832951[/C][C]8.82577580592963[/C][C]-0.04246992509007[/C][C]0.77309961198664[/C][/ROW]
[ROW][C]15[/C][C]2212.3[/C][C]2211.95130935103[/C][C]9.41795876996284[/C][C]-0.149162602939263[/C][C]0.194743488461929[/C][/ROW]
[ROW][C]16[/C][C]2223.8[/C][C]2223.54009298868[/C][C]9.81109606695416[/C][C]-0.0699819550444313[/C][C]0.128722044980108[/C][/ROW]
[ROW][C]17[/C][C]2241.9[/C][C]2240.82510683683[/C][C]11.1663293648552[/C][C]-0.0598406221888267[/C][C]0.442860066748364[/C][/ROW]
[ROW][C]18[/C][C]2269.2[/C][C]2267.00699339347[/C][C]13.8910157298243[/C][C]-0.0863081044880633[/C][C]0.889645698415558[/C][/ROW]
[ROW][C]19[/C][C]2261.4[/C][C]2264.15663374427[/C][C]10.8517157588958[/C][C]-0.215434563799124[/C][C]-0.991911591928025[/C][/ROW]
[ROW][C]20[/C][C]2273.4[/C][C]2273.64073299712[/C][C]10.6033512118381[/C][C]-0.0331399637708015[/C][C]-0.0810327301732154[/C][/ROW]
[ROW][C]21[/C][C]2299.3[/C][C]2297.34008082953[/C][C]12.9821792728377[/C][C]-0.0279754616177687[/C][C]0.775978718740828[/C][/ROW]
[ROW][C]22[/C][C]2315.5[/C][C]2314.98264002979[/C][C]13.8288519838186[/C][C]-0.190072497162177[/C][C]0.276151338771876[/C][/ROW]
[ROW][C]23[/C][C]2338.7[/C][C]2337.42465621441[/C][C]15.3938292107964[/C][C]-0.0321458653903408[/C][C]0.510392187738888[/C][/ROW]
[ROW][C]24[/C][C]2333[/C][C]2335.77485876473[/C][C]12.2969978131147[/C][C]-0.187777531172401[/C][C]-1.0099056674519[/C][/ROW]
[ROW][C]25[/C][C]2311[/C][C]2320.95089101728[/C][C]7.45992613836058[/C][C]-5.9327302801285[/C][C]-1.75314110471905[/C][/ROW]
[ROW][C]26[/C][C]2303.6[/C][C]2306.2128424293[/C][C]3.49328377055339[/C][C]0.155556386652649[/C][C]-1.18622148503997[/C][/ROW]
[ROW][C]27[/C][C]2310.5[/C][C]2310.24034239207[/C][C]3.59012969439314[/C][C]0.17885192241974[/C][C]0.0316573657076356[/C][/ROW]
[ROW][C]28[/C][C]2295.8[/C][C]2298.09750111293[/C][C]0.73108173229416[/C][C]0.0856727581061134[/C][C]-0.93204971921255[/C][/ROW]
[ROW][C]29[/C][C]2265.5[/C][C]2269.88810583958[/C][C]-4.52838885535942[/C][C]-0.00609091702494724[/C][C]-1.71388285780337[/C][/ROW]
[ROW][C]30[/C][C]2271.1[/C][C]2270.00958655709[/C][C]-3.68344197619408[/C][C]0.386312703080863[/C][C]0.275383537670679[/C][/ROW]
[ROW][C]31[/C][C]2231.9[/C][C]2236.51329560895[/C][C]-9.10046592170624[/C][C]-0.0984437279989058[/C][C]-1.76579290324947[/C][/ROW]
[ROW][C]32[/C][C]2245[/C][C]2242.35323849099[/C][C]-6.38587825028812[/C][C]0.383988042745465[/C][C]0.88497753621253[/C][/ROW]
[ROW][C]33[/C][C]2249.7[/C][C]2247.62840525323[/C][C]-4.26716270695098[/C][C]0.305368935497063[/C][C]0.690770785290845[/C][/ROW]
[ROW][C]34[/C][C]2300.5[/C][C]2292.68107642522[/C][C]4.69384001876344[/C][C]0.348337184775301[/C][C]2.92172985896659[/C][/ROW]
[ROW][C]35[/C][C]2280.4[/C][C]2282.54981846525[/C][C]2.00020839158893[/C][C]0.0958955226171737[/C][C]-0.878289893995652[/C][/ROW]
[ROW][C]36[/C][C]2290.7[/C][C]2289.65303401798[/C][C]2.92730820933271[/C][C]0.274062246018663[/C][C]0.302284130445473[/C][/ROW]
[ROW][C]37[/C][C]2261.5[/C][C]2270.69815488851[/C][C]-1.00356739949062[/C][C]-5.93365671376412[/C][C]-1.37562216139352[/C][/ROW]
[ROW][C]38[/C][C]2259.1[/C][C]2260.06256648583[/C][C]-2.73138873679543[/C][C]0.305648124931859[/C][C]-0.529879346582519[/C][/ROW]
[ROW][C]39[/C][C]2249.8[/C][C]2250.41855541737[/C][C]-3.98480709837684[/C][C]0.425119115861769[/C][C]-0.409501904716866[/C][/ROW]
[ROW][C]40[/C][C]2271.2[/C][C]2267.34424915617[/C][C]-0.185736769059303[/C][C]0.694587383376491[/C][C]1.2385299405313[/C][/ROW]
[ROW][C]41[/C][C]2259[/C][C]2260.06682599476[/C][C]-1.47422697491745[/C][C]0.00492642740956051[/C][C]-0.419926104192948[/C][/ROW]
[ROW][C]42[/C][C]2259.4[/C][C]2258.5674886067[/C][C]-1.47878887147969[/C][C]0.836306481705146[/C][C]-0.00148695019982057[/C][/ROW]
[ROW][C]43[/C][C]2250.2[/C][C]2251.11719480113[/C][C]-2.56358774228233[/C][C]-0.0146089468717951[/C][C]-0.353636733507104[/C][/ROW]
[ROW][C]44[/C][C]2243.3[/C][C]2243.50242210972[/C][C]-3.48117037747006[/C][C]0.561111535060136[/C][C]-0.299152701583375[/C][/ROW]
[ROW][C]45[/C][C]2234.3[/C][C]2234.92851387827[/C][C]-4.40628948335344[/C][C]0.141342677743515[/C][C]-0.301628099143173[/C][/ROW]
[ROW][C]46[/C][C]2216.5[/C][C]2217.8488143544[/C][C]-6.70847091621041[/C][C]0.567080919146243[/C][C]-0.750640112749196[/C][/ROW]
[ROW][C]47[/C][C]2197.6[/C][C]2199.22576459562[/C][C]-8.87283655544266[/C][C]0.175504894469541[/C][C]-0.705727349551415[/C][/ROW]
[ROW][C]48[/C][C]2211.7[/C][C]2208.20592194399[/C][C]-5.63017510583331[/C][C]0.795617845285365[/C][C]1.05727504071943[/C][/ROW]
[ROW][C]49[/C][C]2206.7[/C][C]2209.36618296698[/C][C]-4.40680380463882[/C][C]-3.68217100418007[/C][C]0.42060331023624[/C][/ROW]
[ROW][C]50[/C][C]2214.6[/C][C]2213.0553326582[/C][C]-2.95079692251478[/C][C]0.445715695993674[/C][C]0.452826809952015[/C][/ROW]
[ROW][C]51[/C][C]2229.8[/C][C]2226.85957834341[/C][C]0.0873697731847507[/C][C]0.415493182428708[/C][C]0.992259535881776[/C][/ROW]
[ROW][C]52[/C][C]2219.5[/C][C]2219.91566065091[/C][C]-1.18978637611864[/C][C]0.645301478075312[/C][C]-0.4163841691435[/C][/ROW]
[ROW][C]53[/C][C]2213.8[/C][C]2214.45045294454[/C][C]-1.96640063521392[/C][C]-0.00550171437503547[/C][C]-0.253126298639038[/C][/ROW]
[ROW][C]54[/C][C]2214.1[/C][C]2213.08667625146[/C][C]-1.85694462795501[/C][C]0.922413004607261[/C][C]0.0356797736557719[/C][/ROW]
[ROW][C]55[/C][C]2224.1[/C][C]2222.28001238149[/C][C]0.150045066364445[/C][C]0.15284492412842[/C][C]0.654296949413813[/C][/ROW]
[ROW][C]56[/C][C]2229.6[/C][C]2228.12268021904[/C][C]1.18393243673766[/C][C]0.618431688127571[/C][C]0.337081829323051[/C][/ROW]
[ROW][C]57[/C][C]2251.7[/C][C]2248.38534604401[/C][C]4.64895341594922[/C][C]0.435976015919576[/C][C]1.12976876837919[/C][/ROW]
[ROW][C]58[/C][C]2262.9[/C][C]2260.96101908652[/C][C]6.0885808645659[/C][C]0.742917471113593[/C][C]0.469406375047131[/C][/ROW]
[ROW][C]59[/C][C]2268.9[/C][C]2268.61701369116[/C][C]6.37325408823684[/C][C]0.0464680604159117[/C][C]0.0928234846010845[/C][/ROW]
[ROW][C]60[/C][C]2293.7[/C][C]2290.44335336166[/C][C]9.17931588429349[/C][C]0.92551713509914[/C][C]0.914920607108833[/C][/ROW]
[ROW][C]61[/C][C]2312.4[/C][C]2313.56480422696[/C][C]11.695299009555[/C][C]-3.25341356385219[/C][C]0.855583236651448[/C][/ROW]
[ROW][C]62[/C][C]2342[/C][C]2339.6500144129[/C][C]14.2876053060935[/C][C]0.358257728616137[/C][C]0.813614332364[/C][/ROW]
[ROW][C]63[/C][C]2327.4[/C][C]2330.81299696172[/C][C]10.0946897164509[/C][C]0.0654281706989805[/C][C]-1.36908041534213[/C][/ROW]
[ROW][C]64[/C][C]2366.2[/C][C]2362.02484420244[/C][C]13.9295320820333[/C][C]0.994395025263956[/C][C]1.25030016663251[/C][/ROW]
[ROW][C]65[/C][C]2371.8[/C][C]2372.49078209642[/C][C]13.3005235763209[/C][C]-0.169207374242545[/C][C]-0.205028529015853[/C][/ROW]
[ROW][C]66[/C][C]2364.4[/C][C]2366.72763569804[/C][C]9.83868193750524[/C][C]0.54324916704985[/C][C]-1.12852245343061[/C][/ROW]
[ROW][C]67[/C][C]2370.5[/C][C]2371.20774473668[/C][C]8.86563996698714[/C][C]0.0992771190465357[/C][C]-0.317230938975759[/C][/ROW]
[ROW][C]68[/C][C]2412.8[/C][C]2407.85466122096[/C][C]13.9102232792184[/C][C]0.761166705398315[/C][C]1.64473862591387[/C][/ROW]
[ROW][C]69[/C][C]2447.3[/C][C]2443.54505036471[/C][C]17.8650781713734[/C][C]0.474486211169569[/C][C]1.28949776553003[/C][/ROW]
[ROW][C]70[/C][C]2443.5[/C][C]2445.47679317785[/C][C]14.9718884882493[/C][C]0.423125493017191[/C][C]-0.943366276506526[/C][/ROW]
[ROW][C]71[/C][C]2459.3[/C][C]2459.52000198589[/C][C]14.8032554845712[/C][C]-0.0801158784431939[/C][C]-0.0549866234863027[/C][/ROW]
[ROW][C]72[/C][C]2480.7[/C][C]2479.14885212456[/C][C]15.6793046550327[/C][C]0.824544462620104[/C][C]0.285638637047674[/C][/ROW]
[ROW][C]73[/C][C]2504.4[/C][C]2505.97918849403[/C][C]17.6937414660926[/C][C]-3.25038498983337[/C][C]0.679904696229089[/C][/ROW]
[ROW][C]74[/C][C]2505.5[/C][C]2507.45145044214[/C][C]14.7680540461906[/C][C]0.324207429834018[/C][C]-0.924197916057099[/C][/ROW]
[ROW][C]75[/C][C]2534[/C][C]2532.6245583174[/C][C]16.6544934688799[/C][C]-0.186972990155257[/C][C]0.615856475858866[/C][/ROW]
[ROW][C]76[/C][C]2538.7[/C][C]2539.54498023637[/C][C]14.88717087849[/C][C]0.618794675905235[/C][C]-0.576231400048928[/C][/ROW]
[ROW][C]77[/C][C]2538.1[/C][C]2540.46510142757[/C][C]12.3511973164735[/C][C]-0.265273036445513[/C][C]-0.826646812036516[/C][/ROW]
[ROW][C]78[/C][C]2522[/C][C]2525.85163415345[/C][C]7.45556033632426[/C][C]0.202454991631498[/C][C]-1.59597558774809[/C][/ROW]
[ROW][C]79[/C][C]2566.4[/C][C]2561.92478801108[/C][C]12.6511063661366[/C][C]0.172364952260288[/C][C]1.69388929464341[/C][/ROW]
[ROW][C]80[/C][C]2572.8[/C][C]2572.91832638291[/C][C]12.350179275574[/C][C]0.130910862461761[/C][C]-0.0981159234532809[/C][/ROW]
[ROW][C]81[/C][C]2557.3[/C][C]2560.82578488317[/C][C]7.91270021489583[/C][C]0.149627184178221[/C][C]-1.44687441218168[/C][/ROW]
[ROW][C]82[/C][C]2541[/C][C]2544.58726245098[/C][C]3.52812759283951[/C][C]0.0444443342312502[/C][C]-1.42966434485416[/C][/ROW]
[ROW][C]83[/C][C]2540.7[/C][C]2541.90560513549[/C][C]2.40074659461792[/C][C]-0.271781045496277[/C][C]-0.367609935430232[/C][/ROW]
[ROW][C]84[/C][C]2508.5[/C][C]2513.04953896669[/C][C]-3.2723930592958[/C][C]0.148771325096195[/C][C]-1.84976792556492[/C][/ROW]
[ROW][C]85[/C][C]2567.1[/C][C]2558.22708508789[/C][C]5.4864515792675[/C][C]1.61184009940587[/C][C]2.94006873734885[/C][/ROW]
[ROW][C]86[/C][C]2553.6[/C][C]2555.13948307837[/C][C]3.93872600349097[/C][C]-0.324816964604739[/C][C]-0.491279338789482[/C][/ROW]
[ROW][C]87[/C][C]2522.4[/C][C]2528.04302018134[/C][C]-1.68730110454502[/C][C]-0.990392154431384[/C][C]-1.83643767495332[/C][/ROW]
[ROW][C]88[/C][C]2520.6[/C][C]2520.97289686461[/C][C]-2.66441820003894[/C][C]0.435324991054683[/C][C]-0.318596566705055[/C][/ROW]
[ROW][C]89[/C][C]2499.4[/C][C]2502.2228068133[/C][C]-5.58451129487483[/C][C]-0.408120089534752[/C][C]-0.951884685118144[/C][/ROW]
[ROW][C]90[/C][C]2470.8[/C][C]2474.92293586848[/C][C]-9.52636740514243[/C][C]-0.863012404817024[/C][C]-1.28507288981117[/C][/ROW]
[ROW][C]91[/C][C]2479.3[/C][C]2477.45756570253[/C][C]-7.33708187250148[/C][C]0.0317336997568365[/C][C]0.713778370919629[/C][/ROW]
[ROW][C]92[/C][C]2481.8[/C][C]2480.17096040849[/C][C]-5.51277221116602[/C][C]0.120116142726685[/C][C]0.594814582425995[/C][/ROW]
[ROW][C]93[/C][C]2470.3[/C][C]2470.90863700111[/C][C]-6.19336678135286[/C][C]-0.0456821693403476[/C][C]-0.221914834804166[/C][/ROW]
[ROW][C]94[/C][C]2491[/C][C]2487.51062123486[/C][C]-2.05568227252612[/C][C]0.0667838919061692[/C][C]1.34917049792189[/C][/ROW]
[ROW][C]95[/C][C]2479.1[/C][C]2480.1924585532[/C][C]-3.01090943132788[/C][C]-0.302300601287815[/C][C]-0.311475823693473[/C][/ROW]
[ROW][C]96[/C][C]2456.6[/C][C]2460.15129740665[/C][C]-6.10125648167838[/C][C]-0.995498486169947[/C][C]-1.00764949100196[/C][/ROW]
[ROW][C]97[/C][C]2456.1[/C][C]2453.71734759708[/C][C]-6.16143241181032[/C][C]2.432499434825[/C][C]-0.020114486387768[/C][/ROW]
[ROW][C]98[/C][C]2482.2[/C][C]2477.32291823324[/C][C]-0.784663767116208[/C][C]0.628717884644647[/C][C]1.71311886690676[/C][/ROW]
[ROW][C]99[/C][C]2444.7[/C][C]2450.11052472929[/C][C]-5.57486317177258[/C][C]-1.45459926709322[/C][C]-1.56341372861246[/C][/ROW]
[ROW][C]100[/C][C]2425.3[/C][C]2427.30361262367[/C][C]-8.70234367730859[/C][C]0.580166599827987[/C][C]-1.01976991777142[/C][/ROW]
[ROW][C]101[/C][C]2389.3[/C][C]2393.32968373756[/C][C]-13.2891876479713[/C][C]-0.241323985982174[/C][C]-1.49523928222274[/C][/ROW]
[ROW][C]102[/C][C]2367.7[/C][C]2370.11257836805[/C][C]-15.0910327931577[/C][C]-0.924261739980083[/C][C]-0.587424004836978[/C][/ROW]
[ROW][C]103[/C][C]2339.3[/C][C]2341.48887984445[/C][C]-17.5470377316461[/C][C]-0.160063654610066[/C][C]-0.800747436805128[/C][/ROW]
[ROW][C]104[/C][C]2342.4[/C][C]2339.36964877298[/C][C]-14.747131775792[/C][C]0.717330675573567[/C][C]0.912914620770784[/C][/ROW]
[ROW][C]105[/C][C]2343.6[/C][C]2341.20041727363[/C][C]-11.7385178830024[/C][C]-0.085940137108499[/C][C]0.980995259656445[/C][/ROW]
[ROW][C]106[/C][C]2346.3[/C][C]2343.76906470385[/C][C]-9.14199042132208[/C][C]0.385789560197761[/C][C]0.846651218070855[/C][/ROW]
[ROW][C]107[/C][C]2363.5[/C][C]2359.32558371874[/C][C]-4.65955828260701[/C][C]0.47115166727921[/C][C]1.4616110178508[/C][/ROW]
[ROW][C]108[/C][C]2338.7[/C][C]2341.87781670717[/C][C]-6.97967560351426[/C][C]-1.26142974034204[/C][C]-0.756525714467698[/C][/ROW]
[ROW][C]109[/C][C]2369.4[/C][C]2362.74922173045[/C][C]-1.9401851396455[/C][C]2.47956530762287[/C][C]1.67891457914711[/C][/ROW]
[ROW][C]110[/C][C]2356[/C][C]2355.9541006742[/C][C]-2.81755870229996[/C][C]0.742800586069899[/C][C]-0.280386822749344[/C][/ROW]
[ROW][C]111[/C][C]2348.6[/C][C]2350.46532386189[/C][C]-3.30167533028218[/C][C]-1.46602697948677[/C][C]-0.15798702584049[/C][/ROW]
[ROW][C]112[/C][C]2349.7[/C][C]2348.63528716229[/C][C]-3.03462962033039[/C][C]0.844332145970304[/C][C]0.0870775693068053[/C][/ROW]
[ROW][C]113[/C][C]2371.9[/C][C]2368.33404820602[/C][C]1.09086356045998[/C][C]0.162383664794932[/C][C]1.34486765517628[/C][/ROW]
[ROW][C]114[/C][C]2364.9[/C][C]2366.32834976113[/C][C]0.528948762624683[/C][C]-0.964723588326429[/C][C]-0.183193478996922[/C][/ROW]
[ROW][C]115[/C][C]2394.1[/C][C]2390.59346408168[/C][C]4.83608579284691[/C][C]-0.0474890657515876[/C][C]1.40429739421019[/C][/ROW]
[ROW][C]116[/C][C]2399.2[/C][C]2398.46168112138[/C][C]5.38628507775915[/C][C]0.284300880819542[/C][C]0.179394697456704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301200&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
12119.92119.9000
22108.72110.0279752091-0.707250916295394-0.570591932414039-0.41196358187324
320922095.23102559922-1.80894957391344-0.771047769930013-0.908220477971867
42104.22103.19183507849-0.792885279732673-0.6608044378714630.619782096177108
52110.12109.581314310620.117481218137906-0.6695046270089830.447037206068277
621142113.975493107930.732788859469574-0.6655866540259050.26236626859254
72138.82136.011824620754.05805975050061-0.5874400259095381.29326503070542
82165.52162.55063641647.75747608575763-0.567234470270421.35461119985305
92155.12157.716032902735.61271742022658-0.663782324758044-0.75484088934367
102135.22139.548897248741.47014113500555-0.684527318259551-1.42044971724949
112163.12160.648734705544.94054073701393-0.5611133924339521.16971629293666
122175.22174.456546217436.52343729785254-0.6135359435227020.527527019003593
132183.32178.304810568096.076181767388085.38651737995945-0.187149609622243
142201.52199.842708329518.82577580592963-0.042469925090070.77309961198664
152212.32211.951309351039.41795876996284-0.1491626029392630.194743488461929
162223.82223.540092988689.81109606695416-0.06998195504443130.128722044980108
172241.92240.8251068368311.1663293648552-0.05984062218882670.442860066748364
182269.22267.0069933934713.8910157298243-0.08630810448806330.889645698415558
192261.42264.1566337442710.8517157588958-0.215434563799124-0.991911591928025
202273.42273.6407329971210.6033512118381-0.0331399637708015-0.0810327301732154
212299.32297.3400808295312.9821792728377-0.02797546161776870.775978718740828
222315.52314.9826400297913.8288519838186-0.1900724971621770.276151338771876
232338.72337.4246562144115.3938292107964-0.03214586539034080.510392187738888
2423332335.7748587647312.2969978131147-0.187777531172401-1.0099056674519
2523112320.950891017287.45992613836058-5.9327302801285-1.75314110471905
262303.62306.21284242933.493283770553390.155556386652649-1.18622148503997
272310.52310.240342392073.590129694393140.178851922419740.0316573657076356
282295.82298.097501112930.731081732294160.0856727581061134-0.93204971921255
292265.52269.88810583958-4.52838885535942-0.00609091702494724-1.71388285780337
302271.12270.00958655709-3.683441976194080.3863127030808630.275383537670679
312231.92236.51329560895-9.10046592170624-0.0984437279989058-1.76579290324947
3222452242.35323849099-6.385878250288120.3839880427454650.88497753621253
332249.72247.62840525323-4.267162706950980.3053689354970630.690770785290845
342300.52292.681076425224.693840018763440.3483371847753012.92172985896659
352280.42282.549818465252.000208391588930.0958955226171737-0.878289893995652
362290.72289.653034017982.927308209332710.2740622460186630.302284130445473
372261.52270.69815488851-1.00356739949062-5.93365671376412-1.37562216139352
382259.12260.06256648583-2.731388736795430.305648124931859-0.529879346582519
392249.82250.41855541737-3.984807098376840.425119115861769-0.409501904716866
402271.22267.34424915617-0.1857367690593030.6945873833764911.2385299405313
4122592260.06682599476-1.474226974917450.00492642740956051-0.419926104192948
422259.42258.5674886067-1.478788871479690.836306481705146-0.00148695019982057
432250.22251.11719480113-2.56358774228233-0.0146089468717951-0.353636733507104
442243.32243.50242210972-3.481170377470060.561111535060136-0.299152701583375
452234.32234.92851387827-4.406289483353440.141342677743515-0.301628099143173
462216.52217.8488143544-6.708470916210410.567080919146243-0.750640112749196
472197.62199.22576459562-8.872836555442660.175504894469541-0.705727349551415
482211.72208.20592194399-5.630175105833310.7956178452853651.05727504071943
492206.72209.36618296698-4.40680380463882-3.682171004180070.42060331023624
502214.62213.0553326582-2.950796922514780.4457156959936740.452826809952015
512229.82226.859578343410.08736977318475070.4154931824287080.992259535881776
522219.52219.91566065091-1.189786376118640.645301478075312-0.4163841691435
532213.82214.45045294454-1.96640063521392-0.00550171437503547-0.253126298639038
542214.12213.08667625146-1.856944627955010.9224130046072610.0356797736557719
552224.12222.280012381490.1500450663644450.152844924128420.654296949413813
562229.62228.122680219041.183932436737660.6184316881275710.337081829323051
572251.72248.385346044014.648953415949220.4359760159195761.12976876837919
582262.92260.961019086526.08858086456590.7429174711135930.469406375047131
592268.92268.617013691166.373254088236840.04646806041591170.0928234846010845
602293.72290.443353361669.179315884293490.925517135099140.914920607108833
612312.42313.5648042269611.695299009555-3.253413563852190.855583236651448
6223422339.650014412914.28760530609350.3582577286161370.813614332364
632327.42330.8129969617210.09468971645090.0654281706989805-1.36908041534213
642366.22362.0248442024413.92953208203330.9943950252639561.25030016663251
652371.82372.4907820964213.3005235763209-0.169207374242545-0.205028529015853
662364.42366.727635698049.838681937505240.54324916704985-1.12852245343061
672370.52371.207744736688.865639966987140.0992771190465357-0.317230938975759
682412.82407.8546612209613.91022327921840.7611667053983151.64473862591387
692447.32443.5450503647117.86507817137340.4744862111695691.28949776553003
702443.52445.4767931778514.97188848824930.423125493017191-0.943366276506526
712459.32459.5200019858914.8032554845712-0.0801158784431939-0.0549866234863027
722480.72479.1488521245615.67930465503270.8245444626201040.285638637047674
732504.42505.9791884940317.6937414660926-3.250384989833370.679904696229089
742505.52507.4514504421414.76805404619060.324207429834018-0.924197916057099
7525342532.624558317416.6544934688799-0.1869729901552570.615856475858866
762538.72539.5449802363714.887170878490.618794675905235-0.576231400048928
772538.12540.4651014275712.3511973164735-0.265273036445513-0.826646812036516
7825222525.851634153457.455560336324260.202454991631498-1.59597558774809
792566.42561.9247880110812.65110636613660.1723649522602881.69388929464341
802572.82572.9183263829112.3501792755740.130910862461761-0.0981159234532809
812557.32560.825784883177.912700214895830.149627184178221-1.44687441218168
8225412544.587262450983.528127592839510.0444443342312502-1.42966434485416
832540.72541.905605135492.40074659461792-0.271781045496277-0.367609935430232
842508.52513.04953896669-3.27239305929580.148771325096195-1.84976792556492
852567.12558.227085087895.48645157926751.611840099405872.94006873734885
862553.62555.139483078373.93872600349097-0.324816964604739-0.491279338789482
872522.42528.04302018134-1.68730110454502-0.990392154431384-1.83643767495332
882520.62520.97289686461-2.664418200038940.435324991054683-0.318596566705055
892499.42502.2228068133-5.58451129487483-0.408120089534752-0.951884685118144
902470.82474.92293586848-9.52636740514243-0.863012404817024-1.28507288981117
912479.32477.45756570253-7.337081872501480.03173369975683650.713778370919629
922481.82480.17096040849-5.512772211166020.1201161427266850.594814582425995
932470.32470.90863700111-6.19336678135286-0.0456821693403476-0.221914834804166
9424912487.51062123486-2.055682272526120.06678389190616921.34917049792189
952479.12480.1924585532-3.01090943132788-0.302300601287815-0.311475823693473
962456.62460.15129740665-6.10125648167838-0.995498486169947-1.00764949100196
972456.12453.71734759708-6.161432411810322.432499434825-0.020114486387768
982482.22477.32291823324-0.7846637671162080.6287178846446471.71311886690676
992444.72450.11052472929-5.57486317177258-1.45459926709322-1.56341372861246
1002425.32427.30361262367-8.702343677308590.580166599827987-1.01976991777142
1012389.32393.32968373756-13.2891876479713-0.241323985982174-1.49523928222274
1022367.72370.11257836805-15.0910327931577-0.924261739980083-0.587424004836978
1032339.32341.48887984445-17.5470377316461-0.160063654610066-0.800747436805128
1042342.42339.36964877298-14.7471317757920.7173306755735670.912914620770784
1052343.62341.20041727363-11.7385178830024-0.0859401371084990.980995259656445
1062346.32343.76906470385-9.141990421322080.3857895601977610.846651218070855
1072363.52359.32558371874-4.659558282607010.471151667279211.4616110178508
1082338.72341.87781670717-6.97967560351426-1.26142974034204-0.756525714467698
1092369.42362.74922173045-1.94018513964552.479565307622871.67891457914711
11023562355.9541006742-2.817558702299960.742800586069899-0.280386822749344
1112348.62350.46532386189-3.30167533028218-1.46602697948677-0.15798702584049
1122349.72348.63528716229-3.034629620330390.8443321459703040.0870775693068053
1132371.92368.334048206021.090863560459980.1623836647949321.34486765517628
1142364.92366.328349761130.528948762624683-0.964723588326429-0.183193478996922
1152394.12390.593464081684.83608579284691-0.04748906575158761.40429739421019
1162399.22398.461681121385.386285077759150.2843008808195420.179394697456704







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
12408.12021236792408.33852558568-0.21831321777124
22416.294145700612414.030789637252.26335606336602
32424.304002504252419.723053688824.58094881542668
42426.317675249752425.41531774040.902357509354728
52440.106855802142431.107581791978.99927401017616
62446.393168063412436.799845843549.59332221987283
72443.744399774772442.492109895111.25228987965203
82451.118127207752448.184373946692.93375326106343
92449.186913840542453.87663799826-4.68972415772462
102447.12471430092459.56890204983-12.4441877489306
112454.716293985412465.26116610141-10.5448721159971
122468.325225634492470.95343015298-2.6282045184883

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 2408.1202123679 & 2408.33852558568 & -0.21831321777124 \tabularnewline
2 & 2416.29414570061 & 2414.03078963725 & 2.26335606336602 \tabularnewline
3 & 2424.30400250425 & 2419.72305368882 & 4.58094881542668 \tabularnewline
4 & 2426.31767524975 & 2425.4153177404 & 0.902357509354728 \tabularnewline
5 & 2440.10685580214 & 2431.10758179197 & 8.99927401017616 \tabularnewline
6 & 2446.39316806341 & 2436.79984584354 & 9.59332221987283 \tabularnewline
7 & 2443.74439977477 & 2442.49210989511 & 1.25228987965203 \tabularnewline
8 & 2451.11812720775 & 2448.18437394669 & 2.93375326106343 \tabularnewline
9 & 2449.18691384054 & 2453.87663799826 & -4.68972415772462 \tabularnewline
10 & 2447.1247143009 & 2459.56890204983 & -12.4441877489306 \tabularnewline
11 & 2454.71629398541 & 2465.26116610141 & -10.5448721159971 \tabularnewline
12 & 2468.32522563449 & 2470.95343015298 & -2.6282045184883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301200&T=2

[TABLE]
[ROW][C]Structural Time Series Model -- Extrapolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Seasonal[/C][/ROW]
[ROW][C]1[/C][C]2408.1202123679[/C][C]2408.33852558568[/C][C]-0.21831321777124[/C][/ROW]
[ROW][C]2[/C][C]2416.29414570061[/C][C]2414.03078963725[/C][C]2.26335606336602[/C][/ROW]
[ROW][C]3[/C][C]2424.30400250425[/C][C]2419.72305368882[/C][C]4.58094881542668[/C][/ROW]
[ROW][C]4[/C][C]2426.31767524975[/C][C]2425.4153177404[/C][C]0.902357509354728[/C][/ROW]
[ROW][C]5[/C][C]2440.10685580214[/C][C]2431.10758179197[/C][C]8.99927401017616[/C][/ROW]
[ROW][C]6[/C][C]2446.39316806341[/C][C]2436.79984584354[/C][C]9.59332221987283[/C][/ROW]
[ROW][C]7[/C][C]2443.74439977477[/C][C]2442.49210989511[/C][C]1.25228987965203[/C][/ROW]
[ROW][C]8[/C][C]2451.11812720775[/C][C]2448.18437394669[/C][C]2.93375326106343[/C][/ROW]
[ROW][C]9[/C][C]2449.18691384054[/C][C]2453.87663799826[/C][C]-4.68972415772462[/C][/ROW]
[ROW][C]10[/C][C]2447.1247143009[/C][C]2459.56890204983[/C][C]-12.4441877489306[/C][/ROW]
[ROW][C]11[/C][C]2454.71629398541[/C][C]2465.26116610141[/C][C]-10.5448721159971[/C][/ROW]
[ROW][C]12[/C][C]2468.32522563449[/C][C]2470.95343015298[/C][C]-2.6282045184883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301200&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
12408.12021236792408.33852558568-0.21831321777124
22416.294145700612414.030789637252.26335606336602
32424.304002504252419.723053688824.58094881542668
42426.317675249752425.41531774040.902357509354728
52440.106855802142431.107581791978.99927401017616
62446.393168063412436.799845843549.59332221987283
72443.744399774772442.492109895111.25228987965203
82451.118127207752448.184373946692.93375326106343
92449.186913840542453.87663799826-4.68972415772462
102447.12471430092459.56890204983-12.4441877489306
112454.716293985412465.26116610141-10.5448721159971
122468.325225634492470.95343015298-2.6282045184883



Parameters (Session):
par1 = n1862 ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
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()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',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')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,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,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')