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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationTue, 13 Dec 2016 12:25:18 +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/13/t1481628339ok81n4yp7vqpaa8.htm/, Retrieved Sat, 04 May 2024 22:54:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299067, Retrieved Sat, 04 May 2024 22:54:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
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...] [2016-12-13 11:25:18] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataseries X:
4028.8
4076.6
4125.8
4177.2
4183
4222.6
4255.8
4260.8
4279.2
4328.8
4356.6
4393
4419.4
4426.2
4467.2
4517.4
4517
4560.4
4589
4596
4621.2
4654.6
4708.6
4774.4
4824.8
4839
4869.8
4895.8
4895.8
4968.8
5010
5032.4
5054
5083.8
5117.4
5170.8
5182.2
5163.6
5212.6
5288
5303.4
5367.6
5433.8
5465.8
5493.8
5549.4
5590.2
5661.2
5699
5654.2
5671.8
5730.8
5693
5720.4
5747.8
5764.2
5783
5822.4
5836.2
5864.6
5913.4
5906.8
5954
6031.2
6011.2
6059.8
6091.6
6088
6082.2
6108
6151.4
6187
6190
6152.2
6183.8
6222.8
6165.8
6223.4
6292.8
6320.6
6344
6391.2
6443.4
6504
6520.2
6518.8
6563.8
6614
6555.6
6601.8
6632.4
6657.8
6674.4
6687
6697.6
6732
6736.4
6745.8
6805.2
6850.4
6807.2
6844.6
6850.8
6848.2
6837.8
6857.6
6900.8
6940.8
6937.4
6950.4
6978.8
6997.8
6934.8
6946.8
6956.2
6968.2




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=299067&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=299067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299067&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
14028.84028.8000
24076.64071.4925873331343.11468633952015.107412666873613.18324427625824
34125.84127.0636233991653.0980646452199-1.26362339915760.748015158886424
44177.24178.2271059190351.50384469931-1.02710591902977-0.11136139218763
541834189.339681855818.7048272346304-6.33968185580101-2.29195063639123
64222.64219.0607135645527.6701541459663.539286435445960.627453276673477
74255.84255.0074282522834.4108081849860.7925717477185890.471487476437519
84260.84265.0788600801914.5892084154458-4.27886008019277-1.38651999172906
94279.24278.3425901926413.50988601569640.857409807362202-0.0754978025623251
104328.84323.7017497168139.44381443155155.098250283192251.81405874190837
114356.64358.7658495801535.8774878387245-2.16584958015181-0.249461872142069
1243934393.0818982649434.6060258521935-0.081898264939052-0.0889378084383588
134419.44420.4404936022728.7131576371833-1.04049360227512-0.412982005472812
144426.24428.6728816517812.0161443595529-2.47288165178182-1.18354901714989
154467.24464.5539742277630.59394267744392.646025772243471.30491870115938
164517.44507.9259138882740.65122940403159.47408611173040.709235280985577
1745174529.573612673825.7679485724673-12.5736126737983-1.03820486048216
184560.44558.7931427804128.46522373053821.606857219591680.18873821078402
1945894583.438296208825.47607778350765.56170379120464-0.209119054775167
2045964599.6108328844718.1943560461439-3.61083288446558-0.509336622415236
214621.24624.685706947223.5793527800971-3.485706947202650.376678197600356
224654.64648.9162064495324.08895196962845.683793550467930.0356463699267106
234708.64705.6239127864349.61581660195372.976087213571671.78559659026096
244774.44771.6504528847162.45180485678092.749547115290210.89795186182572
254824.84823.5030155249254.16382658650471.29698447507588-0.581054112912117
2648394851.5931402944333.7500330019437-12.5931402944289-1.42996595905468
274869.84872.1294921741123.5437974955195-2.32949217410501-0.713932884417527
284895.84883.9030547793814.427474149109111.8969452206225-0.640937223418529
294895.84907.7192537147421.702938892628-11.91925371473930.508316472259119
304968.84961.3253597619546.35316341268877.474640238052761.72347445808952
3150105003.5259208491343.14271796333056.47407915087069-0.224629585274748
325032.45037.5925512411236.121960156893-5.19255124111596-0.491092222646152
3350545058.0417390256223.9975361789036-4.04173902561687-0.848088365446547
345083.85084.1746390417225.6493819823249-0.3746390417197180.115549892886955
355117.45118.1154833930432.0617683501385-0.7154833930361430.448534645617687
365170.85165.1226472136643.61323743387315.677352786337970.808291758741012
375182.25181.4320545513422.50014064253770.767945448661859-1.47934261917942
385163.65177.060467778621.72879389896969-13.4604677786198-1.45265318520518
395212.65205.2286132712922.04078118698867.371386728707541.42053741887002
4052885269.8664956622354.796855308974918.13350433777362.29796999567432
415303.45323.9134056444654.2193326224473-20.5134056444562-0.0403889756591417
425367.65362.8598299175242.48230678678884.74017008248153-0.820423551321668
435433.85422.4986978477955.665362329548711.30130215221080.922299375864107
445465.85468.683242681448.3759243466899-2.88324268140262-0.509913127833444
455493.85500.3429784805135.5212762202476-6.54297848051269-0.899161057986395
465549.45550.0401349048446.421843744715-0.6401349048377060.762514779510167
475590.25596.6242315949946.5465653033694-6.424231594993720.00872412531505642
485661.25647.862547787450.151658136420913.33745221259860.25229186182698
4956995690.8556853294744.64804425019748.14431467052753-0.385386682295811
505654.25681.866268280843.44372854858633-27.6662682808438-2.88099111466219
515671.85675.5313192939-4.04192283228323-3.73131929390266-0.523541812701493
525730.85706.2656323302122.591565186659224.53436766978571.86635092239484
5356935713.096252792710.5047165066805-20.0962527926959-0.845610391295979
545720.45720.383197672368.040170818729510.0168023276363565-0.172284539807861
555747.85733.213269513311.707190107258414.5867304867030.256507903025478
565764.25759.849516616923.14195086546314.350483383103320.799902424273524
5757835791.3422525111129.5396963703684-8.342252511105980.447513092523713
585822.45823.6390085762531.6518350826126-1.239008576245830.147744819285755
595836.25847.8509343742725.9540931628536-11.6509343742682-0.398564984850663
605864.65854.7613695378611.37218377793199.83863046214156-1.02047252530849
615913.45887.9996228876328.122821557113225.40037711236861.17246048205573
625906.85929.9494104640438.7061069996228-23.14941046404250.739989148715033
6359545966.8350748558637.3158741712887-12.8350748558558-0.0972365951719047
646031.26002.7573274463936.251312512648928.4426725536089-0.0745543115633263
656011.26031.0094777518230.1341741325703-19.8094777518223-0.428014296076105
666059.86060.1847258657229.4013898771675-0.384725865723167-0.0512327864380162
676091.66081.7949218357923.45076189948789.80507816421297-0.416198769068334
6860886088.9032823972110.9652433627557-0.903282397209089-0.873392703207555
696082.26092.887903650365.6307135189045-10.6879036503588-0.373145482157314
7061086105.588468859411.03322018332152.411531140603120.377902653408987
716151.46151.2663012168737.50070902681510.1336987831337621.85151081196775
7261876183.1428637030833.2040678126393.85713629692289-0.300671203993712
7361906174.860426668971.4998119956361215.1395733310306-2.21855182789073
746152.26175.111349932690.546141526119766-22.9113499326945-0.0666847103301515
756183.86194.0602964300214.576792329766-10.26029643002230.981371523781979
766222.86195.696904774714.7092056251914527.1030952252893-0.690811804142912
776165.86188.12371731001-4.66501544923577-22.3237173100057-0.655928441015458
786223.46216.5460198016320.57822594613926.853980198366221.76512709326029
796292.86272.7091753804347.713073573783420.09082461957291.89775015726209
806320.66318.7737180633546.4558266925011.82628193664879-0.0879448130700021
8163446357.3786202660640.4670004937962-13.3786202660632-0.418915884019981
826391.26398.8918605622441.2650758248999-7.691860562238160.0558252308428943
836443.46442.9600247782943.40293936530170.4399752217066120.149557195229577
8465046489.6479725832845.908549383340814.35202741671970.175326093697123
856520.26509.5194793689726.044972637384610.6805206310325-1.38975178280088
866518.86544.3927738264332.7754741298987-25.59277382642840.470649891881673
876563.86570.6563505081827.8166227072361-6.85635050817958-0.346852938405403
8866146583.8303130315816.664728129240230.1696869684227-0.780553803965433
896555.66587.01930809256.3943102610478-31.4193080925045-0.718631267573772
906601.86602.1019279640513.0147723260822-0.3019279640469840.462984212162373
916632.46612.5625730384811.069418399027419.8374269615165-0.13605055658131
926657.86649.3346281697930.6461899309988.465371830212451.36935757144204
936674.46687.1619450715336.116709375457-12.76194507153050.382662411806987
9466876700.0317697014818.4074310442073-13.0317697014833-1.23878100072393
956697.66701.128809987695.22156480095135-3.52880998769029-0.922456668663583
9667326711.12887823338.8619451170588120.87112176670110.254713725643502
976736.46727.8329958815914.83700410611498.567004118413280.417999778892581
986745.86766.6094621898233.065902122045-20.80946218981581.27476350934579
996805.26807.2569283675138.8339571158027-2.056928367507220.403458962178834
1006850.46820.5131737877219.372548365753929.8868262122779-1.36196883768886
1016807.26839.3653396223418.976374122415-32.1653396223426-0.0277202034922632
1026844.66846.244380306119.76717857100821-1.64438030611365-0.644072614184202
1036850.86840.83633271974-1.780577847665449.9636672802594-0.807604431766071
1046848.26842.12376905080.5538846885803356.076230949198190.163286710744634
1056837.86844.72940977342.11523332147556-6.929409773401570.109216495341586
1066857.66862.6591508158214.149974799315-5.059150815823620.841859289661311
1076900.86900.1532863577831.91451578200650.6467136422222081.24279105829806
1086940.86922.8513218542824.899933225598117.9486781457152-0.49077722084971
1096937.46937.0070092228516.72214940688640.392990777145207-0.572057754897533
1106950.46971.1560983504129.9793594405104-20.7560983504130.927120286921028
1116978.86979.7242690489613.7022260071478-0.924269048964877-1.13854906402512
1126997.86972.08057168724-2.5265465348325225.719428312757-1.13563108285419
1136934.86964.97791252492-6.00732466915823-30.1779125249237-0.243544223009893
1146946.86946.51207026577-15.4837640481050.287929734228018-0.662802462480194
1156956.26943.53709906978-5.9722616368404812.66290093021760.665202903538802
1166968.26957.987993050829.5550233021196210.21200694917851.08605114872709

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 4028.8 & 4028.8 & 0 & 0 & 0 \tabularnewline
2 & 4076.6 & 4071.49258733313 & 43.1146863395201 & 5.10741266687361 & 3.18324427625824 \tabularnewline
3 & 4125.8 & 4127.06362339916 & 53.0980646452199 & -1.2636233991576 & 0.748015158886424 \tabularnewline
4 & 4177.2 & 4178.22710591903 & 51.50384469931 & -1.02710591902977 & -0.11136139218763 \tabularnewline
5 & 4183 & 4189.3396818558 & 18.7048272346304 & -6.33968185580101 & -2.29195063639123 \tabularnewline
6 & 4222.6 & 4219.06071356455 & 27.670154145966 & 3.53928643544596 & 0.627453276673477 \tabularnewline
7 & 4255.8 & 4255.00742825228 & 34.410808184986 & 0.792571747718589 & 0.471487476437519 \tabularnewline
8 & 4260.8 & 4265.07886008019 & 14.5892084154458 & -4.27886008019277 & -1.38651999172906 \tabularnewline
9 & 4279.2 & 4278.34259019264 & 13.5098860156964 & 0.857409807362202 & -0.0754978025623251 \tabularnewline
10 & 4328.8 & 4323.70174971681 & 39.4438144315515 & 5.09825028319225 & 1.81405874190837 \tabularnewline
11 & 4356.6 & 4358.76584958015 & 35.8774878387245 & -2.16584958015181 & -0.249461872142069 \tabularnewline
12 & 4393 & 4393.08189826494 & 34.6060258521935 & -0.081898264939052 & -0.0889378084383588 \tabularnewline
13 & 4419.4 & 4420.44049360227 & 28.7131576371833 & -1.04049360227512 & -0.412982005472812 \tabularnewline
14 & 4426.2 & 4428.67288165178 & 12.0161443595529 & -2.47288165178182 & -1.18354901714989 \tabularnewline
15 & 4467.2 & 4464.55397422776 & 30.5939426774439 & 2.64602577224347 & 1.30491870115938 \tabularnewline
16 & 4517.4 & 4507.92591388827 & 40.6512294040315 & 9.4740861117304 & 0.709235280985577 \tabularnewline
17 & 4517 & 4529.5736126738 & 25.7679485724673 & -12.5736126737983 & -1.03820486048216 \tabularnewline
18 & 4560.4 & 4558.79314278041 & 28.4652237305382 & 1.60685721959168 & 0.18873821078402 \tabularnewline
19 & 4589 & 4583.4382962088 & 25.4760777835076 & 5.56170379120464 & -0.209119054775167 \tabularnewline
20 & 4596 & 4599.61083288447 & 18.1943560461439 & -3.61083288446558 & -0.509336622415236 \tabularnewline
21 & 4621.2 & 4624.6857069472 & 23.5793527800971 & -3.48570694720265 & 0.376678197600356 \tabularnewline
22 & 4654.6 & 4648.91620644953 & 24.0889519696284 & 5.68379355046793 & 0.0356463699267106 \tabularnewline
23 & 4708.6 & 4705.62391278643 & 49.6158166019537 & 2.97608721357167 & 1.78559659026096 \tabularnewline
24 & 4774.4 & 4771.65045288471 & 62.4518048567809 & 2.74954711529021 & 0.89795186182572 \tabularnewline
25 & 4824.8 & 4823.50301552492 & 54.1638265865047 & 1.29698447507588 & -0.581054112912117 \tabularnewline
26 & 4839 & 4851.59314029443 & 33.7500330019437 & -12.5931402944289 & -1.42996595905468 \tabularnewline
27 & 4869.8 & 4872.12949217411 & 23.5437974955195 & -2.32949217410501 & -0.713932884417527 \tabularnewline
28 & 4895.8 & 4883.90305477938 & 14.4274741491091 & 11.8969452206225 & -0.640937223418529 \tabularnewline
29 & 4895.8 & 4907.71925371474 & 21.702938892628 & -11.9192537147393 & 0.508316472259119 \tabularnewline
30 & 4968.8 & 4961.32535976195 & 46.3531634126887 & 7.47464023805276 & 1.72347445808952 \tabularnewline
31 & 5010 & 5003.52592084913 & 43.1427179633305 & 6.47407915087069 & -0.224629585274748 \tabularnewline
32 & 5032.4 & 5037.59255124112 & 36.121960156893 & -5.19255124111596 & -0.491092222646152 \tabularnewline
33 & 5054 & 5058.04173902562 & 23.9975361789036 & -4.04173902561687 & -0.848088365446547 \tabularnewline
34 & 5083.8 & 5084.17463904172 & 25.6493819823249 & -0.374639041719718 & 0.115549892886955 \tabularnewline
35 & 5117.4 & 5118.11548339304 & 32.0617683501385 & -0.715483393036143 & 0.448534645617687 \tabularnewline
36 & 5170.8 & 5165.12264721366 & 43.6132374338731 & 5.67735278633797 & 0.808291758741012 \tabularnewline
37 & 5182.2 & 5181.43205455134 & 22.5001406425377 & 0.767945448661859 & -1.47934261917942 \tabularnewline
38 & 5163.6 & 5177.06046777862 & 1.72879389896969 & -13.4604677786198 & -1.45265318520518 \tabularnewline
39 & 5212.6 & 5205.22861327129 & 22.0407811869886 & 7.37138672870754 & 1.42053741887002 \tabularnewline
40 & 5288 & 5269.86649566223 & 54.7968553089749 & 18.1335043377736 & 2.29796999567432 \tabularnewline
41 & 5303.4 & 5323.91340564446 & 54.2193326224473 & -20.5134056444562 & -0.0403889756591417 \tabularnewline
42 & 5367.6 & 5362.85982991752 & 42.4823067867888 & 4.74017008248153 & -0.820423551321668 \tabularnewline
43 & 5433.8 & 5422.49869784779 & 55.6653623295487 & 11.3013021522108 & 0.922299375864107 \tabularnewline
44 & 5465.8 & 5468.6832426814 & 48.3759243466899 & -2.88324268140262 & -0.509913127833444 \tabularnewline
45 & 5493.8 & 5500.34297848051 & 35.5212762202476 & -6.54297848051269 & -0.899161057986395 \tabularnewline
46 & 5549.4 & 5550.04013490484 & 46.421843744715 & -0.640134904837706 & 0.762514779510167 \tabularnewline
47 & 5590.2 & 5596.62423159499 & 46.5465653033694 & -6.42423159499372 & 0.00872412531505642 \tabularnewline
48 & 5661.2 & 5647.8625477874 & 50.1516581364209 & 13.3374522125986 & 0.25229186182698 \tabularnewline
49 & 5699 & 5690.85568532947 & 44.6480442501974 & 8.14431467052753 & -0.385386682295811 \tabularnewline
50 & 5654.2 & 5681.86626828084 & 3.44372854858633 & -27.6662682808438 & -2.88099111466219 \tabularnewline
51 & 5671.8 & 5675.5313192939 & -4.04192283228323 & -3.73131929390266 & -0.523541812701493 \tabularnewline
52 & 5730.8 & 5706.26563233021 & 22.5915651866592 & 24.5343676697857 & 1.86635092239484 \tabularnewline
53 & 5693 & 5713.0962527927 & 10.5047165066805 & -20.0962527926959 & -0.845610391295979 \tabularnewline
54 & 5720.4 & 5720.38319767236 & 8.04017081872951 & 0.0168023276363565 & -0.172284539807861 \tabularnewline
55 & 5747.8 & 5733.2132695133 & 11.7071901072584 & 14.586730486703 & 0.256507903025478 \tabularnewline
56 & 5764.2 & 5759.8495166169 & 23.1419508654631 & 4.35048338310332 & 0.799902424273524 \tabularnewline
57 & 5783 & 5791.34225251111 & 29.5396963703684 & -8.34225251110598 & 0.447513092523713 \tabularnewline
58 & 5822.4 & 5823.63900857625 & 31.6518350826126 & -1.23900857624583 & 0.147744819285755 \tabularnewline
59 & 5836.2 & 5847.85093437427 & 25.9540931628536 & -11.6509343742682 & -0.398564984850663 \tabularnewline
60 & 5864.6 & 5854.76136953786 & 11.3721837779319 & 9.83863046214156 & -1.02047252530849 \tabularnewline
61 & 5913.4 & 5887.99962288763 & 28.1228215571132 & 25.4003771123686 & 1.17246048205573 \tabularnewline
62 & 5906.8 & 5929.94941046404 & 38.7061069996228 & -23.1494104640425 & 0.739989148715033 \tabularnewline
63 & 5954 & 5966.83507485586 & 37.3158741712887 & -12.8350748558558 & -0.0972365951719047 \tabularnewline
64 & 6031.2 & 6002.75732744639 & 36.2513125126489 & 28.4426725536089 & -0.0745543115633263 \tabularnewline
65 & 6011.2 & 6031.00947775182 & 30.1341741325703 & -19.8094777518223 & -0.428014296076105 \tabularnewline
66 & 6059.8 & 6060.18472586572 & 29.4013898771675 & -0.384725865723167 & -0.0512327864380162 \tabularnewline
67 & 6091.6 & 6081.79492183579 & 23.4507618994878 & 9.80507816421297 & -0.416198769068334 \tabularnewline
68 & 6088 & 6088.90328239721 & 10.9652433627557 & -0.903282397209089 & -0.873392703207555 \tabularnewline
69 & 6082.2 & 6092.88790365036 & 5.6307135189045 & -10.6879036503588 & -0.373145482157314 \tabularnewline
70 & 6108 & 6105.5884688594 & 11.0332201833215 & 2.41153114060312 & 0.377902653408987 \tabularnewline
71 & 6151.4 & 6151.26630121687 & 37.5007090268151 & 0.133698783133762 & 1.85151081196775 \tabularnewline
72 & 6187 & 6183.14286370308 & 33.204067812639 & 3.85713629692289 & -0.300671203993712 \tabularnewline
73 & 6190 & 6174.86042666897 & 1.49981199563612 & 15.1395733310306 & -2.21855182789073 \tabularnewline
74 & 6152.2 & 6175.11134993269 & 0.546141526119766 & -22.9113499326945 & -0.0666847103301515 \tabularnewline
75 & 6183.8 & 6194.06029643002 & 14.576792329766 & -10.2602964300223 & 0.981371523781979 \tabularnewline
76 & 6222.8 & 6195.69690477471 & 4.70920562519145 & 27.1030952252893 & -0.690811804142912 \tabularnewline
77 & 6165.8 & 6188.12371731001 & -4.66501544923577 & -22.3237173100057 & -0.655928441015458 \tabularnewline
78 & 6223.4 & 6216.54601980163 & 20.5782259461392 & 6.85398019836622 & 1.76512709326029 \tabularnewline
79 & 6292.8 & 6272.70917538043 & 47.7130735737834 & 20.0908246195729 & 1.89775015726209 \tabularnewline
80 & 6320.6 & 6318.77371806335 & 46.455826692501 & 1.82628193664879 & -0.0879448130700021 \tabularnewline
81 & 6344 & 6357.37862026606 & 40.4670004937962 & -13.3786202660632 & -0.418915884019981 \tabularnewline
82 & 6391.2 & 6398.89186056224 & 41.2650758248999 & -7.69186056223816 & 0.0558252308428943 \tabularnewline
83 & 6443.4 & 6442.96002477829 & 43.4029393653017 & 0.439975221706612 & 0.149557195229577 \tabularnewline
84 & 6504 & 6489.64797258328 & 45.9085493833408 & 14.3520274167197 & 0.175326093697123 \tabularnewline
85 & 6520.2 & 6509.51947936897 & 26.0449726373846 & 10.6805206310325 & -1.38975178280088 \tabularnewline
86 & 6518.8 & 6544.39277382643 & 32.7754741298987 & -25.5927738264284 & 0.470649891881673 \tabularnewline
87 & 6563.8 & 6570.65635050818 & 27.8166227072361 & -6.85635050817958 & -0.346852938405403 \tabularnewline
88 & 6614 & 6583.83031303158 & 16.6647281292402 & 30.1696869684227 & -0.780553803965433 \tabularnewline
89 & 6555.6 & 6587.0193080925 & 6.3943102610478 & -31.4193080925045 & -0.718631267573772 \tabularnewline
90 & 6601.8 & 6602.10192796405 & 13.0147723260822 & -0.301927964046984 & 0.462984212162373 \tabularnewline
91 & 6632.4 & 6612.56257303848 & 11.0694183990274 & 19.8374269615165 & -0.13605055658131 \tabularnewline
92 & 6657.8 & 6649.33462816979 & 30.646189930998 & 8.46537183021245 & 1.36935757144204 \tabularnewline
93 & 6674.4 & 6687.16194507153 & 36.116709375457 & -12.7619450715305 & 0.382662411806987 \tabularnewline
94 & 6687 & 6700.03176970148 & 18.4074310442073 & -13.0317697014833 & -1.23878100072393 \tabularnewline
95 & 6697.6 & 6701.12880998769 & 5.22156480095135 & -3.52880998769029 & -0.922456668663583 \tabularnewline
96 & 6732 & 6711.1288782333 & 8.86194511705881 & 20.8711217667011 & 0.254713725643502 \tabularnewline
97 & 6736.4 & 6727.83299588159 & 14.8370041061149 & 8.56700411841328 & 0.417999778892581 \tabularnewline
98 & 6745.8 & 6766.60946218982 & 33.065902122045 & -20.8094621898158 & 1.27476350934579 \tabularnewline
99 & 6805.2 & 6807.25692836751 & 38.8339571158027 & -2.05692836750722 & 0.403458962178834 \tabularnewline
100 & 6850.4 & 6820.51317378772 & 19.3725483657539 & 29.8868262122779 & -1.36196883768886 \tabularnewline
101 & 6807.2 & 6839.36533962234 & 18.976374122415 & -32.1653396223426 & -0.0277202034922632 \tabularnewline
102 & 6844.6 & 6846.24438030611 & 9.76717857100821 & -1.64438030611365 & -0.644072614184202 \tabularnewline
103 & 6850.8 & 6840.83633271974 & -1.78057784766544 & 9.9636672802594 & -0.807604431766071 \tabularnewline
104 & 6848.2 & 6842.1237690508 & 0.553884688580335 & 6.07623094919819 & 0.163286710744634 \tabularnewline
105 & 6837.8 & 6844.7294097734 & 2.11523332147556 & -6.92940977340157 & 0.109216495341586 \tabularnewline
106 & 6857.6 & 6862.65915081582 & 14.149974799315 & -5.05915081582362 & 0.841859289661311 \tabularnewline
107 & 6900.8 & 6900.15328635778 & 31.9145157820065 & 0.646713642222208 & 1.24279105829806 \tabularnewline
108 & 6940.8 & 6922.85132185428 & 24.8999332255981 & 17.9486781457152 & -0.49077722084971 \tabularnewline
109 & 6937.4 & 6937.00700922285 & 16.7221494068864 & 0.392990777145207 & -0.572057754897533 \tabularnewline
110 & 6950.4 & 6971.15609835041 & 29.9793594405104 & -20.756098350413 & 0.927120286921028 \tabularnewline
111 & 6978.8 & 6979.72426904896 & 13.7022260071478 & -0.924269048964877 & -1.13854906402512 \tabularnewline
112 & 6997.8 & 6972.08057168724 & -2.52654653483252 & 25.719428312757 & -1.13563108285419 \tabularnewline
113 & 6934.8 & 6964.97791252492 & -6.00732466915823 & -30.1779125249237 & -0.243544223009893 \tabularnewline
114 & 6946.8 & 6946.51207026577 & -15.483764048105 & 0.287929734228018 & -0.662802462480194 \tabularnewline
115 & 6956.2 & 6943.53709906978 & -5.97226163684048 & 12.6629009302176 & 0.665202903538802 \tabularnewline
116 & 6968.2 & 6957.98799305082 & 9.55502330211962 & 10.2120069491785 & 1.08605114872709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299067&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]4028.8[/C][C]4028.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]4076.6[/C][C]4071.49258733313[/C][C]43.1146863395201[/C][C]5.10741266687361[/C][C]3.18324427625824[/C][/ROW]
[ROW][C]3[/C][C]4125.8[/C][C]4127.06362339916[/C][C]53.0980646452199[/C][C]-1.2636233991576[/C][C]0.748015158886424[/C][/ROW]
[ROW][C]4[/C][C]4177.2[/C][C]4178.22710591903[/C][C]51.50384469931[/C][C]-1.02710591902977[/C][C]-0.11136139218763[/C][/ROW]
[ROW][C]5[/C][C]4183[/C][C]4189.3396818558[/C][C]18.7048272346304[/C][C]-6.33968185580101[/C][C]-2.29195063639123[/C][/ROW]
[ROW][C]6[/C][C]4222.6[/C][C]4219.06071356455[/C][C]27.670154145966[/C][C]3.53928643544596[/C][C]0.627453276673477[/C][/ROW]
[ROW][C]7[/C][C]4255.8[/C][C]4255.00742825228[/C][C]34.410808184986[/C][C]0.792571747718589[/C][C]0.471487476437519[/C][/ROW]
[ROW][C]8[/C][C]4260.8[/C][C]4265.07886008019[/C][C]14.5892084154458[/C][C]-4.27886008019277[/C][C]-1.38651999172906[/C][/ROW]
[ROW][C]9[/C][C]4279.2[/C][C]4278.34259019264[/C][C]13.5098860156964[/C][C]0.857409807362202[/C][C]-0.0754978025623251[/C][/ROW]
[ROW][C]10[/C][C]4328.8[/C][C]4323.70174971681[/C][C]39.4438144315515[/C][C]5.09825028319225[/C][C]1.81405874190837[/C][/ROW]
[ROW][C]11[/C][C]4356.6[/C][C]4358.76584958015[/C][C]35.8774878387245[/C][C]-2.16584958015181[/C][C]-0.249461872142069[/C][/ROW]
[ROW][C]12[/C][C]4393[/C][C]4393.08189826494[/C][C]34.6060258521935[/C][C]-0.081898264939052[/C][C]-0.0889378084383588[/C][/ROW]
[ROW][C]13[/C][C]4419.4[/C][C]4420.44049360227[/C][C]28.7131576371833[/C][C]-1.04049360227512[/C][C]-0.412982005472812[/C][/ROW]
[ROW][C]14[/C][C]4426.2[/C][C]4428.67288165178[/C][C]12.0161443595529[/C][C]-2.47288165178182[/C][C]-1.18354901714989[/C][/ROW]
[ROW][C]15[/C][C]4467.2[/C][C]4464.55397422776[/C][C]30.5939426774439[/C][C]2.64602577224347[/C][C]1.30491870115938[/C][/ROW]
[ROW][C]16[/C][C]4517.4[/C][C]4507.92591388827[/C][C]40.6512294040315[/C][C]9.4740861117304[/C][C]0.709235280985577[/C][/ROW]
[ROW][C]17[/C][C]4517[/C][C]4529.5736126738[/C][C]25.7679485724673[/C][C]-12.5736126737983[/C][C]-1.03820486048216[/C][/ROW]
[ROW][C]18[/C][C]4560.4[/C][C]4558.79314278041[/C][C]28.4652237305382[/C][C]1.60685721959168[/C][C]0.18873821078402[/C][/ROW]
[ROW][C]19[/C][C]4589[/C][C]4583.4382962088[/C][C]25.4760777835076[/C][C]5.56170379120464[/C][C]-0.209119054775167[/C][/ROW]
[ROW][C]20[/C][C]4596[/C][C]4599.61083288447[/C][C]18.1943560461439[/C][C]-3.61083288446558[/C][C]-0.509336622415236[/C][/ROW]
[ROW][C]21[/C][C]4621.2[/C][C]4624.6857069472[/C][C]23.5793527800971[/C][C]-3.48570694720265[/C][C]0.376678197600356[/C][/ROW]
[ROW][C]22[/C][C]4654.6[/C][C]4648.91620644953[/C][C]24.0889519696284[/C][C]5.68379355046793[/C][C]0.0356463699267106[/C][/ROW]
[ROW][C]23[/C][C]4708.6[/C][C]4705.62391278643[/C][C]49.6158166019537[/C][C]2.97608721357167[/C][C]1.78559659026096[/C][/ROW]
[ROW][C]24[/C][C]4774.4[/C][C]4771.65045288471[/C][C]62.4518048567809[/C][C]2.74954711529021[/C][C]0.89795186182572[/C][/ROW]
[ROW][C]25[/C][C]4824.8[/C][C]4823.50301552492[/C][C]54.1638265865047[/C][C]1.29698447507588[/C][C]-0.581054112912117[/C][/ROW]
[ROW][C]26[/C][C]4839[/C][C]4851.59314029443[/C][C]33.7500330019437[/C][C]-12.5931402944289[/C][C]-1.42996595905468[/C][/ROW]
[ROW][C]27[/C][C]4869.8[/C][C]4872.12949217411[/C][C]23.5437974955195[/C][C]-2.32949217410501[/C][C]-0.713932884417527[/C][/ROW]
[ROW][C]28[/C][C]4895.8[/C][C]4883.90305477938[/C][C]14.4274741491091[/C][C]11.8969452206225[/C][C]-0.640937223418529[/C][/ROW]
[ROW][C]29[/C][C]4895.8[/C][C]4907.71925371474[/C][C]21.702938892628[/C][C]-11.9192537147393[/C][C]0.508316472259119[/C][/ROW]
[ROW][C]30[/C][C]4968.8[/C][C]4961.32535976195[/C][C]46.3531634126887[/C][C]7.47464023805276[/C][C]1.72347445808952[/C][/ROW]
[ROW][C]31[/C][C]5010[/C][C]5003.52592084913[/C][C]43.1427179633305[/C][C]6.47407915087069[/C][C]-0.224629585274748[/C][/ROW]
[ROW][C]32[/C][C]5032.4[/C][C]5037.59255124112[/C][C]36.121960156893[/C][C]-5.19255124111596[/C][C]-0.491092222646152[/C][/ROW]
[ROW][C]33[/C][C]5054[/C][C]5058.04173902562[/C][C]23.9975361789036[/C][C]-4.04173902561687[/C][C]-0.848088365446547[/C][/ROW]
[ROW][C]34[/C][C]5083.8[/C][C]5084.17463904172[/C][C]25.6493819823249[/C][C]-0.374639041719718[/C][C]0.115549892886955[/C][/ROW]
[ROW][C]35[/C][C]5117.4[/C][C]5118.11548339304[/C][C]32.0617683501385[/C][C]-0.715483393036143[/C][C]0.448534645617687[/C][/ROW]
[ROW][C]36[/C][C]5170.8[/C][C]5165.12264721366[/C][C]43.6132374338731[/C][C]5.67735278633797[/C][C]0.808291758741012[/C][/ROW]
[ROW][C]37[/C][C]5182.2[/C][C]5181.43205455134[/C][C]22.5001406425377[/C][C]0.767945448661859[/C][C]-1.47934261917942[/C][/ROW]
[ROW][C]38[/C][C]5163.6[/C][C]5177.06046777862[/C][C]1.72879389896969[/C][C]-13.4604677786198[/C][C]-1.45265318520518[/C][/ROW]
[ROW][C]39[/C][C]5212.6[/C][C]5205.22861327129[/C][C]22.0407811869886[/C][C]7.37138672870754[/C][C]1.42053741887002[/C][/ROW]
[ROW][C]40[/C][C]5288[/C][C]5269.86649566223[/C][C]54.7968553089749[/C][C]18.1335043377736[/C][C]2.29796999567432[/C][/ROW]
[ROW][C]41[/C][C]5303.4[/C][C]5323.91340564446[/C][C]54.2193326224473[/C][C]-20.5134056444562[/C][C]-0.0403889756591417[/C][/ROW]
[ROW][C]42[/C][C]5367.6[/C][C]5362.85982991752[/C][C]42.4823067867888[/C][C]4.74017008248153[/C][C]-0.820423551321668[/C][/ROW]
[ROW][C]43[/C][C]5433.8[/C][C]5422.49869784779[/C][C]55.6653623295487[/C][C]11.3013021522108[/C][C]0.922299375864107[/C][/ROW]
[ROW][C]44[/C][C]5465.8[/C][C]5468.6832426814[/C][C]48.3759243466899[/C][C]-2.88324268140262[/C][C]-0.509913127833444[/C][/ROW]
[ROW][C]45[/C][C]5493.8[/C][C]5500.34297848051[/C][C]35.5212762202476[/C][C]-6.54297848051269[/C][C]-0.899161057986395[/C][/ROW]
[ROW][C]46[/C][C]5549.4[/C][C]5550.04013490484[/C][C]46.421843744715[/C][C]-0.640134904837706[/C][C]0.762514779510167[/C][/ROW]
[ROW][C]47[/C][C]5590.2[/C][C]5596.62423159499[/C][C]46.5465653033694[/C][C]-6.42423159499372[/C][C]0.00872412531505642[/C][/ROW]
[ROW][C]48[/C][C]5661.2[/C][C]5647.8625477874[/C][C]50.1516581364209[/C][C]13.3374522125986[/C][C]0.25229186182698[/C][/ROW]
[ROW][C]49[/C][C]5699[/C][C]5690.85568532947[/C][C]44.6480442501974[/C][C]8.14431467052753[/C][C]-0.385386682295811[/C][/ROW]
[ROW][C]50[/C][C]5654.2[/C][C]5681.86626828084[/C][C]3.44372854858633[/C][C]-27.6662682808438[/C][C]-2.88099111466219[/C][/ROW]
[ROW][C]51[/C][C]5671.8[/C][C]5675.5313192939[/C][C]-4.04192283228323[/C][C]-3.73131929390266[/C][C]-0.523541812701493[/C][/ROW]
[ROW][C]52[/C][C]5730.8[/C][C]5706.26563233021[/C][C]22.5915651866592[/C][C]24.5343676697857[/C][C]1.86635092239484[/C][/ROW]
[ROW][C]53[/C][C]5693[/C][C]5713.0962527927[/C][C]10.5047165066805[/C][C]-20.0962527926959[/C][C]-0.845610391295979[/C][/ROW]
[ROW][C]54[/C][C]5720.4[/C][C]5720.38319767236[/C][C]8.04017081872951[/C][C]0.0168023276363565[/C][C]-0.172284539807861[/C][/ROW]
[ROW][C]55[/C][C]5747.8[/C][C]5733.2132695133[/C][C]11.7071901072584[/C][C]14.586730486703[/C][C]0.256507903025478[/C][/ROW]
[ROW][C]56[/C][C]5764.2[/C][C]5759.8495166169[/C][C]23.1419508654631[/C][C]4.35048338310332[/C][C]0.799902424273524[/C][/ROW]
[ROW][C]57[/C][C]5783[/C][C]5791.34225251111[/C][C]29.5396963703684[/C][C]-8.34225251110598[/C][C]0.447513092523713[/C][/ROW]
[ROW][C]58[/C][C]5822.4[/C][C]5823.63900857625[/C][C]31.6518350826126[/C][C]-1.23900857624583[/C][C]0.147744819285755[/C][/ROW]
[ROW][C]59[/C][C]5836.2[/C][C]5847.85093437427[/C][C]25.9540931628536[/C][C]-11.6509343742682[/C][C]-0.398564984850663[/C][/ROW]
[ROW][C]60[/C][C]5864.6[/C][C]5854.76136953786[/C][C]11.3721837779319[/C][C]9.83863046214156[/C][C]-1.02047252530849[/C][/ROW]
[ROW][C]61[/C][C]5913.4[/C][C]5887.99962288763[/C][C]28.1228215571132[/C][C]25.4003771123686[/C][C]1.17246048205573[/C][/ROW]
[ROW][C]62[/C][C]5906.8[/C][C]5929.94941046404[/C][C]38.7061069996228[/C][C]-23.1494104640425[/C][C]0.739989148715033[/C][/ROW]
[ROW][C]63[/C][C]5954[/C][C]5966.83507485586[/C][C]37.3158741712887[/C][C]-12.8350748558558[/C][C]-0.0972365951719047[/C][/ROW]
[ROW][C]64[/C][C]6031.2[/C][C]6002.75732744639[/C][C]36.2513125126489[/C][C]28.4426725536089[/C][C]-0.0745543115633263[/C][/ROW]
[ROW][C]65[/C][C]6011.2[/C][C]6031.00947775182[/C][C]30.1341741325703[/C][C]-19.8094777518223[/C][C]-0.428014296076105[/C][/ROW]
[ROW][C]66[/C][C]6059.8[/C][C]6060.18472586572[/C][C]29.4013898771675[/C][C]-0.384725865723167[/C][C]-0.0512327864380162[/C][/ROW]
[ROW][C]67[/C][C]6091.6[/C][C]6081.79492183579[/C][C]23.4507618994878[/C][C]9.80507816421297[/C][C]-0.416198769068334[/C][/ROW]
[ROW][C]68[/C][C]6088[/C][C]6088.90328239721[/C][C]10.9652433627557[/C][C]-0.903282397209089[/C][C]-0.873392703207555[/C][/ROW]
[ROW][C]69[/C][C]6082.2[/C][C]6092.88790365036[/C][C]5.6307135189045[/C][C]-10.6879036503588[/C][C]-0.373145482157314[/C][/ROW]
[ROW][C]70[/C][C]6108[/C][C]6105.5884688594[/C][C]11.0332201833215[/C][C]2.41153114060312[/C][C]0.377902653408987[/C][/ROW]
[ROW][C]71[/C][C]6151.4[/C][C]6151.26630121687[/C][C]37.5007090268151[/C][C]0.133698783133762[/C][C]1.85151081196775[/C][/ROW]
[ROW][C]72[/C][C]6187[/C][C]6183.14286370308[/C][C]33.204067812639[/C][C]3.85713629692289[/C][C]-0.300671203993712[/C][/ROW]
[ROW][C]73[/C][C]6190[/C][C]6174.86042666897[/C][C]1.49981199563612[/C][C]15.1395733310306[/C][C]-2.21855182789073[/C][/ROW]
[ROW][C]74[/C][C]6152.2[/C][C]6175.11134993269[/C][C]0.546141526119766[/C][C]-22.9113499326945[/C][C]-0.0666847103301515[/C][/ROW]
[ROW][C]75[/C][C]6183.8[/C][C]6194.06029643002[/C][C]14.576792329766[/C][C]-10.2602964300223[/C][C]0.981371523781979[/C][/ROW]
[ROW][C]76[/C][C]6222.8[/C][C]6195.69690477471[/C][C]4.70920562519145[/C][C]27.1030952252893[/C][C]-0.690811804142912[/C][/ROW]
[ROW][C]77[/C][C]6165.8[/C][C]6188.12371731001[/C][C]-4.66501544923577[/C][C]-22.3237173100057[/C][C]-0.655928441015458[/C][/ROW]
[ROW][C]78[/C][C]6223.4[/C][C]6216.54601980163[/C][C]20.5782259461392[/C][C]6.85398019836622[/C][C]1.76512709326029[/C][/ROW]
[ROW][C]79[/C][C]6292.8[/C][C]6272.70917538043[/C][C]47.7130735737834[/C][C]20.0908246195729[/C][C]1.89775015726209[/C][/ROW]
[ROW][C]80[/C][C]6320.6[/C][C]6318.77371806335[/C][C]46.455826692501[/C][C]1.82628193664879[/C][C]-0.0879448130700021[/C][/ROW]
[ROW][C]81[/C][C]6344[/C][C]6357.37862026606[/C][C]40.4670004937962[/C][C]-13.3786202660632[/C][C]-0.418915884019981[/C][/ROW]
[ROW][C]82[/C][C]6391.2[/C][C]6398.89186056224[/C][C]41.2650758248999[/C][C]-7.69186056223816[/C][C]0.0558252308428943[/C][/ROW]
[ROW][C]83[/C][C]6443.4[/C][C]6442.96002477829[/C][C]43.4029393653017[/C][C]0.439975221706612[/C][C]0.149557195229577[/C][/ROW]
[ROW][C]84[/C][C]6504[/C][C]6489.64797258328[/C][C]45.9085493833408[/C][C]14.3520274167197[/C][C]0.175326093697123[/C][/ROW]
[ROW][C]85[/C][C]6520.2[/C][C]6509.51947936897[/C][C]26.0449726373846[/C][C]10.6805206310325[/C][C]-1.38975178280088[/C][/ROW]
[ROW][C]86[/C][C]6518.8[/C][C]6544.39277382643[/C][C]32.7754741298987[/C][C]-25.5927738264284[/C][C]0.470649891881673[/C][/ROW]
[ROW][C]87[/C][C]6563.8[/C][C]6570.65635050818[/C][C]27.8166227072361[/C][C]-6.85635050817958[/C][C]-0.346852938405403[/C][/ROW]
[ROW][C]88[/C][C]6614[/C][C]6583.83031303158[/C][C]16.6647281292402[/C][C]30.1696869684227[/C][C]-0.780553803965433[/C][/ROW]
[ROW][C]89[/C][C]6555.6[/C][C]6587.0193080925[/C][C]6.3943102610478[/C][C]-31.4193080925045[/C][C]-0.718631267573772[/C][/ROW]
[ROW][C]90[/C][C]6601.8[/C][C]6602.10192796405[/C][C]13.0147723260822[/C][C]-0.301927964046984[/C][C]0.462984212162373[/C][/ROW]
[ROW][C]91[/C][C]6632.4[/C][C]6612.56257303848[/C][C]11.0694183990274[/C][C]19.8374269615165[/C][C]-0.13605055658131[/C][/ROW]
[ROW][C]92[/C][C]6657.8[/C][C]6649.33462816979[/C][C]30.646189930998[/C][C]8.46537183021245[/C][C]1.36935757144204[/C][/ROW]
[ROW][C]93[/C][C]6674.4[/C][C]6687.16194507153[/C][C]36.116709375457[/C][C]-12.7619450715305[/C][C]0.382662411806987[/C][/ROW]
[ROW][C]94[/C][C]6687[/C][C]6700.03176970148[/C][C]18.4074310442073[/C][C]-13.0317697014833[/C][C]-1.23878100072393[/C][/ROW]
[ROW][C]95[/C][C]6697.6[/C][C]6701.12880998769[/C][C]5.22156480095135[/C][C]-3.52880998769029[/C][C]-0.922456668663583[/C][/ROW]
[ROW][C]96[/C][C]6732[/C][C]6711.1288782333[/C][C]8.86194511705881[/C][C]20.8711217667011[/C][C]0.254713725643502[/C][/ROW]
[ROW][C]97[/C][C]6736.4[/C][C]6727.83299588159[/C][C]14.8370041061149[/C][C]8.56700411841328[/C][C]0.417999778892581[/C][/ROW]
[ROW][C]98[/C][C]6745.8[/C][C]6766.60946218982[/C][C]33.065902122045[/C][C]-20.8094621898158[/C][C]1.27476350934579[/C][/ROW]
[ROW][C]99[/C][C]6805.2[/C][C]6807.25692836751[/C][C]38.8339571158027[/C][C]-2.05692836750722[/C][C]0.403458962178834[/C][/ROW]
[ROW][C]100[/C][C]6850.4[/C][C]6820.51317378772[/C][C]19.3725483657539[/C][C]29.8868262122779[/C][C]-1.36196883768886[/C][/ROW]
[ROW][C]101[/C][C]6807.2[/C][C]6839.36533962234[/C][C]18.976374122415[/C][C]-32.1653396223426[/C][C]-0.0277202034922632[/C][/ROW]
[ROW][C]102[/C][C]6844.6[/C][C]6846.24438030611[/C][C]9.76717857100821[/C][C]-1.64438030611365[/C][C]-0.644072614184202[/C][/ROW]
[ROW][C]103[/C][C]6850.8[/C][C]6840.83633271974[/C][C]-1.78057784766544[/C][C]9.9636672802594[/C][C]-0.807604431766071[/C][/ROW]
[ROW][C]104[/C][C]6848.2[/C][C]6842.1237690508[/C][C]0.553884688580335[/C][C]6.07623094919819[/C][C]0.163286710744634[/C][/ROW]
[ROW][C]105[/C][C]6837.8[/C][C]6844.7294097734[/C][C]2.11523332147556[/C][C]-6.92940977340157[/C][C]0.109216495341586[/C][/ROW]
[ROW][C]106[/C][C]6857.6[/C][C]6862.65915081582[/C][C]14.149974799315[/C][C]-5.05915081582362[/C][C]0.841859289661311[/C][/ROW]
[ROW][C]107[/C][C]6900.8[/C][C]6900.15328635778[/C][C]31.9145157820065[/C][C]0.646713642222208[/C][C]1.24279105829806[/C][/ROW]
[ROW][C]108[/C][C]6940.8[/C][C]6922.85132185428[/C][C]24.8999332255981[/C][C]17.9486781457152[/C][C]-0.49077722084971[/C][/ROW]
[ROW][C]109[/C][C]6937.4[/C][C]6937.00700922285[/C][C]16.7221494068864[/C][C]0.392990777145207[/C][C]-0.572057754897533[/C][/ROW]
[ROW][C]110[/C][C]6950.4[/C][C]6971.15609835041[/C][C]29.9793594405104[/C][C]-20.756098350413[/C][C]0.927120286921028[/C][/ROW]
[ROW][C]111[/C][C]6978.8[/C][C]6979.72426904896[/C][C]13.7022260071478[/C][C]-0.924269048964877[/C][C]-1.13854906402512[/C][/ROW]
[ROW][C]112[/C][C]6997.8[/C][C]6972.08057168724[/C][C]-2.52654653483252[/C][C]25.719428312757[/C][C]-1.13563108285419[/C][/ROW]
[ROW][C]113[/C][C]6934.8[/C][C]6964.97791252492[/C][C]-6.00732466915823[/C][C]-30.1779125249237[/C][C]-0.243544223009893[/C][/ROW]
[ROW][C]114[/C][C]6946.8[/C][C]6946.51207026577[/C][C]-15.483764048105[/C][C]0.287929734228018[/C][C]-0.662802462480194[/C][/ROW]
[ROW][C]115[/C][C]6956.2[/C][C]6943.53709906978[/C][C]-5.97226163684048[/C][C]12.6629009302176[/C][C]0.665202903538802[/C][/ROW]
[ROW][C]116[/C][C]6968.2[/C][C]6957.98799305082[/C][C]9.55502330211962[/C][C]10.2120069491785[/C][C]1.08605114872709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299067&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
14028.84028.8000
24076.64071.4925873331343.11468633952015.107412666873613.18324427625824
34125.84127.0636233991653.0980646452199-1.26362339915760.748015158886424
44177.24178.2271059190351.50384469931-1.02710591902977-0.11136139218763
541834189.339681855818.7048272346304-6.33968185580101-2.29195063639123
64222.64219.0607135645527.6701541459663.539286435445960.627453276673477
74255.84255.0074282522834.4108081849860.7925717477185890.471487476437519
84260.84265.0788600801914.5892084154458-4.27886008019277-1.38651999172906
94279.24278.3425901926413.50988601569640.857409807362202-0.0754978025623251
104328.84323.7017497168139.44381443155155.098250283192251.81405874190837
114356.64358.7658495801535.8774878387245-2.16584958015181-0.249461872142069
1243934393.0818982649434.6060258521935-0.081898264939052-0.0889378084383588
134419.44420.4404936022728.7131576371833-1.04049360227512-0.412982005472812
144426.24428.6728816517812.0161443595529-2.47288165178182-1.18354901714989
154467.24464.5539742277630.59394267744392.646025772243471.30491870115938
164517.44507.9259138882740.65122940403159.47408611173040.709235280985577
1745174529.573612673825.7679485724673-12.5736126737983-1.03820486048216
184560.44558.7931427804128.46522373053821.606857219591680.18873821078402
1945894583.438296208825.47607778350765.56170379120464-0.209119054775167
2045964599.6108328844718.1943560461439-3.61083288446558-0.509336622415236
214621.24624.685706947223.5793527800971-3.485706947202650.376678197600356
224654.64648.9162064495324.08895196962845.683793550467930.0356463699267106
234708.64705.6239127864349.61581660195372.976087213571671.78559659026096
244774.44771.6504528847162.45180485678092.749547115290210.89795186182572
254824.84823.5030155249254.16382658650471.29698447507588-0.581054112912117
2648394851.5931402944333.7500330019437-12.5931402944289-1.42996595905468
274869.84872.1294921741123.5437974955195-2.32949217410501-0.713932884417527
284895.84883.9030547793814.427474149109111.8969452206225-0.640937223418529
294895.84907.7192537147421.702938892628-11.91925371473930.508316472259119
304968.84961.3253597619546.35316341268877.474640238052761.72347445808952
3150105003.5259208491343.14271796333056.47407915087069-0.224629585274748
325032.45037.5925512411236.121960156893-5.19255124111596-0.491092222646152
3350545058.0417390256223.9975361789036-4.04173902561687-0.848088365446547
345083.85084.1746390417225.6493819823249-0.3746390417197180.115549892886955
355117.45118.1154833930432.0617683501385-0.7154833930361430.448534645617687
365170.85165.1226472136643.61323743387315.677352786337970.808291758741012
375182.25181.4320545513422.50014064253770.767945448661859-1.47934261917942
385163.65177.060467778621.72879389896969-13.4604677786198-1.45265318520518
395212.65205.2286132712922.04078118698867.371386728707541.42053741887002
4052885269.8664956622354.796855308974918.13350433777362.29796999567432
415303.45323.9134056444654.2193326224473-20.5134056444562-0.0403889756591417
425367.65362.8598299175242.48230678678884.74017008248153-0.820423551321668
435433.85422.4986978477955.665362329548711.30130215221080.922299375864107
445465.85468.683242681448.3759243466899-2.88324268140262-0.509913127833444
455493.85500.3429784805135.5212762202476-6.54297848051269-0.899161057986395
465549.45550.0401349048446.421843744715-0.6401349048377060.762514779510167
475590.25596.6242315949946.5465653033694-6.424231594993720.00872412531505642
485661.25647.862547787450.151658136420913.33745221259860.25229186182698
4956995690.8556853294744.64804425019748.14431467052753-0.385386682295811
505654.25681.866268280843.44372854858633-27.6662682808438-2.88099111466219
515671.85675.5313192939-4.04192283228323-3.73131929390266-0.523541812701493
525730.85706.2656323302122.591565186659224.53436766978571.86635092239484
5356935713.096252792710.5047165066805-20.0962527926959-0.845610391295979
545720.45720.383197672368.040170818729510.0168023276363565-0.172284539807861
555747.85733.213269513311.707190107258414.5867304867030.256507903025478
565764.25759.849516616923.14195086546314.350483383103320.799902424273524
5757835791.3422525111129.5396963703684-8.342252511105980.447513092523713
585822.45823.6390085762531.6518350826126-1.239008576245830.147744819285755
595836.25847.8509343742725.9540931628536-11.6509343742682-0.398564984850663
605864.65854.7613695378611.37218377793199.83863046214156-1.02047252530849
615913.45887.9996228876328.122821557113225.40037711236861.17246048205573
625906.85929.9494104640438.7061069996228-23.14941046404250.739989148715033
6359545966.8350748558637.3158741712887-12.8350748558558-0.0972365951719047
646031.26002.7573274463936.251312512648928.4426725536089-0.0745543115633263
656011.26031.0094777518230.1341741325703-19.8094777518223-0.428014296076105
666059.86060.1847258657229.4013898771675-0.384725865723167-0.0512327864380162
676091.66081.7949218357923.45076189948789.80507816421297-0.416198769068334
6860886088.9032823972110.9652433627557-0.903282397209089-0.873392703207555
696082.26092.887903650365.6307135189045-10.6879036503588-0.373145482157314
7061086105.588468859411.03322018332152.411531140603120.377902653408987
716151.46151.2663012168737.50070902681510.1336987831337621.85151081196775
7261876183.1428637030833.2040678126393.85713629692289-0.300671203993712
7361906174.860426668971.4998119956361215.1395733310306-2.21855182789073
746152.26175.111349932690.546141526119766-22.9113499326945-0.0666847103301515
756183.86194.0602964300214.576792329766-10.26029643002230.981371523781979
766222.86195.696904774714.7092056251914527.1030952252893-0.690811804142912
776165.86188.12371731001-4.66501544923577-22.3237173100057-0.655928441015458
786223.46216.5460198016320.57822594613926.853980198366221.76512709326029
796292.86272.7091753804347.713073573783420.09082461957291.89775015726209
806320.66318.7737180633546.4558266925011.82628193664879-0.0879448130700021
8163446357.3786202660640.4670004937962-13.3786202660632-0.418915884019981
826391.26398.8918605622441.2650758248999-7.691860562238160.0558252308428943
836443.46442.9600247782943.40293936530170.4399752217066120.149557195229577
8465046489.6479725832845.908549383340814.35202741671970.175326093697123
856520.26509.5194793689726.044972637384610.6805206310325-1.38975178280088
866518.86544.3927738264332.7754741298987-25.59277382642840.470649891881673
876563.86570.6563505081827.8166227072361-6.85635050817958-0.346852938405403
8866146583.8303130315816.664728129240230.1696869684227-0.780553803965433
896555.66587.01930809256.3943102610478-31.4193080925045-0.718631267573772
906601.86602.1019279640513.0147723260822-0.3019279640469840.462984212162373
916632.46612.5625730384811.069418399027419.8374269615165-0.13605055658131
926657.86649.3346281697930.6461899309988.465371830212451.36935757144204
936674.46687.1619450715336.116709375457-12.76194507153050.382662411806987
9466876700.0317697014818.4074310442073-13.0317697014833-1.23878100072393
956697.66701.128809987695.22156480095135-3.52880998769029-0.922456668663583
9667326711.12887823338.8619451170588120.87112176670110.254713725643502
976736.46727.8329958815914.83700410611498.567004118413280.417999778892581
986745.86766.6094621898233.065902122045-20.80946218981581.27476350934579
996805.26807.2569283675138.8339571158027-2.056928367507220.403458962178834
1006850.46820.5131737877219.372548365753929.8868262122779-1.36196883768886
1016807.26839.3653396223418.976374122415-32.1653396223426-0.0277202034922632
1026844.66846.244380306119.76717857100821-1.64438030611365-0.644072614184202
1036850.86840.83633271974-1.780577847665449.9636672802594-0.807604431766071
1046848.26842.12376905080.5538846885803356.076230949198190.163286710744634
1056837.86844.72940977342.11523332147556-6.929409773401570.109216495341586
1066857.66862.6591508158214.149974799315-5.059150815823620.841859289661311
1076900.86900.1532863577831.91451578200650.6467136422222081.24279105829806
1086940.86922.8513218542824.899933225598117.9486781457152-0.49077722084971
1096937.46937.0070092228516.72214940688640.392990777145207-0.572057754897533
1106950.46971.1560983504129.9793594405104-20.7560983504130.927120286921028
1116978.86979.7242690489613.7022260071478-0.924269048964877-1.13854906402512
1126997.86972.08057168724-2.5265465348325225.719428312757-1.13563108285419
1136934.86964.97791252492-6.00732466915823-30.1779125249237-0.243544223009893
1146946.86946.51207026577-15.4837640481050.287929734228018-0.662802462480194
1156956.26943.53709906978-5.9722616368404812.66290093021760.665202903538802
1166968.26957.987993050829.5550233021196210.21200694917851.08605114872709







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
16958.385446083126976.84781774974-18.462371666627
26973.559342339396983.14796126834-9.58861892894724
36989.826385323686989.448104786930.378280536742501
47018.297688093126995.7482483055322.549439787587
57020.754480519557002.0483918241218.7060886954266
66998.380337320517008.34853534272-9.96819802221382
77018.090025229177014.648678861313.44134636785743
87047.503545349827020.9488223799126.554722969911
97002.160902398627027.24896589851-25.0880634998891
107027.982085827567033.5491094171-5.56702358953927
117043.627100168937039.84925293573.77784723323952
127039.415946570747046.14939645429-6.73344988354771

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 6958.38544608312 & 6976.84781774974 & -18.462371666627 \tabularnewline
2 & 6973.55934233939 & 6983.14796126834 & -9.58861892894724 \tabularnewline
3 & 6989.82638532368 & 6989.44810478693 & 0.378280536742501 \tabularnewline
4 & 7018.29768809312 & 6995.74824830553 & 22.549439787587 \tabularnewline
5 & 7020.75448051955 & 7002.04839182412 & 18.7060886954266 \tabularnewline
6 & 6998.38033732051 & 7008.34853534272 & -9.96819802221382 \tabularnewline
7 & 7018.09002522917 & 7014.64867886131 & 3.44134636785743 \tabularnewline
8 & 7047.50354534982 & 7020.94882237991 & 26.554722969911 \tabularnewline
9 & 7002.16090239862 & 7027.24896589851 & -25.0880634998891 \tabularnewline
10 & 7027.98208582756 & 7033.5491094171 & -5.56702358953927 \tabularnewline
11 & 7043.62710016893 & 7039.8492529357 & 3.77784723323952 \tabularnewline
12 & 7039.41594657074 & 7046.14939645429 & -6.73344988354771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299067&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]6958.38544608312[/C][C]6976.84781774974[/C][C]-18.462371666627[/C][/ROW]
[ROW][C]2[/C][C]6973.55934233939[/C][C]6983.14796126834[/C][C]-9.58861892894724[/C][/ROW]
[ROW][C]3[/C][C]6989.82638532368[/C][C]6989.44810478693[/C][C]0.378280536742501[/C][/ROW]
[ROW][C]4[/C][C]7018.29768809312[/C][C]6995.74824830553[/C][C]22.549439787587[/C][/ROW]
[ROW][C]5[/C][C]7020.75448051955[/C][C]7002.04839182412[/C][C]18.7060886954266[/C][/ROW]
[ROW][C]6[/C][C]6998.38033732051[/C][C]7008.34853534272[/C][C]-9.96819802221382[/C][/ROW]
[ROW][C]7[/C][C]7018.09002522917[/C][C]7014.64867886131[/C][C]3.44134636785743[/C][/ROW]
[ROW][C]8[/C][C]7047.50354534982[/C][C]7020.94882237991[/C][C]26.554722969911[/C][/ROW]
[ROW][C]9[/C][C]7002.16090239862[/C][C]7027.24896589851[/C][C]-25.0880634998891[/C][/ROW]
[ROW][C]10[/C][C]7027.98208582756[/C][C]7033.5491094171[/C][C]-5.56702358953927[/C][/ROW]
[ROW][C]11[/C][C]7043.62710016893[/C][C]7039.8492529357[/C][C]3.77784723323952[/C][/ROW]
[ROW][C]12[/C][C]7039.41594657074[/C][C]7046.14939645429[/C][C]-6.73344988354771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299067&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
16958.385446083126976.84781774974-18.462371666627
26973.559342339396983.14796126834-9.58861892894724
36989.826385323686989.448104786930.378280536742501
47018.297688093126995.7482483055322.549439787587
57020.754480519557002.0483918241218.7060886954266
66998.380337320517008.34853534272-9.96819802221382
77018.090025229177014.648678861313.44134636785743
87047.503545349827020.9488223799126.554722969911
97002.160902398627027.24896589851-25.0880634998891
107027.982085827567033.5491094171-5.56702358953927
117043.627100168937039.84925293573.77784723323952
127039.415946570747046.14939645429-6.73344988354771



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
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')