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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 22:13:34 +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/t14816636497xszhbn5psmk9rj.htm/, Retrieved Sat, 04 May 2024 20:19:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299232, Retrieved Sat, 04 May 2024 20:19:00 +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] [] [2016-12-13 21:13:34] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
5290
5135
5075
5115
5115
5115
5230
5305
5360
5415
5370
5355
5595
5485
5510
5565
5665
5690
5750
5690
5720
5530
5495
5475
5455
5500
5495
5485
5495
5500
5430
5420
5455
5405
5300
5470
5440
5350
5250
5100
5065
4980
4970
4910
4840
4850
4910
4895
4955
4960
4940
4905
4925
4960
4925
5025
5045
5090
5120
5145
5095
5075
5125
5075
5100
5085
5065
5090
5020
5030
5000
5030
5015
4955
4940
5060
5070
5005
4945
5015
5035
4985
5020
4920
5125
5080
5060
5095
5105
5105
5115
5070
5115
5150
5115
5060
5075
5155
5120
5030
4995
5035
4970
4970
4975
4965
4915
4910
4895
4880
4910
4935
4975
4895
4940
4880




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299232&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299232&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 time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
152905290000
251355146.73752896576-8.01198161578281-8.01198131039125-1.49148952814135
350755087.08790702499-8.43073442270776-8.43073442270775-0.885956714721333
451155120.26029835938-8.2247989997459-8.224798999745950.715065614400823
551155122.43452551071-8.17570966543589-8.17570966543590.178740847593554
651155122.54619674921-8.1368848754368-8.136884875436770.14244434611817
752305229.4044039392-7.60077047549514-7.600770475495141.9765291815708
853055306.19415602284-7.20916724906511-7.209167249065111.45048618359517
953605362.39654993881-6.91627354669988-6.916273546699881.08989433193356
1054155417.23100942045-6.63236247911456-6.632362479114551.06133901789837
1153705379.02715154831-6.77685427170862-6.77685427170862-0.542629332507163
1253555362.51509548203-6.82120593416755-6.82120593416756-0.167320520757332
1355955459.51319407531-11.6418214033133128.060035310182.16791471341947
1454855493.18629164599-10.4974612148945-10.49746124882950.658951698164242
1555105517.86641098379-10.366954543253-10.3669545432530.603492649843244
1655655570.71665327551-10.2227646740159-10.2227646740161.08540340487926
1756655667.37058124658-9.98959569301597-9.989595693015981.8350380164468
1856905697.07379739884-9.90343565952137-9.903435659521360.681511896785288
1957505754.9264751861-9.75670608796712-9.75670608796711.16334684181513
2056905702.86403525015-9.84812233546144-9.84812233546145-0.726371998607179
2157205727.32807502955-9.77413890882208-9.774138908822050.589124495385385
2255305551.93706034998-10.1304714693426-10.1304714693426-2.8435621287255
2354955507.63954581967-10.203825657142-10.203825657142-0.58663054275104
2454755486.04058137984-10.2282377906807-10.2282377906807-0.195648282604884
2554555374.17161288604-8.0078734779798788.0866078201324-1.93075360682491
2655005498.17227507429-5.85030993616982-5.850309960732612.04828331789303
2754955500.26589973215-5.83118448330163-5.831184483301660.136277860976107
2854855491.07562143323-5.83616264339963-5.83616264339968-0.0576552429711589
2954955499.77898470495-5.81553590980169-5.815535909801690.249557767154946
3055005505.01223512081-5.79992846829852-5.799928468298530.189642339443071
3154305440.09771636944-5.88329958717624-5.88329958717622-1.01464719653269
3254205426.44792846364-5.894237338314-5.89423733831402-0.133304466487612
3354555458.16028690918-5.84134950199462-5.841349501994640.645481295030846
3454055413.65228843223-5.8956517677187-5.89565176771868-0.663675534373865
3553005312.79860412673-6.02882092113337-6.02882092113337-1.62986117296517
3654705464.55870017148-5.80784762274613-5.807847622746182.70828919040842
3754405391.48289361414-4.8471056707879953.3181622312386-1.23627592326576
3853505357.02830987195-5.20481489686227-5.20481464624699-0.472550119121403
3952505261.77625582012-5.3652775981891-5.36527759818916-1.54472792915408
4051005115.56106596421-5.51987050305888-5.51987050305891-2.41716441725211
4150655073.18614820607-5.55860783150188-5.55860783150187-0.632484293157182
4249804991.09505350645-5.63873408952112-5.63873408952114-1.31340475232087
4349704976.3010265548-5.64830743381718-5.64830743381716-0.157117589586811
4449104919.35884216603-5.70188679608801-5.70188679608802-0.880274031071453
4548404850.28599390398-5.76801222986015-5.76801222986018-1.08753303479495
4648504855.00911923443-5.75707649783519-5.757076497835150.18004229525723
4749104911.27091075875-5.6924967048977-5.692496704897711.06432825739597
4848954901.02207672692-5.69723625032258-5.69723625032263-0.0781929189044419
4949554892.80438681851-5.6704959525218662.3754562031212-0.0455474322030843
5049604960.31507956621-4.96922632967964-4.969227309409851.1866303302477
5149404945.67186350818-4.98290976329148-4.9829097632915-0.165951977320116
5249054912.04962384022-5.00786913389724-5.00786913389726-0.491442842609252
5349254928.46277456984-4.98998744963037-4.989987449630340.367580825774506
5449604962.19693318774-4.95778118919754-4.957781189197570.664499374229441
5549254931.79310550958-4.97892262952082-4.97892262952081-0.436649456898676
5650255023.03869029286-4.8990434233044-4.899043423304411.6511942855718
5750455047.76250300308-4.87447290985289-4.874472909852940.508322439510842
5850905091.37723536738-4.83428714205001-4.834287142049960.832065069837648
5951205122.2583708396-4.80471224642592-4.804712246425920.612869332630037
6051455147.62842710607-4.7797460779773-4.779746077977350.517792691781423
6150955056.58488298514-4.0517620646046344.5693834273259-1.54301549064513
6250755077.25087902432-3.85549729622677-3.855498098656380.404874954446986
6351255125.11108297018-3.79485496646537-3.794854966465360.887147951469214
6450755081.6513575264-3.82351923697795-3.82351923697797-0.680597301805169
6551005102.0778093863-3.80673088846273-3.806730888462710.416099826504656
6650855089.44227926152-3.81282135243578-3.81282135243581-0.151491402638929
6750655069.94208077184-3.82363361126378-3.82363361126376-0.269176165804333
6850905091.96320522515-3.80583304551928-3.805833045519290.443464284377183
6950205028.12707079435-3.84715039680768-3.84715039680771-1.03004598356574
7050305033.20471008186-3.84101191315264-3.841011913152590.15313835999552
7150005005.55485203768-3.8573764174374-3.8573764174374-0.408530289277695
7250305031.69786262869-3.83677045222113-3.836770452221190.514769352399508
7350154979.91127617713-3.5008390037051538.5092294487438-0.851813488093777
7449554959.71353340777-3.61401803036867-3.61401838050206-0.275424645125602
7549404944.45523107455-3.62567850015187-3.62567850015185-0.199748800002559
7650605055.38764349423-3.55496842647078-3.554968426470811.96558372572426
7750705072.0981308348-3.54298394050636-3.542983940506330.347715445980282
7850055012.56768855229-3.57597904973134-3.57597904973137-0.960634991119436
7949454952.62772523602-3.60917013738867-3.60917013738865-0.967095309411084
8050155013.94213689937-3.57096154237549-3.570961542375491.11396103365054
8150355036.67977621021-3.55548761814021-3.555487618140250.451403804953884
8249854991.54442823639-3.57992925865282-3.57992925865278-0.713428452485945
8350205021.19144383397-3.56040913694686-3.560409136946860.570108801220722
8449204929.86906006573-3.61193715433657-3.61193715433663-1.50582206616133
8551255066.0834937081-4.4493362201217248.94269902952182.47174772857095
8650805082.9078441633-4.3235398474733-4.3235405292980.352741290937674
8750605065.28287129689-4.33516265442168-4.33516265442172-0.228175032992276
8850955096.76246282262-4.31587054668909-4.315870546689120.614488891619274
8951055108.1856065374-4.30774716701375-4.307747167013710.270041923414982
9051055108.94394515975-4.30514125229224-4.305141252292270.0869213068585799
9151155118.32250244674-4.298107538884-4.298107538883970.234777872137004
9250705076.95974379781-4.31714953067084-4.31714953067084-0.635936177462497
9351155116.18999437455-4.29478852877235-4.29478852877240.747163758588907
9451505151.45406254578-4.27448601626563-4.27448601626560.678730317932974
9551155121.14409040612-4.28784117062389-4.28784117062388-0.446703298701171
9650605067.80984344897-4.31298709987458-4.31298709987464-0.841512567945591
9750755031.65946354584-4.1464883968952145.611373040089-0.560711617836507
9851555150.26779330157-3.50277413729099-3.502775236152962.04349632344593
9951205125.06575911517-3.51959216005722-3.51959216005727-0.372231656043024
10050305039.41444940287-3.55883739516081-3.55883739516083-1.40913416900031
10149955001.05588926511-3.57477120615892-3.57477120615889-0.597060926871562
10250355035.82356556-3.55727364864971-3.557273648649750.6578437338147
10349704977.48780711812-3.5822555975884-3.58225559758837-0.93983776608231
10449704973.60390000551-3.58239310251568-3.58239310251567-0.00517545277243627
10549754978.00925004335-3.57875362912397-3.578753629124020.137046166340534
10649654968.97052110251-3.58124023684945-3.58124023684941-0.0936771006660597
10749154921.71497650971-3.60112154015372-3.60112154015371-0.749322406904662
10849104913.9032422517-3.60303741219153-3.6030374121916-0.0722417041961376
10948954861.35622121851-3.3758739787179737.1346151260257-0.859494581706584
11048804881.6652555113-3.26430180064034-3.264303242648480.395520170116776
11149104910.92408978979-3.24165419413131-3.241654194131320.557904352883424
11249354936.19648020879-3.22941177204722-3.229411772047250.489206028048586
11349754975.20087837737-3.21203545950156-3.212035459501520.724593645565032
11448954903.14841015825-3.24026571617744-3.24026571617748-1.1810761358387
11549404940.34094100515-3.22369490367184-3.223694903671810.693694189710265
11648804886.8296701194-3.24429585313902-3.24429585313902-0.862769824372271

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5290 & 5290 & 0 & 0 & 0 \tabularnewline
2 & 5135 & 5146.73752896576 & -8.01198161578281 & -8.01198131039125 & -1.49148952814135 \tabularnewline
3 & 5075 & 5087.08790702499 & -8.43073442270776 & -8.43073442270775 & -0.885956714721333 \tabularnewline
4 & 5115 & 5120.26029835938 & -8.2247989997459 & -8.22479899974595 & 0.715065614400823 \tabularnewline
5 & 5115 & 5122.43452551071 & -8.17570966543589 & -8.1757096654359 & 0.178740847593554 \tabularnewline
6 & 5115 & 5122.54619674921 & -8.1368848754368 & -8.13688487543677 & 0.14244434611817 \tabularnewline
7 & 5230 & 5229.4044039392 & -7.60077047549514 & -7.60077047549514 & 1.9765291815708 \tabularnewline
8 & 5305 & 5306.19415602284 & -7.20916724906511 & -7.20916724906511 & 1.45048618359517 \tabularnewline
9 & 5360 & 5362.39654993881 & -6.91627354669988 & -6.91627354669988 & 1.08989433193356 \tabularnewline
10 & 5415 & 5417.23100942045 & -6.63236247911456 & -6.63236247911455 & 1.06133901789837 \tabularnewline
11 & 5370 & 5379.02715154831 & -6.77685427170862 & -6.77685427170862 & -0.542629332507163 \tabularnewline
12 & 5355 & 5362.51509548203 & -6.82120593416755 & -6.82120593416756 & -0.167320520757332 \tabularnewline
13 & 5595 & 5459.51319407531 & -11.6418214033133 & 128.06003531018 & 2.16791471341947 \tabularnewline
14 & 5485 & 5493.18629164599 & -10.4974612148945 & -10.4974612488295 & 0.658951698164242 \tabularnewline
15 & 5510 & 5517.86641098379 & -10.366954543253 & -10.366954543253 & 0.603492649843244 \tabularnewline
16 & 5565 & 5570.71665327551 & -10.2227646740159 & -10.222764674016 & 1.08540340487926 \tabularnewline
17 & 5665 & 5667.37058124658 & -9.98959569301597 & -9.98959569301598 & 1.8350380164468 \tabularnewline
18 & 5690 & 5697.07379739884 & -9.90343565952137 & -9.90343565952136 & 0.681511896785288 \tabularnewline
19 & 5750 & 5754.9264751861 & -9.75670608796712 & -9.7567060879671 & 1.16334684181513 \tabularnewline
20 & 5690 & 5702.86403525015 & -9.84812233546144 & -9.84812233546145 & -0.726371998607179 \tabularnewline
21 & 5720 & 5727.32807502955 & -9.77413890882208 & -9.77413890882205 & 0.589124495385385 \tabularnewline
22 & 5530 & 5551.93706034998 & -10.1304714693426 & -10.1304714693426 & -2.8435621287255 \tabularnewline
23 & 5495 & 5507.63954581967 & -10.203825657142 & -10.203825657142 & -0.58663054275104 \tabularnewline
24 & 5475 & 5486.04058137984 & -10.2282377906807 & -10.2282377906807 & -0.195648282604884 \tabularnewline
25 & 5455 & 5374.17161288604 & -8.00787347797987 & 88.0866078201324 & -1.93075360682491 \tabularnewline
26 & 5500 & 5498.17227507429 & -5.85030993616982 & -5.85030996073261 & 2.04828331789303 \tabularnewline
27 & 5495 & 5500.26589973215 & -5.83118448330163 & -5.83118448330166 & 0.136277860976107 \tabularnewline
28 & 5485 & 5491.07562143323 & -5.83616264339963 & -5.83616264339968 & -0.0576552429711589 \tabularnewline
29 & 5495 & 5499.77898470495 & -5.81553590980169 & -5.81553590980169 & 0.249557767154946 \tabularnewline
30 & 5500 & 5505.01223512081 & -5.79992846829852 & -5.79992846829853 & 0.189642339443071 \tabularnewline
31 & 5430 & 5440.09771636944 & -5.88329958717624 & -5.88329958717622 & -1.01464719653269 \tabularnewline
32 & 5420 & 5426.44792846364 & -5.894237338314 & -5.89423733831402 & -0.133304466487612 \tabularnewline
33 & 5455 & 5458.16028690918 & -5.84134950199462 & -5.84134950199464 & 0.645481295030846 \tabularnewline
34 & 5405 & 5413.65228843223 & -5.8956517677187 & -5.89565176771868 & -0.663675534373865 \tabularnewline
35 & 5300 & 5312.79860412673 & -6.02882092113337 & -6.02882092113337 & -1.62986117296517 \tabularnewline
36 & 5470 & 5464.55870017148 & -5.80784762274613 & -5.80784762274618 & 2.70828919040842 \tabularnewline
37 & 5440 & 5391.48289361414 & -4.84710567078799 & 53.3181622312386 & -1.23627592326576 \tabularnewline
38 & 5350 & 5357.02830987195 & -5.20481489686227 & -5.20481464624699 & -0.472550119121403 \tabularnewline
39 & 5250 & 5261.77625582012 & -5.3652775981891 & -5.36527759818916 & -1.54472792915408 \tabularnewline
40 & 5100 & 5115.56106596421 & -5.51987050305888 & -5.51987050305891 & -2.41716441725211 \tabularnewline
41 & 5065 & 5073.18614820607 & -5.55860783150188 & -5.55860783150187 & -0.632484293157182 \tabularnewline
42 & 4980 & 4991.09505350645 & -5.63873408952112 & -5.63873408952114 & -1.31340475232087 \tabularnewline
43 & 4970 & 4976.3010265548 & -5.64830743381718 & -5.64830743381716 & -0.157117589586811 \tabularnewline
44 & 4910 & 4919.35884216603 & -5.70188679608801 & -5.70188679608802 & -0.880274031071453 \tabularnewline
45 & 4840 & 4850.28599390398 & -5.76801222986015 & -5.76801222986018 & -1.08753303479495 \tabularnewline
46 & 4850 & 4855.00911923443 & -5.75707649783519 & -5.75707649783515 & 0.18004229525723 \tabularnewline
47 & 4910 & 4911.27091075875 & -5.6924967048977 & -5.69249670489771 & 1.06432825739597 \tabularnewline
48 & 4895 & 4901.02207672692 & -5.69723625032258 & -5.69723625032263 & -0.0781929189044419 \tabularnewline
49 & 4955 & 4892.80438681851 & -5.67049595252186 & 62.3754562031212 & -0.0455474322030843 \tabularnewline
50 & 4960 & 4960.31507956621 & -4.96922632967964 & -4.96922730940985 & 1.1866303302477 \tabularnewline
51 & 4940 & 4945.67186350818 & -4.98290976329148 & -4.9829097632915 & -0.165951977320116 \tabularnewline
52 & 4905 & 4912.04962384022 & -5.00786913389724 & -5.00786913389726 & -0.491442842609252 \tabularnewline
53 & 4925 & 4928.46277456984 & -4.98998744963037 & -4.98998744963034 & 0.367580825774506 \tabularnewline
54 & 4960 & 4962.19693318774 & -4.95778118919754 & -4.95778118919757 & 0.664499374229441 \tabularnewline
55 & 4925 & 4931.79310550958 & -4.97892262952082 & -4.97892262952081 & -0.436649456898676 \tabularnewline
56 & 5025 & 5023.03869029286 & -4.8990434233044 & -4.89904342330441 & 1.6511942855718 \tabularnewline
57 & 5045 & 5047.76250300308 & -4.87447290985289 & -4.87447290985294 & 0.508322439510842 \tabularnewline
58 & 5090 & 5091.37723536738 & -4.83428714205001 & -4.83428714204996 & 0.832065069837648 \tabularnewline
59 & 5120 & 5122.2583708396 & -4.80471224642592 & -4.80471224642592 & 0.612869332630037 \tabularnewline
60 & 5145 & 5147.62842710607 & -4.7797460779773 & -4.77974607797735 & 0.517792691781423 \tabularnewline
61 & 5095 & 5056.58488298514 & -4.05176206460463 & 44.5693834273259 & -1.54301549064513 \tabularnewline
62 & 5075 & 5077.25087902432 & -3.85549729622677 & -3.85549809865638 & 0.404874954446986 \tabularnewline
63 & 5125 & 5125.11108297018 & -3.79485496646537 & -3.79485496646536 & 0.887147951469214 \tabularnewline
64 & 5075 & 5081.6513575264 & -3.82351923697795 & -3.82351923697797 & -0.680597301805169 \tabularnewline
65 & 5100 & 5102.0778093863 & -3.80673088846273 & -3.80673088846271 & 0.416099826504656 \tabularnewline
66 & 5085 & 5089.44227926152 & -3.81282135243578 & -3.81282135243581 & -0.151491402638929 \tabularnewline
67 & 5065 & 5069.94208077184 & -3.82363361126378 & -3.82363361126376 & -0.269176165804333 \tabularnewline
68 & 5090 & 5091.96320522515 & -3.80583304551928 & -3.80583304551929 & 0.443464284377183 \tabularnewline
69 & 5020 & 5028.12707079435 & -3.84715039680768 & -3.84715039680771 & -1.03004598356574 \tabularnewline
70 & 5030 & 5033.20471008186 & -3.84101191315264 & -3.84101191315259 & 0.15313835999552 \tabularnewline
71 & 5000 & 5005.55485203768 & -3.8573764174374 & -3.8573764174374 & -0.408530289277695 \tabularnewline
72 & 5030 & 5031.69786262869 & -3.83677045222113 & -3.83677045222119 & 0.514769352399508 \tabularnewline
73 & 5015 & 4979.91127617713 & -3.50083900370515 & 38.5092294487438 & -0.851813488093777 \tabularnewline
74 & 4955 & 4959.71353340777 & -3.61401803036867 & -3.61401838050206 & -0.275424645125602 \tabularnewline
75 & 4940 & 4944.45523107455 & -3.62567850015187 & -3.62567850015185 & -0.199748800002559 \tabularnewline
76 & 5060 & 5055.38764349423 & -3.55496842647078 & -3.55496842647081 & 1.96558372572426 \tabularnewline
77 & 5070 & 5072.0981308348 & -3.54298394050636 & -3.54298394050633 & 0.347715445980282 \tabularnewline
78 & 5005 & 5012.56768855229 & -3.57597904973134 & -3.57597904973137 & -0.960634991119436 \tabularnewline
79 & 4945 & 4952.62772523602 & -3.60917013738867 & -3.60917013738865 & -0.967095309411084 \tabularnewline
80 & 5015 & 5013.94213689937 & -3.57096154237549 & -3.57096154237549 & 1.11396103365054 \tabularnewline
81 & 5035 & 5036.67977621021 & -3.55548761814021 & -3.55548761814025 & 0.451403804953884 \tabularnewline
82 & 4985 & 4991.54442823639 & -3.57992925865282 & -3.57992925865278 & -0.713428452485945 \tabularnewline
83 & 5020 & 5021.19144383397 & -3.56040913694686 & -3.56040913694686 & 0.570108801220722 \tabularnewline
84 & 4920 & 4929.86906006573 & -3.61193715433657 & -3.61193715433663 & -1.50582206616133 \tabularnewline
85 & 5125 & 5066.0834937081 & -4.44933622012172 & 48.9426990295218 & 2.47174772857095 \tabularnewline
86 & 5080 & 5082.9078441633 & -4.3235398474733 & -4.323540529298 & 0.352741290937674 \tabularnewline
87 & 5060 & 5065.28287129689 & -4.33516265442168 & -4.33516265442172 & -0.228175032992276 \tabularnewline
88 & 5095 & 5096.76246282262 & -4.31587054668909 & -4.31587054668912 & 0.614488891619274 \tabularnewline
89 & 5105 & 5108.1856065374 & -4.30774716701375 & -4.30774716701371 & 0.270041923414982 \tabularnewline
90 & 5105 & 5108.94394515975 & -4.30514125229224 & -4.30514125229227 & 0.0869213068585799 \tabularnewline
91 & 5115 & 5118.32250244674 & -4.298107538884 & -4.29810753888397 & 0.234777872137004 \tabularnewline
92 & 5070 & 5076.95974379781 & -4.31714953067084 & -4.31714953067084 & -0.635936177462497 \tabularnewline
93 & 5115 & 5116.18999437455 & -4.29478852877235 & -4.2947885287724 & 0.747163758588907 \tabularnewline
94 & 5150 & 5151.45406254578 & -4.27448601626563 & -4.2744860162656 & 0.678730317932974 \tabularnewline
95 & 5115 & 5121.14409040612 & -4.28784117062389 & -4.28784117062388 & -0.446703298701171 \tabularnewline
96 & 5060 & 5067.80984344897 & -4.31298709987458 & -4.31298709987464 & -0.841512567945591 \tabularnewline
97 & 5075 & 5031.65946354584 & -4.14648839689521 & 45.611373040089 & -0.560711617836507 \tabularnewline
98 & 5155 & 5150.26779330157 & -3.50277413729099 & -3.50277523615296 & 2.04349632344593 \tabularnewline
99 & 5120 & 5125.06575911517 & -3.51959216005722 & -3.51959216005727 & -0.372231656043024 \tabularnewline
100 & 5030 & 5039.41444940287 & -3.55883739516081 & -3.55883739516083 & -1.40913416900031 \tabularnewline
101 & 4995 & 5001.05588926511 & -3.57477120615892 & -3.57477120615889 & -0.597060926871562 \tabularnewline
102 & 5035 & 5035.82356556 & -3.55727364864971 & -3.55727364864975 & 0.6578437338147 \tabularnewline
103 & 4970 & 4977.48780711812 & -3.5822555975884 & -3.58225559758837 & -0.93983776608231 \tabularnewline
104 & 4970 & 4973.60390000551 & -3.58239310251568 & -3.58239310251567 & -0.00517545277243627 \tabularnewline
105 & 4975 & 4978.00925004335 & -3.57875362912397 & -3.57875362912402 & 0.137046166340534 \tabularnewline
106 & 4965 & 4968.97052110251 & -3.58124023684945 & -3.58124023684941 & -0.0936771006660597 \tabularnewline
107 & 4915 & 4921.71497650971 & -3.60112154015372 & -3.60112154015371 & -0.749322406904662 \tabularnewline
108 & 4910 & 4913.9032422517 & -3.60303741219153 & -3.6030374121916 & -0.0722417041961376 \tabularnewline
109 & 4895 & 4861.35622121851 & -3.37587397871797 & 37.1346151260257 & -0.859494581706584 \tabularnewline
110 & 4880 & 4881.6652555113 & -3.26430180064034 & -3.26430324264848 & 0.395520170116776 \tabularnewline
111 & 4910 & 4910.92408978979 & -3.24165419413131 & -3.24165419413132 & 0.557904352883424 \tabularnewline
112 & 4935 & 4936.19648020879 & -3.22941177204722 & -3.22941177204725 & 0.489206028048586 \tabularnewline
113 & 4975 & 4975.20087837737 & -3.21203545950156 & -3.21203545950152 & 0.724593645565032 \tabularnewline
114 & 4895 & 4903.14841015825 & -3.24026571617744 & -3.24026571617748 & -1.1810761358387 \tabularnewline
115 & 4940 & 4940.34094100515 & -3.22369490367184 & -3.22369490367181 & 0.693694189710265 \tabularnewline
116 & 4880 & 4886.8296701194 & -3.24429585313902 & -3.24429585313902 & -0.862769824372271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299232&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]5290[/C][C]5290[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5135[/C][C]5146.73752896576[/C][C]-8.01198161578281[/C][C]-8.01198131039125[/C][C]-1.49148952814135[/C][/ROW]
[ROW][C]3[/C][C]5075[/C][C]5087.08790702499[/C][C]-8.43073442270776[/C][C]-8.43073442270775[/C][C]-0.885956714721333[/C][/ROW]
[ROW][C]4[/C][C]5115[/C][C]5120.26029835938[/C][C]-8.2247989997459[/C][C]-8.22479899974595[/C][C]0.715065614400823[/C][/ROW]
[ROW][C]5[/C][C]5115[/C][C]5122.43452551071[/C][C]-8.17570966543589[/C][C]-8.1757096654359[/C][C]0.178740847593554[/C][/ROW]
[ROW][C]6[/C][C]5115[/C][C]5122.54619674921[/C][C]-8.1368848754368[/C][C]-8.13688487543677[/C][C]0.14244434611817[/C][/ROW]
[ROW][C]7[/C][C]5230[/C][C]5229.4044039392[/C][C]-7.60077047549514[/C][C]-7.60077047549514[/C][C]1.9765291815708[/C][/ROW]
[ROW][C]8[/C][C]5305[/C][C]5306.19415602284[/C][C]-7.20916724906511[/C][C]-7.20916724906511[/C][C]1.45048618359517[/C][/ROW]
[ROW][C]9[/C][C]5360[/C][C]5362.39654993881[/C][C]-6.91627354669988[/C][C]-6.91627354669988[/C][C]1.08989433193356[/C][/ROW]
[ROW][C]10[/C][C]5415[/C][C]5417.23100942045[/C][C]-6.63236247911456[/C][C]-6.63236247911455[/C][C]1.06133901789837[/C][/ROW]
[ROW][C]11[/C][C]5370[/C][C]5379.02715154831[/C][C]-6.77685427170862[/C][C]-6.77685427170862[/C][C]-0.542629332507163[/C][/ROW]
[ROW][C]12[/C][C]5355[/C][C]5362.51509548203[/C][C]-6.82120593416755[/C][C]-6.82120593416756[/C][C]-0.167320520757332[/C][/ROW]
[ROW][C]13[/C][C]5595[/C][C]5459.51319407531[/C][C]-11.6418214033133[/C][C]128.06003531018[/C][C]2.16791471341947[/C][/ROW]
[ROW][C]14[/C][C]5485[/C][C]5493.18629164599[/C][C]-10.4974612148945[/C][C]-10.4974612488295[/C][C]0.658951698164242[/C][/ROW]
[ROW][C]15[/C][C]5510[/C][C]5517.86641098379[/C][C]-10.366954543253[/C][C]-10.366954543253[/C][C]0.603492649843244[/C][/ROW]
[ROW][C]16[/C][C]5565[/C][C]5570.71665327551[/C][C]-10.2227646740159[/C][C]-10.222764674016[/C][C]1.08540340487926[/C][/ROW]
[ROW][C]17[/C][C]5665[/C][C]5667.37058124658[/C][C]-9.98959569301597[/C][C]-9.98959569301598[/C][C]1.8350380164468[/C][/ROW]
[ROW][C]18[/C][C]5690[/C][C]5697.07379739884[/C][C]-9.90343565952137[/C][C]-9.90343565952136[/C][C]0.681511896785288[/C][/ROW]
[ROW][C]19[/C][C]5750[/C][C]5754.9264751861[/C][C]-9.75670608796712[/C][C]-9.7567060879671[/C][C]1.16334684181513[/C][/ROW]
[ROW][C]20[/C][C]5690[/C][C]5702.86403525015[/C][C]-9.84812233546144[/C][C]-9.84812233546145[/C][C]-0.726371998607179[/C][/ROW]
[ROW][C]21[/C][C]5720[/C][C]5727.32807502955[/C][C]-9.77413890882208[/C][C]-9.77413890882205[/C][C]0.589124495385385[/C][/ROW]
[ROW][C]22[/C][C]5530[/C][C]5551.93706034998[/C][C]-10.1304714693426[/C][C]-10.1304714693426[/C][C]-2.8435621287255[/C][/ROW]
[ROW][C]23[/C][C]5495[/C][C]5507.63954581967[/C][C]-10.203825657142[/C][C]-10.203825657142[/C][C]-0.58663054275104[/C][/ROW]
[ROW][C]24[/C][C]5475[/C][C]5486.04058137984[/C][C]-10.2282377906807[/C][C]-10.2282377906807[/C][C]-0.195648282604884[/C][/ROW]
[ROW][C]25[/C][C]5455[/C][C]5374.17161288604[/C][C]-8.00787347797987[/C][C]88.0866078201324[/C][C]-1.93075360682491[/C][/ROW]
[ROW][C]26[/C][C]5500[/C][C]5498.17227507429[/C][C]-5.85030993616982[/C][C]-5.85030996073261[/C][C]2.04828331789303[/C][/ROW]
[ROW][C]27[/C][C]5495[/C][C]5500.26589973215[/C][C]-5.83118448330163[/C][C]-5.83118448330166[/C][C]0.136277860976107[/C][/ROW]
[ROW][C]28[/C][C]5485[/C][C]5491.07562143323[/C][C]-5.83616264339963[/C][C]-5.83616264339968[/C][C]-0.0576552429711589[/C][/ROW]
[ROW][C]29[/C][C]5495[/C][C]5499.77898470495[/C][C]-5.81553590980169[/C][C]-5.81553590980169[/C][C]0.249557767154946[/C][/ROW]
[ROW][C]30[/C][C]5500[/C][C]5505.01223512081[/C][C]-5.79992846829852[/C][C]-5.79992846829853[/C][C]0.189642339443071[/C][/ROW]
[ROW][C]31[/C][C]5430[/C][C]5440.09771636944[/C][C]-5.88329958717624[/C][C]-5.88329958717622[/C][C]-1.01464719653269[/C][/ROW]
[ROW][C]32[/C][C]5420[/C][C]5426.44792846364[/C][C]-5.894237338314[/C][C]-5.89423733831402[/C][C]-0.133304466487612[/C][/ROW]
[ROW][C]33[/C][C]5455[/C][C]5458.16028690918[/C][C]-5.84134950199462[/C][C]-5.84134950199464[/C][C]0.645481295030846[/C][/ROW]
[ROW][C]34[/C][C]5405[/C][C]5413.65228843223[/C][C]-5.8956517677187[/C][C]-5.89565176771868[/C][C]-0.663675534373865[/C][/ROW]
[ROW][C]35[/C][C]5300[/C][C]5312.79860412673[/C][C]-6.02882092113337[/C][C]-6.02882092113337[/C][C]-1.62986117296517[/C][/ROW]
[ROW][C]36[/C][C]5470[/C][C]5464.55870017148[/C][C]-5.80784762274613[/C][C]-5.80784762274618[/C][C]2.70828919040842[/C][/ROW]
[ROW][C]37[/C][C]5440[/C][C]5391.48289361414[/C][C]-4.84710567078799[/C][C]53.3181622312386[/C][C]-1.23627592326576[/C][/ROW]
[ROW][C]38[/C][C]5350[/C][C]5357.02830987195[/C][C]-5.20481489686227[/C][C]-5.20481464624699[/C][C]-0.472550119121403[/C][/ROW]
[ROW][C]39[/C][C]5250[/C][C]5261.77625582012[/C][C]-5.3652775981891[/C][C]-5.36527759818916[/C][C]-1.54472792915408[/C][/ROW]
[ROW][C]40[/C][C]5100[/C][C]5115.56106596421[/C][C]-5.51987050305888[/C][C]-5.51987050305891[/C][C]-2.41716441725211[/C][/ROW]
[ROW][C]41[/C][C]5065[/C][C]5073.18614820607[/C][C]-5.55860783150188[/C][C]-5.55860783150187[/C][C]-0.632484293157182[/C][/ROW]
[ROW][C]42[/C][C]4980[/C][C]4991.09505350645[/C][C]-5.63873408952112[/C][C]-5.63873408952114[/C][C]-1.31340475232087[/C][/ROW]
[ROW][C]43[/C][C]4970[/C][C]4976.3010265548[/C][C]-5.64830743381718[/C][C]-5.64830743381716[/C][C]-0.157117589586811[/C][/ROW]
[ROW][C]44[/C][C]4910[/C][C]4919.35884216603[/C][C]-5.70188679608801[/C][C]-5.70188679608802[/C][C]-0.880274031071453[/C][/ROW]
[ROW][C]45[/C][C]4840[/C][C]4850.28599390398[/C][C]-5.76801222986015[/C][C]-5.76801222986018[/C][C]-1.08753303479495[/C][/ROW]
[ROW][C]46[/C][C]4850[/C][C]4855.00911923443[/C][C]-5.75707649783519[/C][C]-5.75707649783515[/C][C]0.18004229525723[/C][/ROW]
[ROW][C]47[/C][C]4910[/C][C]4911.27091075875[/C][C]-5.6924967048977[/C][C]-5.69249670489771[/C][C]1.06432825739597[/C][/ROW]
[ROW][C]48[/C][C]4895[/C][C]4901.02207672692[/C][C]-5.69723625032258[/C][C]-5.69723625032263[/C][C]-0.0781929189044419[/C][/ROW]
[ROW][C]49[/C][C]4955[/C][C]4892.80438681851[/C][C]-5.67049595252186[/C][C]62.3754562031212[/C][C]-0.0455474322030843[/C][/ROW]
[ROW][C]50[/C][C]4960[/C][C]4960.31507956621[/C][C]-4.96922632967964[/C][C]-4.96922730940985[/C][C]1.1866303302477[/C][/ROW]
[ROW][C]51[/C][C]4940[/C][C]4945.67186350818[/C][C]-4.98290976329148[/C][C]-4.9829097632915[/C][C]-0.165951977320116[/C][/ROW]
[ROW][C]52[/C][C]4905[/C][C]4912.04962384022[/C][C]-5.00786913389724[/C][C]-5.00786913389726[/C][C]-0.491442842609252[/C][/ROW]
[ROW][C]53[/C][C]4925[/C][C]4928.46277456984[/C][C]-4.98998744963037[/C][C]-4.98998744963034[/C][C]0.367580825774506[/C][/ROW]
[ROW][C]54[/C][C]4960[/C][C]4962.19693318774[/C][C]-4.95778118919754[/C][C]-4.95778118919757[/C][C]0.664499374229441[/C][/ROW]
[ROW][C]55[/C][C]4925[/C][C]4931.79310550958[/C][C]-4.97892262952082[/C][C]-4.97892262952081[/C][C]-0.436649456898676[/C][/ROW]
[ROW][C]56[/C][C]5025[/C][C]5023.03869029286[/C][C]-4.8990434233044[/C][C]-4.89904342330441[/C][C]1.6511942855718[/C][/ROW]
[ROW][C]57[/C][C]5045[/C][C]5047.76250300308[/C][C]-4.87447290985289[/C][C]-4.87447290985294[/C][C]0.508322439510842[/C][/ROW]
[ROW][C]58[/C][C]5090[/C][C]5091.37723536738[/C][C]-4.83428714205001[/C][C]-4.83428714204996[/C][C]0.832065069837648[/C][/ROW]
[ROW][C]59[/C][C]5120[/C][C]5122.2583708396[/C][C]-4.80471224642592[/C][C]-4.80471224642592[/C][C]0.612869332630037[/C][/ROW]
[ROW][C]60[/C][C]5145[/C][C]5147.62842710607[/C][C]-4.7797460779773[/C][C]-4.77974607797735[/C][C]0.517792691781423[/C][/ROW]
[ROW][C]61[/C][C]5095[/C][C]5056.58488298514[/C][C]-4.05176206460463[/C][C]44.5693834273259[/C][C]-1.54301549064513[/C][/ROW]
[ROW][C]62[/C][C]5075[/C][C]5077.25087902432[/C][C]-3.85549729622677[/C][C]-3.85549809865638[/C][C]0.404874954446986[/C][/ROW]
[ROW][C]63[/C][C]5125[/C][C]5125.11108297018[/C][C]-3.79485496646537[/C][C]-3.79485496646536[/C][C]0.887147951469214[/C][/ROW]
[ROW][C]64[/C][C]5075[/C][C]5081.6513575264[/C][C]-3.82351923697795[/C][C]-3.82351923697797[/C][C]-0.680597301805169[/C][/ROW]
[ROW][C]65[/C][C]5100[/C][C]5102.0778093863[/C][C]-3.80673088846273[/C][C]-3.80673088846271[/C][C]0.416099826504656[/C][/ROW]
[ROW][C]66[/C][C]5085[/C][C]5089.44227926152[/C][C]-3.81282135243578[/C][C]-3.81282135243581[/C][C]-0.151491402638929[/C][/ROW]
[ROW][C]67[/C][C]5065[/C][C]5069.94208077184[/C][C]-3.82363361126378[/C][C]-3.82363361126376[/C][C]-0.269176165804333[/C][/ROW]
[ROW][C]68[/C][C]5090[/C][C]5091.96320522515[/C][C]-3.80583304551928[/C][C]-3.80583304551929[/C][C]0.443464284377183[/C][/ROW]
[ROW][C]69[/C][C]5020[/C][C]5028.12707079435[/C][C]-3.84715039680768[/C][C]-3.84715039680771[/C][C]-1.03004598356574[/C][/ROW]
[ROW][C]70[/C][C]5030[/C][C]5033.20471008186[/C][C]-3.84101191315264[/C][C]-3.84101191315259[/C][C]0.15313835999552[/C][/ROW]
[ROW][C]71[/C][C]5000[/C][C]5005.55485203768[/C][C]-3.8573764174374[/C][C]-3.8573764174374[/C][C]-0.408530289277695[/C][/ROW]
[ROW][C]72[/C][C]5030[/C][C]5031.69786262869[/C][C]-3.83677045222113[/C][C]-3.83677045222119[/C][C]0.514769352399508[/C][/ROW]
[ROW][C]73[/C][C]5015[/C][C]4979.91127617713[/C][C]-3.50083900370515[/C][C]38.5092294487438[/C][C]-0.851813488093777[/C][/ROW]
[ROW][C]74[/C][C]4955[/C][C]4959.71353340777[/C][C]-3.61401803036867[/C][C]-3.61401838050206[/C][C]-0.275424645125602[/C][/ROW]
[ROW][C]75[/C][C]4940[/C][C]4944.45523107455[/C][C]-3.62567850015187[/C][C]-3.62567850015185[/C][C]-0.199748800002559[/C][/ROW]
[ROW][C]76[/C][C]5060[/C][C]5055.38764349423[/C][C]-3.55496842647078[/C][C]-3.55496842647081[/C][C]1.96558372572426[/C][/ROW]
[ROW][C]77[/C][C]5070[/C][C]5072.0981308348[/C][C]-3.54298394050636[/C][C]-3.54298394050633[/C][C]0.347715445980282[/C][/ROW]
[ROW][C]78[/C][C]5005[/C][C]5012.56768855229[/C][C]-3.57597904973134[/C][C]-3.57597904973137[/C][C]-0.960634991119436[/C][/ROW]
[ROW][C]79[/C][C]4945[/C][C]4952.62772523602[/C][C]-3.60917013738867[/C][C]-3.60917013738865[/C][C]-0.967095309411084[/C][/ROW]
[ROW][C]80[/C][C]5015[/C][C]5013.94213689937[/C][C]-3.57096154237549[/C][C]-3.57096154237549[/C][C]1.11396103365054[/C][/ROW]
[ROW][C]81[/C][C]5035[/C][C]5036.67977621021[/C][C]-3.55548761814021[/C][C]-3.55548761814025[/C][C]0.451403804953884[/C][/ROW]
[ROW][C]82[/C][C]4985[/C][C]4991.54442823639[/C][C]-3.57992925865282[/C][C]-3.57992925865278[/C][C]-0.713428452485945[/C][/ROW]
[ROW][C]83[/C][C]5020[/C][C]5021.19144383397[/C][C]-3.56040913694686[/C][C]-3.56040913694686[/C][C]0.570108801220722[/C][/ROW]
[ROW][C]84[/C][C]4920[/C][C]4929.86906006573[/C][C]-3.61193715433657[/C][C]-3.61193715433663[/C][C]-1.50582206616133[/C][/ROW]
[ROW][C]85[/C][C]5125[/C][C]5066.0834937081[/C][C]-4.44933622012172[/C][C]48.9426990295218[/C][C]2.47174772857095[/C][/ROW]
[ROW][C]86[/C][C]5080[/C][C]5082.9078441633[/C][C]-4.3235398474733[/C][C]-4.323540529298[/C][C]0.352741290937674[/C][/ROW]
[ROW][C]87[/C][C]5060[/C][C]5065.28287129689[/C][C]-4.33516265442168[/C][C]-4.33516265442172[/C][C]-0.228175032992276[/C][/ROW]
[ROW][C]88[/C][C]5095[/C][C]5096.76246282262[/C][C]-4.31587054668909[/C][C]-4.31587054668912[/C][C]0.614488891619274[/C][/ROW]
[ROW][C]89[/C][C]5105[/C][C]5108.1856065374[/C][C]-4.30774716701375[/C][C]-4.30774716701371[/C][C]0.270041923414982[/C][/ROW]
[ROW][C]90[/C][C]5105[/C][C]5108.94394515975[/C][C]-4.30514125229224[/C][C]-4.30514125229227[/C][C]0.0869213068585799[/C][/ROW]
[ROW][C]91[/C][C]5115[/C][C]5118.32250244674[/C][C]-4.298107538884[/C][C]-4.29810753888397[/C][C]0.234777872137004[/C][/ROW]
[ROW][C]92[/C][C]5070[/C][C]5076.95974379781[/C][C]-4.31714953067084[/C][C]-4.31714953067084[/C][C]-0.635936177462497[/C][/ROW]
[ROW][C]93[/C][C]5115[/C][C]5116.18999437455[/C][C]-4.29478852877235[/C][C]-4.2947885287724[/C][C]0.747163758588907[/C][/ROW]
[ROW][C]94[/C][C]5150[/C][C]5151.45406254578[/C][C]-4.27448601626563[/C][C]-4.2744860162656[/C][C]0.678730317932974[/C][/ROW]
[ROW][C]95[/C][C]5115[/C][C]5121.14409040612[/C][C]-4.28784117062389[/C][C]-4.28784117062388[/C][C]-0.446703298701171[/C][/ROW]
[ROW][C]96[/C][C]5060[/C][C]5067.80984344897[/C][C]-4.31298709987458[/C][C]-4.31298709987464[/C][C]-0.841512567945591[/C][/ROW]
[ROW][C]97[/C][C]5075[/C][C]5031.65946354584[/C][C]-4.14648839689521[/C][C]45.611373040089[/C][C]-0.560711617836507[/C][/ROW]
[ROW][C]98[/C][C]5155[/C][C]5150.26779330157[/C][C]-3.50277413729099[/C][C]-3.50277523615296[/C][C]2.04349632344593[/C][/ROW]
[ROW][C]99[/C][C]5120[/C][C]5125.06575911517[/C][C]-3.51959216005722[/C][C]-3.51959216005727[/C][C]-0.372231656043024[/C][/ROW]
[ROW][C]100[/C][C]5030[/C][C]5039.41444940287[/C][C]-3.55883739516081[/C][C]-3.55883739516083[/C][C]-1.40913416900031[/C][/ROW]
[ROW][C]101[/C][C]4995[/C][C]5001.05588926511[/C][C]-3.57477120615892[/C][C]-3.57477120615889[/C][C]-0.597060926871562[/C][/ROW]
[ROW][C]102[/C][C]5035[/C][C]5035.82356556[/C][C]-3.55727364864971[/C][C]-3.55727364864975[/C][C]0.6578437338147[/C][/ROW]
[ROW][C]103[/C][C]4970[/C][C]4977.48780711812[/C][C]-3.5822555975884[/C][C]-3.58225559758837[/C][C]-0.93983776608231[/C][/ROW]
[ROW][C]104[/C][C]4970[/C][C]4973.60390000551[/C][C]-3.58239310251568[/C][C]-3.58239310251567[/C][C]-0.00517545277243627[/C][/ROW]
[ROW][C]105[/C][C]4975[/C][C]4978.00925004335[/C][C]-3.57875362912397[/C][C]-3.57875362912402[/C][C]0.137046166340534[/C][/ROW]
[ROW][C]106[/C][C]4965[/C][C]4968.97052110251[/C][C]-3.58124023684945[/C][C]-3.58124023684941[/C][C]-0.0936771006660597[/C][/ROW]
[ROW][C]107[/C][C]4915[/C][C]4921.71497650971[/C][C]-3.60112154015372[/C][C]-3.60112154015371[/C][C]-0.749322406904662[/C][/ROW]
[ROW][C]108[/C][C]4910[/C][C]4913.9032422517[/C][C]-3.60303741219153[/C][C]-3.6030374121916[/C][C]-0.0722417041961376[/C][/ROW]
[ROW][C]109[/C][C]4895[/C][C]4861.35622121851[/C][C]-3.37587397871797[/C][C]37.1346151260257[/C][C]-0.859494581706584[/C][/ROW]
[ROW][C]110[/C][C]4880[/C][C]4881.6652555113[/C][C]-3.26430180064034[/C][C]-3.26430324264848[/C][C]0.395520170116776[/C][/ROW]
[ROW][C]111[/C][C]4910[/C][C]4910.92408978979[/C][C]-3.24165419413131[/C][C]-3.24165419413132[/C][C]0.557904352883424[/C][/ROW]
[ROW][C]112[/C][C]4935[/C][C]4936.19648020879[/C][C]-3.22941177204722[/C][C]-3.22941177204725[/C][C]0.489206028048586[/C][/ROW]
[ROW][C]113[/C][C]4975[/C][C]4975.20087837737[/C][C]-3.21203545950156[/C][C]-3.21203545950152[/C][C]0.724593645565032[/C][/ROW]
[ROW][C]114[/C][C]4895[/C][C]4903.14841015825[/C][C]-3.24026571617744[/C][C]-3.24026571617748[/C][C]-1.1810761358387[/C][/ROW]
[ROW][C]115[/C][C]4940[/C][C]4940.34094100515[/C][C]-3.22369490367184[/C][C]-3.22369490367181[/C][C]0.693694189710265[/C][/ROW]
[ROW][C]116[/C][C]4880[/C][C]4886.8296701194[/C][C]-3.24429585313902[/C][C]-3.24429585313902[/C][C]-0.862769824372271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299232&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
152905290000
251355146.73752896576-8.01198161578281-8.01198131039125-1.49148952814135
350755087.08790702499-8.43073442270776-8.43073442270775-0.885956714721333
451155120.26029835938-8.2247989997459-8.224798999745950.715065614400823
551155122.43452551071-8.17570966543589-8.17570966543590.178740847593554
651155122.54619674921-8.1368848754368-8.136884875436770.14244434611817
752305229.4044039392-7.60077047549514-7.600770475495141.9765291815708
853055306.19415602284-7.20916724906511-7.209167249065111.45048618359517
953605362.39654993881-6.91627354669988-6.916273546699881.08989433193356
1054155417.23100942045-6.63236247911456-6.632362479114551.06133901789837
1153705379.02715154831-6.77685427170862-6.77685427170862-0.542629332507163
1253555362.51509548203-6.82120593416755-6.82120593416756-0.167320520757332
1355955459.51319407531-11.6418214033133128.060035310182.16791471341947
1454855493.18629164599-10.4974612148945-10.49746124882950.658951698164242
1555105517.86641098379-10.366954543253-10.3669545432530.603492649843244
1655655570.71665327551-10.2227646740159-10.2227646740161.08540340487926
1756655667.37058124658-9.98959569301597-9.989595693015981.8350380164468
1856905697.07379739884-9.90343565952137-9.903435659521360.681511896785288
1957505754.9264751861-9.75670608796712-9.75670608796711.16334684181513
2056905702.86403525015-9.84812233546144-9.84812233546145-0.726371998607179
2157205727.32807502955-9.77413890882208-9.774138908822050.589124495385385
2255305551.93706034998-10.1304714693426-10.1304714693426-2.8435621287255
2354955507.63954581967-10.203825657142-10.203825657142-0.58663054275104
2454755486.04058137984-10.2282377906807-10.2282377906807-0.195648282604884
2554555374.17161288604-8.0078734779798788.0866078201324-1.93075360682491
2655005498.17227507429-5.85030993616982-5.850309960732612.04828331789303
2754955500.26589973215-5.83118448330163-5.831184483301660.136277860976107
2854855491.07562143323-5.83616264339963-5.83616264339968-0.0576552429711589
2954955499.77898470495-5.81553590980169-5.815535909801690.249557767154946
3055005505.01223512081-5.79992846829852-5.799928468298530.189642339443071
3154305440.09771636944-5.88329958717624-5.88329958717622-1.01464719653269
3254205426.44792846364-5.894237338314-5.89423733831402-0.133304466487612
3354555458.16028690918-5.84134950199462-5.841349501994640.645481295030846
3454055413.65228843223-5.8956517677187-5.89565176771868-0.663675534373865
3553005312.79860412673-6.02882092113337-6.02882092113337-1.62986117296517
3654705464.55870017148-5.80784762274613-5.807847622746182.70828919040842
3754405391.48289361414-4.8471056707879953.3181622312386-1.23627592326576
3853505357.02830987195-5.20481489686227-5.20481464624699-0.472550119121403
3952505261.77625582012-5.3652775981891-5.36527759818916-1.54472792915408
4051005115.56106596421-5.51987050305888-5.51987050305891-2.41716441725211
4150655073.18614820607-5.55860783150188-5.55860783150187-0.632484293157182
4249804991.09505350645-5.63873408952112-5.63873408952114-1.31340475232087
4349704976.3010265548-5.64830743381718-5.64830743381716-0.157117589586811
4449104919.35884216603-5.70188679608801-5.70188679608802-0.880274031071453
4548404850.28599390398-5.76801222986015-5.76801222986018-1.08753303479495
4648504855.00911923443-5.75707649783519-5.757076497835150.18004229525723
4749104911.27091075875-5.6924967048977-5.692496704897711.06432825739597
4848954901.02207672692-5.69723625032258-5.69723625032263-0.0781929189044419
4949554892.80438681851-5.6704959525218662.3754562031212-0.0455474322030843
5049604960.31507956621-4.96922632967964-4.969227309409851.1866303302477
5149404945.67186350818-4.98290976329148-4.9829097632915-0.165951977320116
5249054912.04962384022-5.00786913389724-5.00786913389726-0.491442842609252
5349254928.46277456984-4.98998744963037-4.989987449630340.367580825774506
5449604962.19693318774-4.95778118919754-4.957781189197570.664499374229441
5549254931.79310550958-4.97892262952082-4.97892262952081-0.436649456898676
5650255023.03869029286-4.8990434233044-4.899043423304411.6511942855718
5750455047.76250300308-4.87447290985289-4.874472909852940.508322439510842
5850905091.37723536738-4.83428714205001-4.834287142049960.832065069837648
5951205122.2583708396-4.80471224642592-4.804712246425920.612869332630037
6051455147.62842710607-4.7797460779773-4.779746077977350.517792691781423
6150955056.58488298514-4.0517620646046344.5693834273259-1.54301549064513
6250755077.25087902432-3.85549729622677-3.855498098656380.404874954446986
6351255125.11108297018-3.79485496646537-3.794854966465360.887147951469214
6450755081.6513575264-3.82351923697795-3.82351923697797-0.680597301805169
6551005102.0778093863-3.80673088846273-3.806730888462710.416099826504656
6650855089.44227926152-3.81282135243578-3.81282135243581-0.151491402638929
6750655069.94208077184-3.82363361126378-3.82363361126376-0.269176165804333
6850905091.96320522515-3.80583304551928-3.805833045519290.443464284377183
6950205028.12707079435-3.84715039680768-3.84715039680771-1.03004598356574
7050305033.20471008186-3.84101191315264-3.841011913152590.15313835999552
7150005005.55485203768-3.8573764174374-3.8573764174374-0.408530289277695
7250305031.69786262869-3.83677045222113-3.836770452221190.514769352399508
7350154979.91127617713-3.5008390037051538.5092294487438-0.851813488093777
7449554959.71353340777-3.61401803036867-3.61401838050206-0.275424645125602
7549404944.45523107455-3.62567850015187-3.62567850015185-0.199748800002559
7650605055.38764349423-3.55496842647078-3.554968426470811.96558372572426
7750705072.0981308348-3.54298394050636-3.542983940506330.347715445980282
7850055012.56768855229-3.57597904973134-3.57597904973137-0.960634991119436
7949454952.62772523602-3.60917013738867-3.60917013738865-0.967095309411084
8050155013.94213689937-3.57096154237549-3.570961542375491.11396103365054
8150355036.67977621021-3.55548761814021-3.555487618140250.451403804953884
8249854991.54442823639-3.57992925865282-3.57992925865278-0.713428452485945
8350205021.19144383397-3.56040913694686-3.560409136946860.570108801220722
8449204929.86906006573-3.61193715433657-3.61193715433663-1.50582206616133
8551255066.0834937081-4.4493362201217248.94269902952182.47174772857095
8650805082.9078441633-4.3235398474733-4.3235405292980.352741290937674
8750605065.28287129689-4.33516265442168-4.33516265442172-0.228175032992276
8850955096.76246282262-4.31587054668909-4.315870546689120.614488891619274
8951055108.1856065374-4.30774716701375-4.307747167013710.270041923414982
9051055108.94394515975-4.30514125229224-4.305141252292270.0869213068585799
9151155118.32250244674-4.298107538884-4.298107538883970.234777872137004
9250705076.95974379781-4.31714953067084-4.31714953067084-0.635936177462497
9351155116.18999437455-4.29478852877235-4.29478852877240.747163758588907
9451505151.45406254578-4.27448601626563-4.27448601626560.678730317932974
9551155121.14409040612-4.28784117062389-4.28784117062388-0.446703298701171
9650605067.80984344897-4.31298709987458-4.31298709987464-0.841512567945591
9750755031.65946354584-4.1464883968952145.611373040089-0.560711617836507
9851555150.26779330157-3.50277413729099-3.502775236152962.04349632344593
9951205125.06575911517-3.51959216005722-3.51959216005727-0.372231656043024
10050305039.41444940287-3.55883739516081-3.55883739516083-1.40913416900031
10149955001.05588926511-3.57477120615892-3.57477120615889-0.597060926871562
10250355035.82356556-3.55727364864971-3.557273648649750.6578437338147
10349704977.48780711812-3.5822555975884-3.58225559758837-0.93983776608231
10449704973.60390000551-3.58239310251568-3.58239310251567-0.00517545277243627
10549754978.00925004335-3.57875362912397-3.578753629124020.137046166340534
10649654968.97052110251-3.58124023684945-3.58124023684941-0.0936771006660597
10749154921.71497650971-3.60112154015372-3.60112154015371-0.749322406904662
10849104913.9032422517-3.60303741219153-3.6030374121916-0.0722417041961376
10948954861.35622121851-3.3758739787179737.1346151260257-0.859494581706584
11048804881.6652555113-3.26430180064034-3.264303242648480.395520170116776
11149104910.92408978979-3.24165419413131-3.241654194131320.557904352883424
11249354936.19648020879-3.22941177204722-3.229411772047250.489206028048586
11349754975.20087837737-3.21203545950156-3.212035459501520.724593645565032
11448954903.14841015825-3.24026571617744-3.24026571617748-1.1810761358387
11549404940.34094100515-3.22369490367184-3.223694903671810.693694189710265
11648804886.8296701194-3.24429585313902-3.24429585313902-0.862769824372271







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14903.207646740974890.246209563512.9614371774633
24882.103395560594882.84709620062-0.743700640036892
34857.70812237714875.44798283775-17.7398604606429
44854.466258540044868.04886947487-13.5826109348276
54898.919004259674860.6497561119938.269248147677
64857.62054558634853.250642749114.36990283718543
74837.860172540344845.85152938623-7.99135684589313
84827.137873174144838.45241602336-11.3145428492121
94836.953642667154831.053302660485.90034000667371
104818.30750077064823.6541892976-5.34668852699876
114810.699432189654816.25507593472-5.55564374507662
124809.629438405534808.855962571850.773475833688636

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4903.20764674097 & 4890.2462095635 & 12.9614371774633 \tabularnewline
2 & 4882.10339556059 & 4882.84709620062 & -0.743700640036892 \tabularnewline
3 & 4857.7081223771 & 4875.44798283775 & -17.7398604606429 \tabularnewline
4 & 4854.46625854004 & 4868.04886947487 & -13.5826109348276 \tabularnewline
5 & 4898.91900425967 & 4860.64975611199 & 38.269248147677 \tabularnewline
6 & 4857.6205455863 & 4853.25064274911 & 4.36990283718543 \tabularnewline
7 & 4837.86017254034 & 4845.85152938623 & -7.99135684589313 \tabularnewline
8 & 4827.13787317414 & 4838.45241602336 & -11.3145428492121 \tabularnewline
9 & 4836.95364266715 & 4831.05330266048 & 5.90034000667371 \tabularnewline
10 & 4818.3075007706 & 4823.6541892976 & -5.34668852699876 \tabularnewline
11 & 4810.69943218965 & 4816.25507593472 & -5.55564374507662 \tabularnewline
12 & 4809.62943840553 & 4808.85596257185 & 0.773475833688636 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299232&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]4903.20764674097[/C][C]4890.2462095635[/C][C]12.9614371774633[/C][/ROW]
[ROW][C]2[/C][C]4882.10339556059[/C][C]4882.84709620062[/C][C]-0.743700640036892[/C][/ROW]
[ROW][C]3[/C][C]4857.7081223771[/C][C]4875.44798283775[/C][C]-17.7398604606429[/C][/ROW]
[ROW][C]4[/C][C]4854.46625854004[/C][C]4868.04886947487[/C][C]-13.5826109348276[/C][/ROW]
[ROW][C]5[/C][C]4898.91900425967[/C][C]4860.64975611199[/C][C]38.269248147677[/C][/ROW]
[ROW][C]6[/C][C]4857.6205455863[/C][C]4853.25064274911[/C][C]4.36990283718543[/C][/ROW]
[ROW][C]7[/C][C]4837.86017254034[/C][C]4845.85152938623[/C][C]-7.99135684589313[/C][/ROW]
[ROW][C]8[/C][C]4827.13787317414[/C][C]4838.45241602336[/C][C]-11.3145428492121[/C][/ROW]
[ROW][C]9[/C][C]4836.95364266715[/C][C]4831.05330266048[/C][C]5.90034000667371[/C][/ROW]
[ROW][C]10[/C][C]4818.3075007706[/C][C]4823.6541892976[/C][C]-5.34668852699876[/C][/ROW]
[ROW][C]11[/C][C]4810.69943218965[/C][C]4816.25507593472[/C][C]-5.55564374507662[/C][/ROW]
[ROW][C]12[/C][C]4809.62943840553[/C][C]4808.85596257185[/C][C]0.773475833688636[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299232&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299232&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
14903.207646740974890.246209563512.9614371774633
24882.103395560594882.84709620062-0.743700640036892
34857.70812237714875.44798283775-17.7398604606429
44854.466258540044868.04886947487-13.5826109348276
54898.919004259674860.6497561119938.269248147677
64857.62054558634853.250642749114.36990283718543
74837.860172540344845.85152938623-7.99135684589313
84827.137873174144838.45241602336-11.3145428492121
94836.953642667154831.053302660485.90034000667371
104818.30750077064823.6541892976-5.34668852699876
114810.699432189654816.25507593472-5.55564374507662
124809.629438405534808.855962571850.773475833688636



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')