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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 computationFri, 16 Dec 2016 15:34:17 +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/16/t148189890809c3h1pxkny4fq9.htm/, Retrieved Fri, 03 May 2024 00:35:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300316, Retrieved Fri, 03 May 2024 00:35:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- RM D      [Structural Time Series Models] [] [2016-12-16 14:34:17] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
5495
5365
5315
5335
5330
5365
5435
5535
5585
5615
5610
5585
5820
5645
5650
5725
5825
5870
5860
5835
5840
5805
5770
5680
5675
5690
5610
5610
5630
5615
5585
5555
5585
5530
5425
5630
5560
5435
5320
5150
5125
5025
5020
4935
4880
4870
4920
4935
5000
4955
4970
4990
4920
4930
4955
5000
5025
5075
5075
5105
5050
5055
5095
5025
5050
5035
4985
5005
4910
4910
4870
4850
4810
4810
4730
4850
4895
4845
4805
4825
4830
4720
4785
4705
4840
4820
4795
4810
4840
4810
4835
4860
4845
4935
4870
4830
4895
4920
4925
4860
4820
4790
4775
4735
4755
4745
4705
4665
4650
4590
4625
4685
4665
4675
4690
4600




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=300316&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=300316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300316&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
154955495000
253655374.16987160095-6.72853389405677-6.72853309339802-1.25996653230632
353155324.44250574811-7.04004230075169-7.04004230075171-0.741174820368646
453355340.62739996116-6.93077384185098-6.930773841850940.400780749370675
553305336.74575495444-6.91689698888454-6.916896988884540.052617668939103
653655369.51014074326-6.7373986521393-6.737398652139320.684759290319083
754355437.22334490429-6.40216525412068-6.402165254120681.2847438826135
855355535.08272803707-5.93480669042458-5.93480669042461.79915524001438
955855587.40493022815-5.67483161297657-5.674831612976571.00528409557785
1056155618.45060851115-5.51169235594655-5.511692355946550.633644292722778
1156105615.36480000684-5.50096248246528-5.500962482465270.0418603694332497
1255855591.60614926143-5.58136204809818-5.58136204809817-0.315046821855894
1358205696.83615832125-10.629695504376116.9266509564842.32040272911747
1456455657.49936833537-11.3483868444198-11.3483869466342-0.419568876032247
1556505660.49720270982-11.3008813917608-11.30088139176080.247172005012632
1657255731.5027498893-11.1227939403919-11.12279394039191.4187858112974
1758255829.75344237603-10.8932479586497-10.89324795864971.88537483361634
1858705877.47996540882-10.7706657743034-10.77066577430341.01048316416969
1958605870.54721110066-10.7626575607034-10.76265756070340.0661575000414766
2058355846.5340820999-10.7902483986991-10.7902483986991-0.228409744849296
2158405849.96251719565-10.7607030257049-10.76070302570480.245099177029462
2258055817.05015215025-10.8066370933639-10.8066370933639-0.381845743385626
2357705782.20577223552-10.8563790248804-10.8563790248804-0.414356824492194
2456805695.28352673423-11.013459067056-11.013459067056-1.31120261425175
2556755583.28157557313-8.8540932174797397.3950235420936-1.92436038083257
2656905691.59555670432-6.95861779019515-6.958617318287221.82699062158532
2756105620.68153590907-7.09598122372875-7.09598122372868-1.10173284331129
2856105616.90497827903-7.0913174329372-7.091317432937180.0572012259382349
2956305635.6080774184-7.05613802114956-7.056138021149590.444498428871634
3056155622.40932929014-7.06449135805804-7.06449135805804-0.105851548825893
3155855593.33025546005-7.09438590554344-7.09438590554342-0.3793624749908
3255555563.40693071424-7.12534412900014-7.12534412900016-0.393395409045091
3355855590.17661878299-7.07944148399902-7.079441483999030.584089312926274
3455305539.58122258386-7.13829364602765-7.13829364602765-0.749879312936291
3554255437.59125044106-7.26640038356735-7.2664003835673-1.63450978796167
3656305626.01657505692-7.00245549897448-7.002455498974553.3722100307538
3755605506.56949036477-5.431675877853459.7484349382198-2.07346015168834
3854355443.89121236281-6.11574297824377-6.11574255663637-0.918032147820063
3953205332.20438530305-6.28353067801403-6.28353067801392-1.81850211804483
4051505165.45845645071-6.45044970149996-6.45044970149988-2.76470240546074
4151255132.94021875951-6.47678154096431-6.47678154096436-0.449138969358577
4250255036.61157690194-6.56731345338511-6.56731345338506-1.54811604362685
4350205026.7552672784-6.57062373777645-6.57062373777643-0.056668225655537
4449354945.82019822522-6.64539393358396-6.64539393358393-1.28127217577133
4548804889.48488645383-6.69530477704132-6.69530477704132-0.85613871472022
4648704877.02472720429-6.70108945208433-6.70108945208439-0.099326243786898
4749204923.65369121049-6.64762968425022-6.647629684250110.918856070635037
4849354940.31568889522-6.62428676071269-6.62428676071280.401615631142065
4950004928.08713692871-6.5661529242768772.2276863401306-0.101627447158389
5049554959.31572757888-6.20810132329567-6.208105972410310.61567626382057
5149704974.9549896555-6.18054397863697-6.180543978636980.376313736327567
5249904994.70350293432-6.15913082719939-6.159130827199320.446706346433353
5349204929.52011701796-6.2064744764831-6.20647447648313-1.01687387704941
5449304935.5118976583-6.19671297137431-6.196712971374290.210152337395403
5549554959.47917616814-6.17259586708487-6.17259586708490.519667075496179
5650005003.32460310404-6.13263693248371-6.132636932483730.861713288017558
5750255029.30420779285-6.10700324484036-6.107003244840380.553231334161135
5850755077.9873581607-6.06330173523595-6.0633017352360.943927290416377
5950755080.57096879455-6.05641031527546-6.056410315275330.14896936262701
6051055109.08791427169-6.02887796996131-6.028877969961440.59563103067538
6150504998.97379185532-5.1702332507095956.8725681844933-1.86842595161155
6250555056.47513181713-4.67841274350417-4.678415972194021.03120759263439
6350955097.0899157165-4.63105466629226-4.631054666292290.780139541890442
6450255033.0092366207-4.67176050226921-4.67176050226912-1.0241377255391
6550505053.2562277038-4.65518631054772-4.655186310547770.429275917776717
6650355040.13603695218-4.66080429542583-4.66080429542579-0.145826818241773
6749854992.12336572655-4.68955428720495-4.68955428720493-0.746823426679043
6850055008.4932994507-4.67559742046729-4.675597420467330.362792125308705
6949104919.46698528856-4.73146258389992-4.73146258389983-1.45311081751631
7049104914.73168081379-4.73146512668573-4.7314651266858-6.61842876500476e-05
7148704876.62713278851-4.75353875551266-4.75353875551248-0.574918279317641
7248504855.67372160936-4.76424659485509-4.76424659485526-0.279075235607469
7348104768.43733465957-4.1995157634464846.1946753472308-1.47040366591485
7448104811.43618728589-3.88338209871308-3.883384658758710.782035431382779
7547304737.85627431788-3.9456110935278-3.94561109352782-1.20044474727862
7648504847.50215193084-3.87918505768862-3.879185057688621.9567553195819
7748954895.91381172242-3.84947797292351-3.849477972923560.900776923085087
7848454851.168597139-3.87266269076906-3.872662690769-0.704481525659969
7948054810.93462966852-3.89326338114588-3.8932633811458-0.626370034445806
8048254827.72059780733-3.88155413726924-3.881554137269360.356226191502401
8148304833.34263326239-3.87617594669138-3.876175946691290.163711453282523
8247204729.54253835653-3.93269205707819-3.93269205707818-1.7213167202625
8347854785.5345735953-3.89881830469657-3.898818304696481.03227957326616
8447054712.80210806286-3.93770603524519-3.93770603524533-1.18574687156532
8548404787.23783740844-4.3964177327820448.36060018390111.39051451289002
8648204822.10945394901-4.16700791938706-4.167013554967340.653975088210219
8747954800.17770015629-4.18084766543919-4.18084766543906-0.305973505082433
8848104813.20594022762-4.17206581648085-4.172065816480810.296438617230246
8948404842.28861244991-4.15557828000888-4.155578280008980.572837208028107
9048104815.44078101483-4.16680623465732-4.16680623465727-0.390890664321924
9148354837.67174459321-4.15375233973803-4.153752339737960.454720852751043
9248604862.51167588638-4.13942189449297-4.139421894493080.499437309020221
9348454849.63429959461-4.14373858945616-4.14373858945616-0.150517609735045
9449354934.123969973-4.09997383069378-4.09997383069381.52677466718829
9548704877.09746435669-4.12609461011063-4.12609461011053-0.9116977464523
9648304836.20816716475-4.14422936745984-4.14422936745992-0.63327265542402
9748954847.66077242101-4.2239379885487646.46332389512910.275705485475884
9849204919.79498949305-3.82838359329704-3.828390616812251.27667417989073
9949254928.13700353875-3.8199740123453-3.819974012345150.209616177105218
10048604867.06032389751-3.84589145743062-3.84589145743048-0.986262685881112
10148204825.95412933454-3.86227890586249-3.8622789058626-0.641820089451044
10247904795.37398931886-3.87400657582494-3.87400657582484-0.460223305143299
10347754779.55013258982-3.87924917427866-3.87924917427856-0.205839796198758
10447354740.84944935021-3.89451915259351-3.89451915259363-0.599809720556691
10547554757.71965306426-3.88541735023551-3.885417350235440.357678593440651
10647454749.150425973-3.88746950532508-3.88746950532513-0.0806800239102576
10747054710.83536618489-3.9025469352923-3.9025469352922-0.593025490852171
10846654670.93905037573-3.91830336664539-3.91830336664544-0.620003330560988
10946504612.66306908381-3.6717728885293240.3895088465935-0.958128487204923
11045904594.50904451569-3.73915981796151-3.73916669966361-0.242888392694798
11146254626.70043326284-3.71685391710071-3.716853917100690.618842389239052
11246854685.1987331324-3.69155056453386-3.69155056453381.07165232200328
11346654669.3773341143-3.6963441040977-3.69634410409779-0.208936212248564
11446754677.99988153816-3.69148521443794-3.691485214437880.212192472400676
11546904692.65428300708-3.68425256315284-3.68425256315280.316007230875384
11646004608.24794031454-3.71606362447271-3.71606362447269-1.39043497101418

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5495 & 5495 & 0 & 0 & 0 \tabularnewline
2 & 5365 & 5374.16987160095 & -6.72853389405677 & -6.72853309339802 & -1.25996653230632 \tabularnewline
3 & 5315 & 5324.44250574811 & -7.04004230075169 & -7.04004230075171 & -0.741174820368646 \tabularnewline
4 & 5335 & 5340.62739996116 & -6.93077384185098 & -6.93077384185094 & 0.400780749370675 \tabularnewline
5 & 5330 & 5336.74575495444 & -6.91689698888454 & -6.91689698888454 & 0.052617668939103 \tabularnewline
6 & 5365 & 5369.51014074326 & -6.7373986521393 & -6.73739865213932 & 0.684759290319083 \tabularnewline
7 & 5435 & 5437.22334490429 & -6.40216525412068 & -6.40216525412068 & 1.2847438826135 \tabularnewline
8 & 5535 & 5535.08272803707 & -5.93480669042458 & -5.9348066904246 & 1.79915524001438 \tabularnewline
9 & 5585 & 5587.40493022815 & -5.67483161297657 & -5.67483161297657 & 1.00528409557785 \tabularnewline
10 & 5615 & 5618.45060851115 & -5.51169235594655 & -5.51169235594655 & 0.633644292722778 \tabularnewline
11 & 5610 & 5615.36480000684 & -5.50096248246528 & -5.50096248246527 & 0.0418603694332497 \tabularnewline
12 & 5585 & 5591.60614926143 & -5.58136204809818 & -5.58136204809817 & -0.315046821855894 \tabularnewline
13 & 5820 & 5696.83615832125 & -10.629695504376 & 116.926650956484 & 2.32040272911747 \tabularnewline
14 & 5645 & 5657.49936833537 & -11.3483868444198 & -11.3483869466342 & -0.419568876032247 \tabularnewline
15 & 5650 & 5660.49720270982 & -11.3008813917608 & -11.3008813917608 & 0.247172005012632 \tabularnewline
16 & 5725 & 5731.5027498893 & -11.1227939403919 & -11.1227939403919 & 1.4187858112974 \tabularnewline
17 & 5825 & 5829.75344237603 & -10.8932479586497 & -10.8932479586497 & 1.88537483361634 \tabularnewline
18 & 5870 & 5877.47996540882 & -10.7706657743034 & -10.7706657743034 & 1.01048316416969 \tabularnewline
19 & 5860 & 5870.54721110066 & -10.7626575607034 & -10.7626575607034 & 0.0661575000414766 \tabularnewline
20 & 5835 & 5846.5340820999 & -10.7902483986991 & -10.7902483986991 & -0.228409744849296 \tabularnewline
21 & 5840 & 5849.96251719565 & -10.7607030257049 & -10.7607030257048 & 0.245099177029462 \tabularnewline
22 & 5805 & 5817.05015215025 & -10.8066370933639 & -10.8066370933639 & -0.381845743385626 \tabularnewline
23 & 5770 & 5782.20577223552 & -10.8563790248804 & -10.8563790248804 & -0.414356824492194 \tabularnewline
24 & 5680 & 5695.28352673423 & -11.013459067056 & -11.013459067056 & -1.31120261425175 \tabularnewline
25 & 5675 & 5583.28157557313 & -8.85409321747973 & 97.3950235420936 & -1.92436038083257 \tabularnewline
26 & 5690 & 5691.59555670432 & -6.95861779019515 & -6.95861731828722 & 1.82699062158532 \tabularnewline
27 & 5610 & 5620.68153590907 & -7.09598122372875 & -7.09598122372868 & -1.10173284331129 \tabularnewline
28 & 5610 & 5616.90497827903 & -7.0913174329372 & -7.09131743293718 & 0.0572012259382349 \tabularnewline
29 & 5630 & 5635.6080774184 & -7.05613802114956 & -7.05613802114959 & 0.444498428871634 \tabularnewline
30 & 5615 & 5622.40932929014 & -7.06449135805804 & -7.06449135805804 & -0.105851548825893 \tabularnewline
31 & 5585 & 5593.33025546005 & -7.09438590554344 & -7.09438590554342 & -0.3793624749908 \tabularnewline
32 & 5555 & 5563.40693071424 & -7.12534412900014 & -7.12534412900016 & -0.393395409045091 \tabularnewline
33 & 5585 & 5590.17661878299 & -7.07944148399902 & -7.07944148399903 & 0.584089312926274 \tabularnewline
34 & 5530 & 5539.58122258386 & -7.13829364602765 & -7.13829364602765 & -0.749879312936291 \tabularnewline
35 & 5425 & 5437.59125044106 & -7.26640038356735 & -7.2664003835673 & -1.63450978796167 \tabularnewline
36 & 5630 & 5626.01657505692 & -7.00245549897448 & -7.00245549897455 & 3.3722100307538 \tabularnewline
37 & 5560 & 5506.56949036477 & -5.4316758778534 & 59.7484349382198 & -2.07346015168834 \tabularnewline
38 & 5435 & 5443.89121236281 & -6.11574297824377 & -6.11574255663637 & -0.918032147820063 \tabularnewline
39 & 5320 & 5332.20438530305 & -6.28353067801403 & -6.28353067801392 & -1.81850211804483 \tabularnewline
40 & 5150 & 5165.45845645071 & -6.45044970149996 & -6.45044970149988 & -2.76470240546074 \tabularnewline
41 & 5125 & 5132.94021875951 & -6.47678154096431 & -6.47678154096436 & -0.449138969358577 \tabularnewline
42 & 5025 & 5036.61157690194 & -6.56731345338511 & -6.56731345338506 & -1.54811604362685 \tabularnewline
43 & 5020 & 5026.7552672784 & -6.57062373777645 & -6.57062373777643 & -0.056668225655537 \tabularnewline
44 & 4935 & 4945.82019822522 & -6.64539393358396 & -6.64539393358393 & -1.28127217577133 \tabularnewline
45 & 4880 & 4889.48488645383 & -6.69530477704132 & -6.69530477704132 & -0.85613871472022 \tabularnewline
46 & 4870 & 4877.02472720429 & -6.70108945208433 & -6.70108945208439 & -0.099326243786898 \tabularnewline
47 & 4920 & 4923.65369121049 & -6.64762968425022 & -6.64762968425011 & 0.918856070635037 \tabularnewline
48 & 4935 & 4940.31568889522 & -6.62428676071269 & -6.6242867607128 & 0.401615631142065 \tabularnewline
49 & 5000 & 4928.08713692871 & -6.56615292427687 & 72.2276863401306 & -0.101627447158389 \tabularnewline
50 & 4955 & 4959.31572757888 & -6.20810132329567 & -6.20810597241031 & 0.61567626382057 \tabularnewline
51 & 4970 & 4974.9549896555 & -6.18054397863697 & -6.18054397863698 & 0.376313736327567 \tabularnewline
52 & 4990 & 4994.70350293432 & -6.15913082719939 & -6.15913082719932 & 0.446706346433353 \tabularnewline
53 & 4920 & 4929.52011701796 & -6.2064744764831 & -6.20647447648313 & -1.01687387704941 \tabularnewline
54 & 4930 & 4935.5118976583 & -6.19671297137431 & -6.19671297137429 & 0.210152337395403 \tabularnewline
55 & 4955 & 4959.47917616814 & -6.17259586708487 & -6.1725958670849 & 0.519667075496179 \tabularnewline
56 & 5000 & 5003.32460310404 & -6.13263693248371 & -6.13263693248373 & 0.861713288017558 \tabularnewline
57 & 5025 & 5029.30420779285 & -6.10700324484036 & -6.10700324484038 & 0.553231334161135 \tabularnewline
58 & 5075 & 5077.9873581607 & -6.06330173523595 & -6.063301735236 & 0.943927290416377 \tabularnewline
59 & 5075 & 5080.57096879455 & -6.05641031527546 & -6.05641031527533 & 0.14896936262701 \tabularnewline
60 & 5105 & 5109.08791427169 & -6.02887796996131 & -6.02887796996144 & 0.59563103067538 \tabularnewline
61 & 5050 & 4998.97379185532 & -5.17023325070959 & 56.8725681844933 & -1.86842595161155 \tabularnewline
62 & 5055 & 5056.47513181713 & -4.67841274350417 & -4.67841597219402 & 1.03120759263439 \tabularnewline
63 & 5095 & 5097.0899157165 & -4.63105466629226 & -4.63105466629229 & 0.780139541890442 \tabularnewline
64 & 5025 & 5033.0092366207 & -4.67176050226921 & -4.67176050226912 & -1.0241377255391 \tabularnewline
65 & 5050 & 5053.2562277038 & -4.65518631054772 & -4.65518631054777 & 0.429275917776717 \tabularnewline
66 & 5035 & 5040.13603695218 & -4.66080429542583 & -4.66080429542579 & -0.145826818241773 \tabularnewline
67 & 4985 & 4992.12336572655 & -4.68955428720495 & -4.68955428720493 & -0.746823426679043 \tabularnewline
68 & 5005 & 5008.4932994507 & -4.67559742046729 & -4.67559742046733 & 0.362792125308705 \tabularnewline
69 & 4910 & 4919.46698528856 & -4.73146258389992 & -4.73146258389983 & -1.45311081751631 \tabularnewline
70 & 4910 & 4914.73168081379 & -4.73146512668573 & -4.7314651266858 & -6.61842876500476e-05 \tabularnewline
71 & 4870 & 4876.62713278851 & -4.75353875551266 & -4.75353875551248 & -0.574918279317641 \tabularnewline
72 & 4850 & 4855.67372160936 & -4.76424659485509 & -4.76424659485526 & -0.279075235607469 \tabularnewline
73 & 4810 & 4768.43733465957 & -4.19951576344648 & 46.1946753472308 & -1.47040366591485 \tabularnewline
74 & 4810 & 4811.43618728589 & -3.88338209871308 & -3.88338465875871 & 0.782035431382779 \tabularnewline
75 & 4730 & 4737.85627431788 & -3.9456110935278 & -3.94561109352782 & -1.20044474727862 \tabularnewline
76 & 4850 & 4847.50215193084 & -3.87918505768862 & -3.87918505768862 & 1.9567553195819 \tabularnewline
77 & 4895 & 4895.91381172242 & -3.84947797292351 & -3.84947797292356 & 0.900776923085087 \tabularnewline
78 & 4845 & 4851.168597139 & -3.87266269076906 & -3.872662690769 & -0.704481525659969 \tabularnewline
79 & 4805 & 4810.93462966852 & -3.89326338114588 & -3.8932633811458 & -0.626370034445806 \tabularnewline
80 & 4825 & 4827.72059780733 & -3.88155413726924 & -3.88155413726936 & 0.356226191502401 \tabularnewline
81 & 4830 & 4833.34263326239 & -3.87617594669138 & -3.87617594669129 & 0.163711453282523 \tabularnewline
82 & 4720 & 4729.54253835653 & -3.93269205707819 & -3.93269205707818 & -1.7213167202625 \tabularnewline
83 & 4785 & 4785.5345735953 & -3.89881830469657 & -3.89881830469648 & 1.03227957326616 \tabularnewline
84 & 4705 & 4712.80210806286 & -3.93770603524519 & -3.93770603524533 & -1.18574687156532 \tabularnewline
85 & 4840 & 4787.23783740844 & -4.39641773278204 & 48.3606001839011 & 1.39051451289002 \tabularnewline
86 & 4820 & 4822.10945394901 & -4.16700791938706 & -4.16701355496734 & 0.653975088210219 \tabularnewline
87 & 4795 & 4800.17770015629 & -4.18084766543919 & -4.18084766543906 & -0.305973505082433 \tabularnewline
88 & 4810 & 4813.20594022762 & -4.17206581648085 & -4.17206581648081 & 0.296438617230246 \tabularnewline
89 & 4840 & 4842.28861244991 & -4.15557828000888 & -4.15557828000898 & 0.572837208028107 \tabularnewline
90 & 4810 & 4815.44078101483 & -4.16680623465732 & -4.16680623465727 & -0.390890664321924 \tabularnewline
91 & 4835 & 4837.67174459321 & -4.15375233973803 & -4.15375233973796 & 0.454720852751043 \tabularnewline
92 & 4860 & 4862.51167588638 & -4.13942189449297 & -4.13942189449308 & 0.499437309020221 \tabularnewline
93 & 4845 & 4849.63429959461 & -4.14373858945616 & -4.14373858945616 & -0.150517609735045 \tabularnewline
94 & 4935 & 4934.123969973 & -4.09997383069378 & -4.0999738306938 & 1.52677466718829 \tabularnewline
95 & 4870 & 4877.09746435669 & -4.12609461011063 & -4.12609461011053 & -0.9116977464523 \tabularnewline
96 & 4830 & 4836.20816716475 & -4.14422936745984 & -4.14422936745992 & -0.63327265542402 \tabularnewline
97 & 4895 & 4847.66077242101 & -4.22393798854876 & 46.4633238951291 & 0.275705485475884 \tabularnewline
98 & 4920 & 4919.79498949305 & -3.82838359329704 & -3.82839061681225 & 1.27667417989073 \tabularnewline
99 & 4925 & 4928.13700353875 & -3.8199740123453 & -3.81997401234515 & 0.209616177105218 \tabularnewline
100 & 4860 & 4867.06032389751 & -3.84589145743062 & -3.84589145743048 & -0.986262685881112 \tabularnewline
101 & 4820 & 4825.95412933454 & -3.86227890586249 & -3.8622789058626 & -0.641820089451044 \tabularnewline
102 & 4790 & 4795.37398931886 & -3.87400657582494 & -3.87400657582484 & -0.460223305143299 \tabularnewline
103 & 4775 & 4779.55013258982 & -3.87924917427866 & -3.87924917427856 & -0.205839796198758 \tabularnewline
104 & 4735 & 4740.84944935021 & -3.89451915259351 & -3.89451915259363 & -0.599809720556691 \tabularnewline
105 & 4755 & 4757.71965306426 & -3.88541735023551 & -3.88541735023544 & 0.357678593440651 \tabularnewline
106 & 4745 & 4749.150425973 & -3.88746950532508 & -3.88746950532513 & -0.0806800239102576 \tabularnewline
107 & 4705 & 4710.83536618489 & -3.9025469352923 & -3.9025469352922 & -0.593025490852171 \tabularnewline
108 & 4665 & 4670.93905037573 & -3.91830336664539 & -3.91830336664544 & -0.620003330560988 \tabularnewline
109 & 4650 & 4612.66306908381 & -3.67177288852932 & 40.3895088465935 & -0.958128487204923 \tabularnewline
110 & 4590 & 4594.50904451569 & -3.73915981796151 & -3.73916669966361 & -0.242888392694798 \tabularnewline
111 & 4625 & 4626.70043326284 & -3.71685391710071 & -3.71685391710069 & 0.618842389239052 \tabularnewline
112 & 4685 & 4685.1987331324 & -3.69155056453386 & -3.6915505645338 & 1.07165232200328 \tabularnewline
113 & 4665 & 4669.3773341143 & -3.6963441040977 & -3.69634410409779 & -0.208936212248564 \tabularnewline
114 & 4675 & 4677.99988153816 & -3.69148521443794 & -3.69148521443788 & 0.212192472400676 \tabularnewline
115 & 4690 & 4692.65428300708 & -3.68425256315284 & -3.6842525631528 & 0.316007230875384 \tabularnewline
116 & 4600 & 4608.24794031454 & -3.71606362447271 & -3.71606362447269 & -1.39043497101418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300316&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]5495[/C][C]5495[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5365[/C][C]5374.16987160095[/C][C]-6.72853389405677[/C][C]-6.72853309339802[/C][C]-1.25996653230632[/C][/ROW]
[ROW][C]3[/C][C]5315[/C][C]5324.44250574811[/C][C]-7.04004230075169[/C][C]-7.04004230075171[/C][C]-0.741174820368646[/C][/ROW]
[ROW][C]4[/C][C]5335[/C][C]5340.62739996116[/C][C]-6.93077384185098[/C][C]-6.93077384185094[/C][C]0.400780749370675[/C][/ROW]
[ROW][C]5[/C][C]5330[/C][C]5336.74575495444[/C][C]-6.91689698888454[/C][C]-6.91689698888454[/C][C]0.052617668939103[/C][/ROW]
[ROW][C]6[/C][C]5365[/C][C]5369.51014074326[/C][C]-6.7373986521393[/C][C]-6.73739865213932[/C][C]0.684759290319083[/C][/ROW]
[ROW][C]7[/C][C]5435[/C][C]5437.22334490429[/C][C]-6.40216525412068[/C][C]-6.40216525412068[/C][C]1.2847438826135[/C][/ROW]
[ROW][C]8[/C][C]5535[/C][C]5535.08272803707[/C][C]-5.93480669042458[/C][C]-5.9348066904246[/C][C]1.79915524001438[/C][/ROW]
[ROW][C]9[/C][C]5585[/C][C]5587.40493022815[/C][C]-5.67483161297657[/C][C]-5.67483161297657[/C][C]1.00528409557785[/C][/ROW]
[ROW][C]10[/C][C]5615[/C][C]5618.45060851115[/C][C]-5.51169235594655[/C][C]-5.51169235594655[/C][C]0.633644292722778[/C][/ROW]
[ROW][C]11[/C][C]5610[/C][C]5615.36480000684[/C][C]-5.50096248246528[/C][C]-5.50096248246527[/C][C]0.0418603694332497[/C][/ROW]
[ROW][C]12[/C][C]5585[/C][C]5591.60614926143[/C][C]-5.58136204809818[/C][C]-5.58136204809817[/C][C]-0.315046821855894[/C][/ROW]
[ROW][C]13[/C][C]5820[/C][C]5696.83615832125[/C][C]-10.629695504376[/C][C]116.926650956484[/C][C]2.32040272911747[/C][/ROW]
[ROW][C]14[/C][C]5645[/C][C]5657.49936833537[/C][C]-11.3483868444198[/C][C]-11.3483869466342[/C][C]-0.419568876032247[/C][/ROW]
[ROW][C]15[/C][C]5650[/C][C]5660.49720270982[/C][C]-11.3008813917608[/C][C]-11.3008813917608[/C][C]0.247172005012632[/C][/ROW]
[ROW][C]16[/C][C]5725[/C][C]5731.5027498893[/C][C]-11.1227939403919[/C][C]-11.1227939403919[/C][C]1.4187858112974[/C][/ROW]
[ROW][C]17[/C][C]5825[/C][C]5829.75344237603[/C][C]-10.8932479586497[/C][C]-10.8932479586497[/C][C]1.88537483361634[/C][/ROW]
[ROW][C]18[/C][C]5870[/C][C]5877.47996540882[/C][C]-10.7706657743034[/C][C]-10.7706657743034[/C][C]1.01048316416969[/C][/ROW]
[ROW][C]19[/C][C]5860[/C][C]5870.54721110066[/C][C]-10.7626575607034[/C][C]-10.7626575607034[/C][C]0.0661575000414766[/C][/ROW]
[ROW][C]20[/C][C]5835[/C][C]5846.5340820999[/C][C]-10.7902483986991[/C][C]-10.7902483986991[/C][C]-0.228409744849296[/C][/ROW]
[ROW][C]21[/C][C]5840[/C][C]5849.96251719565[/C][C]-10.7607030257049[/C][C]-10.7607030257048[/C][C]0.245099177029462[/C][/ROW]
[ROW][C]22[/C][C]5805[/C][C]5817.05015215025[/C][C]-10.8066370933639[/C][C]-10.8066370933639[/C][C]-0.381845743385626[/C][/ROW]
[ROW][C]23[/C][C]5770[/C][C]5782.20577223552[/C][C]-10.8563790248804[/C][C]-10.8563790248804[/C][C]-0.414356824492194[/C][/ROW]
[ROW][C]24[/C][C]5680[/C][C]5695.28352673423[/C][C]-11.013459067056[/C][C]-11.013459067056[/C][C]-1.31120261425175[/C][/ROW]
[ROW][C]25[/C][C]5675[/C][C]5583.28157557313[/C][C]-8.85409321747973[/C][C]97.3950235420936[/C][C]-1.92436038083257[/C][/ROW]
[ROW][C]26[/C][C]5690[/C][C]5691.59555670432[/C][C]-6.95861779019515[/C][C]-6.95861731828722[/C][C]1.82699062158532[/C][/ROW]
[ROW][C]27[/C][C]5610[/C][C]5620.68153590907[/C][C]-7.09598122372875[/C][C]-7.09598122372868[/C][C]-1.10173284331129[/C][/ROW]
[ROW][C]28[/C][C]5610[/C][C]5616.90497827903[/C][C]-7.0913174329372[/C][C]-7.09131743293718[/C][C]0.0572012259382349[/C][/ROW]
[ROW][C]29[/C][C]5630[/C][C]5635.6080774184[/C][C]-7.05613802114956[/C][C]-7.05613802114959[/C][C]0.444498428871634[/C][/ROW]
[ROW][C]30[/C][C]5615[/C][C]5622.40932929014[/C][C]-7.06449135805804[/C][C]-7.06449135805804[/C][C]-0.105851548825893[/C][/ROW]
[ROW][C]31[/C][C]5585[/C][C]5593.33025546005[/C][C]-7.09438590554344[/C][C]-7.09438590554342[/C][C]-0.3793624749908[/C][/ROW]
[ROW][C]32[/C][C]5555[/C][C]5563.40693071424[/C][C]-7.12534412900014[/C][C]-7.12534412900016[/C][C]-0.393395409045091[/C][/ROW]
[ROW][C]33[/C][C]5585[/C][C]5590.17661878299[/C][C]-7.07944148399902[/C][C]-7.07944148399903[/C][C]0.584089312926274[/C][/ROW]
[ROW][C]34[/C][C]5530[/C][C]5539.58122258386[/C][C]-7.13829364602765[/C][C]-7.13829364602765[/C][C]-0.749879312936291[/C][/ROW]
[ROW][C]35[/C][C]5425[/C][C]5437.59125044106[/C][C]-7.26640038356735[/C][C]-7.2664003835673[/C][C]-1.63450978796167[/C][/ROW]
[ROW][C]36[/C][C]5630[/C][C]5626.01657505692[/C][C]-7.00245549897448[/C][C]-7.00245549897455[/C][C]3.3722100307538[/C][/ROW]
[ROW][C]37[/C][C]5560[/C][C]5506.56949036477[/C][C]-5.4316758778534[/C][C]59.7484349382198[/C][C]-2.07346015168834[/C][/ROW]
[ROW][C]38[/C][C]5435[/C][C]5443.89121236281[/C][C]-6.11574297824377[/C][C]-6.11574255663637[/C][C]-0.918032147820063[/C][/ROW]
[ROW][C]39[/C][C]5320[/C][C]5332.20438530305[/C][C]-6.28353067801403[/C][C]-6.28353067801392[/C][C]-1.81850211804483[/C][/ROW]
[ROW][C]40[/C][C]5150[/C][C]5165.45845645071[/C][C]-6.45044970149996[/C][C]-6.45044970149988[/C][C]-2.76470240546074[/C][/ROW]
[ROW][C]41[/C][C]5125[/C][C]5132.94021875951[/C][C]-6.47678154096431[/C][C]-6.47678154096436[/C][C]-0.449138969358577[/C][/ROW]
[ROW][C]42[/C][C]5025[/C][C]5036.61157690194[/C][C]-6.56731345338511[/C][C]-6.56731345338506[/C][C]-1.54811604362685[/C][/ROW]
[ROW][C]43[/C][C]5020[/C][C]5026.7552672784[/C][C]-6.57062373777645[/C][C]-6.57062373777643[/C][C]-0.056668225655537[/C][/ROW]
[ROW][C]44[/C][C]4935[/C][C]4945.82019822522[/C][C]-6.64539393358396[/C][C]-6.64539393358393[/C][C]-1.28127217577133[/C][/ROW]
[ROW][C]45[/C][C]4880[/C][C]4889.48488645383[/C][C]-6.69530477704132[/C][C]-6.69530477704132[/C][C]-0.85613871472022[/C][/ROW]
[ROW][C]46[/C][C]4870[/C][C]4877.02472720429[/C][C]-6.70108945208433[/C][C]-6.70108945208439[/C][C]-0.099326243786898[/C][/ROW]
[ROW][C]47[/C][C]4920[/C][C]4923.65369121049[/C][C]-6.64762968425022[/C][C]-6.64762968425011[/C][C]0.918856070635037[/C][/ROW]
[ROW][C]48[/C][C]4935[/C][C]4940.31568889522[/C][C]-6.62428676071269[/C][C]-6.6242867607128[/C][C]0.401615631142065[/C][/ROW]
[ROW][C]49[/C][C]5000[/C][C]4928.08713692871[/C][C]-6.56615292427687[/C][C]72.2276863401306[/C][C]-0.101627447158389[/C][/ROW]
[ROW][C]50[/C][C]4955[/C][C]4959.31572757888[/C][C]-6.20810132329567[/C][C]-6.20810597241031[/C][C]0.61567626382057[/C][/ROW]
[ROW][C]51[/C][C]4970[/C][C]4974.9549896555[/C][C]-6.18054397863697[/C][C]-6.18054397863698[/C][C]0.376313736327567[/C][/ROW]
[ROW][C]52[/C][C]4990[/C][C]4994.70350293432[/C][C]-6.15913082719939[/C][C]-6.15913082719932[/C][C]0.446706346433353[/C][/ROW]
[ROW][C]53[/C][C]4920[/C][C]4929.52011701796[/C][C]-6.2064744764831[/C][C]-6.20647447648313[/C][C]-1.01687387704941[/C][/ROW]
[ROW][C]54[/C][C]4930[/C][C]4935.5118976583[/C][C]-6.19671297137431[/C][C]-6.19671297137429[/C][C]0.210152337395403[/C][/ROW]
[ROW][C]55[/C][C]4955[/C][C]4959.47917616814[/C][C]-6.17259586708487[/C][C]-6.1725958670849[/C][C]0.519667075496179[/C][/ROW]
[ROW][C]56[/C][C]5000[/C][C]5003.32460310404[/C][C]-6.13263693248371[/C][C]-6.13263693248373[/C][C]0.861713288017558[/C][/ROW]
[ROW][C]57[/C][C]5025[/C][C]5029.30420779285[/C][C]-6.10700324484036[/C][C]-6.10700324484038[/C][C]0.553231334161135[/C][/ROW]
[ROW][C]58[/C][C]5075[/C][C]5077.9873581607[/C][C]-6.06330173523595[/C][C]-6.063301735236[/C][C]0.943927290416377[/C][/ROW]
[ROW][C]59[/C][C]5075[/C][C]5080.57096879455[/C][C]-6.05641031527546[/C][C]-6.05641031527533[/C][C]0.14896936262701[/C][/ROW]
[ROW][C]60[/C][C]5105[/C][C]5109.08791427169[/C][C]-6.02887796996131[/C][C]-6.02887796996144[/C][C]0.59563103067538[/C][/ROW]
[ROW][C]61[/C][C]5050[/C][C]4998.97379185532[/C][C]-5.17023325070959[/C][C]56.8725681844933[/C][C]-1.86842595161155[/C][/ROW]
[ROW][C]62[/C][C]5055[/C][C]5056.47513181713[/C][C]-4.67841274350417[/C][C]-4.67841597219402[/C][C]1.03120759263439[/C][/ROW]
[ROW][C]63[/C][C]5095[/C][C]5097.0899157165[/C][C]-4.63105466629226[/C][C]-4.63105466629229[/C][C]0.780139541890442[/C][/ROW]
[ROW][C]64[/C][C]5025[/C][C]5033.0092366207[/C][C]-4.67176050226921[/C][C]-4.67176050226912[/C][C]-1.0241377255391[/C][/ROW]
[ROW][C]65[/C][C]5050[/C][C]5053.2562277038[/C][C]-4.65518631054772[/C][C]-4.65518631054777[/C][C]0.429275917776717[/C][/ROW]
[ROW][C]66[/C][C]5035[/C][C]5040.13603695218[/C][C]-4.66080429542583[/C][C]-4.66080429542579[/C][C]-0.145826818241773[/C][/ROW]
[ROW][C]67[/C][C]4985[/C][C]4992.12336572655[/C][C]-4.68955428720495[/C][C]-4.68955428720493[/C][C]-0.746823426679043[/C][/ROW]
[ROW][C]68[/C][C]5005[/C][C]5008.4932994507[/C][C]-4.67559742046729[/C][C]-4.67559742046733[/C][C]0.362792125308705[/C][/ROW]
[ROW][C]69[/C][C]4910[/C][C]4919.46698528856[/C][C]-4.73146258389992[/C][C]-4.73146258389983[/C][C]-1.45311081751631[/C][/ROW]
[ROW][C]70[/C][C]4910[/C][C]4914.73168081379[/C][C]-4.73146512668573[/C][C]-4.7314651266858[/C][C]-6.61842876500476e-05[/C][/ROW]
[ROW][C]71[/C][C]4870[/C][C]4876.62713278851[/C][C]-4.75353875551266[/C][C]-4.75353875551248[/C][C]-0.574918279317641[/C][/ROW]
[ROW][C]72[/C][C]4850[/C][C]4855.67372160936[/C][C]-4.76424659485509[/C][C]-4.76424659485526[/C][C]-0.279075235607469[/C][/ROW]
[ROW][C]73[/C][C]4810[/C][C]4768.43733465957[/C][C]-4.19951576344648[/C][C]46.1946753472308[/C][C]-1.47040366591485[/C][/ROW]
[ROW][C]74[/C][C]4810[/C][C]4811.43618728589[/C][C]-3.88338209871308[/C][C]-3.88338465875871[/C][C]0.782035431382779[/C][/ROW]
[ROW][C]75[/C][C]4730[/C][C]4737.85627431788[/C][C]-3.9456110935278[/C][C]-3.94561109352782[/C][C]-1.20044474727862[/C][/ROW]
[ROW][C]76[/C][C]4850[/C][C]4847.50215193084[/C][C]-3.87918505768862[/C][C]-3.87918505768862[/C][C]1.9567553195819[/C][/ROW]
[ROW][C]77[/C][C]4895[/C][C]4895.91381172242[/C][C]-3.84947797292351[/C][C]-3.84947797292356[/C][C]0.900776923085087[/C][/ROW]
[ROW][C]78[/C][C]4845[/C][C]4851.168597139[/C][C]-3.87266269076906[/C][C]-3.872662690769[/C][C]-0.704481525659969[/C][/ROW]
[ROW][C]79[/C][C]4805[/C][C]4810.93462966852[/C][C]-3.89326338114588[/C][C]-3.8932633811458[/C][C]-0.626370034445806[/C][/ROW]
[ROW][C]80[/C][C]4825[/C][C]4827.72059780733[/C][C]-3.88155413726924[/C][C]-3.88155413726936[/C][C]0.356226191502401[/C][/ROW]
[ROW][C]81[/C][C]4830[/C][C]4833.34263326239[/C][C]-3.87617594669138[/C][C]-3.87617594669129[/C][C]0.163711453282523[/C][/ROW]
[ROW][C]82[/C][C]4720[/C][C]4729.54253835653[/C][C]-3.93269205707819[/C][C]-3.93269205707818[/C][C]-1.7213167202625[/C][/ROW]
[ROW][C]83[/C][C]4785[/C][C]4785.5345735953[/C][C]-3.89881830469657[/C][C]-3.89881830469648[/C][C]1.03227957326616[/C][/ROW]
[ROW][C]84[/C][C]4705[/C][C]4712.80210806286[/C][C]-3.93770603524519[/C][C]-3.93770603524533[/C][C]-1.18574687156532[/C][/ROW]
[ROW][C]85[/C][C]4840[/C][C]4787.23783740844[/C][C]-4.39641773278204[/C][C]48.3606001839011[/C][C]1.39051451289002[/C][/ROW]
[ROW][C]86[/C][C]4820[/C][C]4822.10945394901[/C][C]-4.16700791938706[/C][C]-4.16701355496734[/C][C]0.653975088210219[/C][/ROW]
[ROW][C]87[/C][C]4795[/C][C]4800.17770015629[/C][C]-4.18084766543919[/C][C]-4.18084766543906[/C][C]-0.305973505082433[/C][/ROW]
[ROW][C]88[/C][C]4810[/C][C]4813.20594022762[/C][C]-4.17206581648085[/C][C]-4.17206581648081[/C][C]0.296438617230246[/C][/ROW]
[ROW][C]89[/C][C]4840[/C][C]4842.28861244991[/C][C]-4.15557828000888[/C][C]-4.15557828000898[/C][C]0.572837208028107[/C][/ROW]
[ROW][C]90[/C][C]4810[/C][C]4815.44078101483[/C][C]-4.16680623465732[/C][C]-4.16680623465727[/C][C]-0.390890664321924[/C][/ROW]
[ROW][C]91[/C][C]4835[/C][C]4837.67174459321[/C][C]-4.15375233973803[/C][C]-4.15375233973796[/C][C]0.454720852751043[/C][/ROW]
[ROW][C]92[/C][C]4860[/C][C]4862.51167588638[/C][C]-4.13942189449297[/C][C]-4.13942189449308[/C][C]0.499437309020221[/C][/ROW]
[ROW][C]93[/C][C]4845[/C][C]4849.63429959461[/C][C]-4.14373858945616[/C][C]-4.14373858945616[/C][C]-0.150517609735045[/C][/ROW]
[ROW][C]94[/C][C]4935[/C][C]4934.123969973[/C][C]-4.09997383069378[/C][C]-4.0999738306938[/C][C]1.52677466718829[/C][/ROW]
[ROW][C]95[/C][C]4870[/C][C]4877.09746435669[/C][C]-4.12609461011063[/C][C]-4.12609461011053[/C][C]-0.9116977464523[/C][/ROW]
[ROW][C]96[/C][C]4830[/C][C]4836.20816716475[/C][C]-4.14422936745984[/C][C]-4.14422936745992[/C][C]-0.63327265542402[/C][/ROW]
[ROW][C]97[/C][C]4895[/C][C]4847.66077242101[/C][C]-4.22393798854876[/C][C]46.4633238951291[/C][C]0.275705485475884[/C][/ROW]
[ROW][C]98[/C][C]4920[/C][C]4919.79498949305[/C][C]-3.82838359329704[/C][C]-3.82839061681225[/C][C]1.27667417989073[/C][/ROW]
[ROW][C]99[/C][C]4925[/C][C]4928.13700353875[/C][C]-3.8199740123453[/C][C]-3.81997401234515[/C][C]0.209616177105218[/C][/ROW]
[ROW][C]100[/C][C]4860[/C][C]4867.06032389751[/C][C]-3.84589145743062[/C][C]-3.84589145743048[/C][C]-0.986262685881112[/C][/ROW]
[ROW][C]101[/C][C]4820[/C][C]4825.95412933454[/C][C]-3.86227890586249[/C][C]-3.8622789058626[/C][C]-0.641820089451044[/C][/ROW]
[ROW][C]102[/C][C]4790[/C][C]4795.37398931886[/C][C]-3.87400657582494[/C][C]-3.87400657582484[/C][C]-0.460223305143299[/C][/ROW]
[ROW][C]103[/C][C]4775[/C][C]4779.55013258982[/C][C]-3.87924917427866[/C][C]-3.87924917427856[/C][C]-0.205839796198758[/C][/ROW]
[ROW][C]104[/C][C]4735[/C][C]4740.84944935021[/C][C]-3.89451915259351[/C][C]-3.89451915259363[/C][C]-0.599809720556691[/C][/ROW]
[ROW][C]105[/C][C]4755[/C][C]4757.71965306426[/C][C]-3.88541735023551[/C][C]-3.88541735023544[/C][C]0.357678593440651[/C][/ROW]
[ROW][C]106[/C][C]4745[/C][C]4749.150425973[/C][C]-3.88746950532508[/C][C]-3.88746950532513[/C][C]-0.0806800239102576[/C][/ROW]
[ROW][C]107[/C][C]4705[/C][C]4710.83536618489[/C][C]-3.9025469352923[/C][C]-3.9025469352922[/C][C]-0.593025490852171[/C][/ROW]
[ROW][C]108[/C][C]4665[/C][C]4670.93905037573[/C][C]-3.91830336664539[/C][C]-3.91830336664544[/C][C]-0.620003330560988[/C][/ROW]
[ROW][C]109[/C][C]4650[/C][C]4612.66306908381[/C][C]-3.67177288852932[/C][C]40.3895088465935[/C][C]-0.958128487204923[/C][/ROW]
[ROW][C]110[/C][C]4590[/C][C]4594.50904451569[/C][C]-3.73915981796151[/C][C]-3.73916669966361[/C][C]-0.242888392694798[/C][/ROW]
[ROW][C]111[/C][C]4625[/C][C]4626.70043326284[/C][C]-3.71685391710071[/C][C]-3.71685391710069[/C][C]0.618842389239052[/C][/ROW]
[ROW][C]112[/C][C]4685[/C][C]4685.1987331324[/C][C]-3.69155056453386[/C][C]-3.6915505645338[/C][C]1.07165232200328[/C][/ROW]
[ROW][C]113[/C][C]4665[/C][C]4669.3773341143[/C][C]-3.6963441040977[/C][C]-3.69634410409779[/C][C]-0.208936212248564[/C][/ROW]
[ROW][C]114[/C][C]4675[/C][C]4677.99988153816[/C][C]-3.69148521443794[/C][C]-3.69148521443788[/C][C]0.212192472400676[/C][/ROW]
[ROW][C]115[/C][C]4690[/C][C]4692.65428300708[/C][C]-3.68425256315284[/C][C]-3.6842525631528[/C][C]0.316007230875384[/C][/ROW]
[ROW][C]116[/C][C]4600[/C][C]4608.24794031454[/C][C]-3.71606362447271[/C][C]-3.71606362447269[/C][C]-1.39043497101418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300316&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
154955495000
253655374.16987160095-6.72853389405677-6.72853309339802-1.25996653230632
353155324.44250574811-7.04004230075169-7.04004230075171-0.741174820368646
453355340.62739996116-6.93077384185098-6.930773841850940.400780749370675
553305336.74575495444-6.91689698888454-6.916896988884540.052617668939103
653655369.51014074326-6.7373986521393-6.737398652139320.684759290319083
754355437.22334490429-6.40216525412068-6.402165254120681.2847438826135
855355535.08272803707-5.93480669042458-5.93480669042461.79915524001438
955855587.40493022815-5.67483161297657-5.674831612976571.00528409557785
1056155618.45060851115-5.51169235594655-5.511692355946550.633644292722778
1156105615.36480000684-5.50096248246528-5.500962482465270.0418603694332497
1255855591.60614926143-5.58136204809818-5.58136204809817-0.315046821855894
1358205696.83615832125-10.629695504376116.9266509564842.32040272911747
1456455657.49936833537-11.3483868444198-11.3483869466342-0.419568876032247
1556505660.49720270982-11.3008813917608-11.30088139176080.247172005012632
1657255731.5027498893-11.1227939403919-11.12279394039191.4187858112974
1758255829.75344237603-10.8932479586497-10.89324795864971.88537483361634
1858705877.47996540882-10.7706657743034-10.77066577430341.01048316416969
1958605870.54721110066-10.7626575607034-10.76265756070340.0661575000414766
2058355846.5340820999-10.7902483986991-10.7902483986991-0.228409744849296
2158405849.96251719565-10.7607030257049-10.76070302570480.245099177029462
2258055817.05015215025-10.8066370933639-10.8066370933639-0.381845743385626
2357705782.20577223552-10.8563790248804-10.8563790248804-0.414356824492194
2456805695.28352673423-11.013459067056-11.013459067056-1.31120261425175
2556755583.28157557313-8.8540932174797397.3950235420936-1.92436038083257
2656905691.59555670432-6.95861779019515-6.958617318287221.82699062158532
2756105620.68153590907-7.09598122372875-7.09598122372868-1.10173284331129
2856105616.90497827903-7.0913174329372-7.091317432937180.0572012259382349
2956305635.6080774184-7.05613802114956-7.056138021149590.444498428871634
3056155622.40932929014-7.06449135805804-7.06449135805804-0.105851548825893
3155855593.33025546005-7.09438590554344-7.09438590554342-0.3793624749908
3255555563.40693071424-7.12534412900014-7.12534412900016-0.393395409045091
3355855590.17661878299-7.07944148399902-7.079441483999030.584089312926274
3455305539.58122258386-7.13829364602765-7.13829364602765-0.749879312936291
3554255437.59125044106-7.26640038356735-7.2664003835673-1.63450978796167
3656305626.01657505692-7.00245549897448-7.002455498974553.3722100307538
3755605506.56949036477-5.431675877853459.7484349382198-2.07346015168834
3854355443.89121236281-6.11574297824377-6.11574255663637-0.918032147820063
3953205332.20438530305-6.28353067801403-6.28353067801392-1.81850211804483
4051505165.45845645071-6.45044970149996-6.45044970149988-2.76470240546074
4151255132.94021875951-6.47678154096431-6.47678154096436-0.449138969358577
4250255036.61157690194-6.56731345338511-6.56731345338506-1.54811604362685
4350205026.7552672784-6.57062373777645-6.57062373777643-0.056668225655537
4449354945.82019822522-6.64539393358396-6.64539393358393-1.28127217577133
4548804889.48488645383-6.69530477704132-6.69530477704132-0.85613871472022
4648704877.02472720429-6.70108945208433-6.70108945208439-0.099326243786898
4749204923.65369121049-6.64762968425022-6.647629684250110.918856070635037
4849354940.31568889522-6.62428676071269-6.62428676071280.401615631142065
4950004928.08713692871-6.5661529242768772.2276863401306-0.101627447158389
5049554959.31572757888-6.20810132329567-6.208105972410310.61567626382057
5149704974.9549896555-6.18054397863697-6.180543978636980.376313736327567
5249904994.70350293432-6.15913082719939-6.159130827199320.446706346433353
5349204929.52011701796-6.2064744764831-6.20647447648313-1.01687387704941
5449304935.5118976583-6.19671297137431-6.196712971374290.210152337395403
5549554959.47917616814-6.17259586708487-6.17259586708490.519667075496179
5650005003.32460310404-6.13263693248371-6.132636932483730.861713288017558
5750255029.30420779285-6.10700324484036-6.107003244840380.553231334161135
5850755077.9873581607-6.06330173523595-6.0633017352360.943927290416377
5950755080.57096879455-6.05641031527546-6.056410315275330.14896936262701
6051055109.08791427169-6.02887796996131-6.028877969961440.59563103067538
6150504998.97379185532-5.1702332507095956.8725681844933-1.86842595161155
6250555056.47513181713-4.67841274350417-4.678415972194021.03120759263439
6350955097.0899157165-4.63105466629226-4.631054666292290.780139541890442
6450255033.0092366207-4.67176050226921-4.67176050226912-1.0241377255391
6550505053.2562277038-4.65518631054772-4.655186310547770.429275917776717
6650355040.13603695218-4.66080429542583-4.66080429542579-0.145826818241773
6749854992.12336572655-4.68955428720495-4.68955428720493-0.746823426679043
6850055008.4932994507-4.67559742046729-4.675597420467330.362792125308705
6949104919.46698528856-4.73146258389992-4.73146258389983-1.45311081751631
7049104914.73168081379-4.73146512668573-4.7314651266858-6.61842876500476e-05
7148704876.62713278851-4.75353875551266-4.75353875551248-0.574918279317641
7248504855.67372160936-4.76424659485509-4.76424659485526-0.279075235607469
7348104768.43733465957-4.1995157634464846.1946753472308-1.47040366591485
7448104811.43618728589-3.88338209871308-3.883384658758710.782035431382779
7547304737.85627431788-3.9456110935278-3.94561109352782-1.20044474727862
7648504847.50215193084-3.87918505768862-3.879185057688621.9567553195819
7748954895.91381172242-3.84947797292351-3.849477972923560.900776923085087
7848454851.168597139-3.87266269076906-3.872662690769-0.704481525659969
7948054810.93462966852-3.89326338114588-3.8932633811458-0.626370034445806
8048254827.72059780733-3.88155413726924-3.881554137269360.356226191502401
8148304833.34263326239-3.87617594669138-3.876175946691290.163711453282523
8247204729.54253835653-3.93269205707819-3.93269205707818-1.7213167202625
8347854785.5345735953-3.89881830469657-3.898818304696481.03227957326616
8447054712.80210806286-3.93770603524519-3.93770603524533-1.18574687156532
8548404787.23783740844-4.3964177327820448.36060018390111.39051451289002
8648204822.10945394901-4.16700791938706-4.167013554967340.653975088210219
8747954800.17770015629-4.18084766543919-4.18084766543906-0.305973505082433
8848104813.20594022762-4.17206581648085-4.172065816480810.296438617230246
8948404842.28861244991-4.15557828000888-4.155578280008980.572837208028107
9048104815.44078101483-4.16680623465732-4.16680623465727-0.390890664321924
9148354837.67174459321-4.15375233973803-4.153752339737960.454720852751043
9248604862.51167588638-4.13942189449297-4.139421894493080.499437309020221
9348454849.63429959461-4.14373858945616-4.14373858945616-0.150517609735045
9449354934.123969973-4.09997383069378-4.09997383069381.52677466718829
9548704877.09746435669-4.12609461011063-4.12609461011053-0.9116977464523
9648304836.20816716475-4.14422936745984-4.14422936745992-0.63327265542402
9748954847.66077242101-4.2239379885487646.46332389512910.275705485475884
9849204919.79498949305-3.82838359329704-3.828390616812251.27667417989073
9949254928.13700353875-3.8199740123453-3.819974012345150.209616177105218
10048604867.06032389751-3.84589145743062-3.84589145743048-0.986262685881112
10148204825.95412933454-3.86227890586249-3.8622789058626-0.641820089451044
10247904795.37398931886-3.87400657582494-3.87400657582484-0.460223305143299
10347754779.55013258982-3.87924917427866-3.87924917427856-0.205839796198758
10447354740.84944935021-3.89451915259351-3.89451915259363-0.599809720556691
10547554757.71965306426-3.88541735023551-3.885417350235440.357678593440651
10647454749.150425973-3.88746950532508-3.88746950532513-0.0806800239102576
10747054710.83536618489-3.9025469352923-3.9025469352922-0.593025490852171
10846654670.93905037573-3.91830336664539-3.91830336664544-0.620003330560988
10946504612.66306908381-3.6717728885293240.3895088465935-0.958128487204923
11045904594.50904451569-3.73915981796151-3.73916669966361-0.242888392694798
11146254626.70043326284-3.71685391710071-3.716853917100690.618842389239052
11246854685.1987331324-3.69155056453386-3.69155056453381.07165232200328
11346654669.3773341143-3.6963441040977-3.69634410409779-0.208936212248564
11446754677.99988153816-3.69148521443794-3.691485214437880.212192472400676
11546904692.65428300708-3.68425256315284-3.68425256315280.316007230875384
11646004608.24794031454-3.71606362447271-3.71606362447269-1.39043497101418







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14597.412651653744589.71356136197.69909029183754
24571.359182399884563.488649640347.87053275954274
34531.338246261864537.26373791878-5.92549165691865
44505.683172778534511.03882619722-5.35565341868948
54522.011411120324484.8139144756637.197496644652
64453.129074946634458.5890027541-5.4599278074704
74410.176016042614432.36409103254-22.1880749899319
84392.652229835314406.13917931098-13.4869494756749
94380.557718331274379.914267589420.64345074184379
104348.392484824024353.68935586786-5.29687104384352
114328.656527119674327.464444146311.19208297336104
124304.349847406044301.239532424753.11031498129171

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4597.41265165374 & 4589.7135613619 & 7.69909029183754 \tabularnewline
2 & 4571.35918239988 & 4563.48864964034 & 7.87053275954274 \tabularnewline
3 & 4531.33824626186 & 4537.26373791878 & -5.92549165691865 \tabularnewline
4 & 4505.68317277853 & 4511.03882619722 & -5.35565341868948 \tabularnewline
5 & 4522.01141112032 & 4484.81391447566 & 37.197496644652 \tabularnewline
6 & 4453.12907494663 & 4458.5890027541 & -5.4599278074704 \tabularnewline
7 & 4410.17601604261 & 4432.36409103254 & -22.1880749899319 \tabularnewline
8 & 4392.65222983531 & 4406.13917931098 & -13.4869494756749 \tabularnewline
9 & 4380.55771833127 & 4379.91426758942 & 0.64345074184379 \tabularnewline
10 & 4348.39248482402 & 4353.68935586786 & -5.29687104384352 \tabularnewline
11 & 4328.65652711967 & 4327.46444414631 & 1.19208297336104 \tabularnewline
12 & 4304.34984740604 & 4301.23953242475 & 3.11031498129171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300316&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]4597.41265165374[/C][C]4589.7135613619[/C][C]7.69909029183754[/C][/ROW]
[ROW][C]2[/C][C]4571.35918239988[/C][C]4563.48864964034[/C][C]7.87053275954274[/C][/ROW]
[ROW][C]3[/C][C]4531.33824626186[/C][C]4537.26373791878[/C][C]-5.92549165691865[/C][/ROW]
[ROW][C]4[/C][C]4505.68317277853[/C][C]4511.03882619722[/C][C]-5.35565341868948[/C][/ROW]
[ROW][C]5[/C][C]4522.01141112032[/C][C]4484.81391447566[/C][C]37.197496644652[/C][/ROW]
[ROW][C]6[/C][C]4453.12907494663[/C][C]4458.5890027541[/C][C]-5.4599278074704[/C][/ROW]
[ROW][C]7[/C][C]4410.17601604261[/C][C]4432.36409103254[/C][C]-22.1880749899319[/C][/ROW]
[ROW][C]8[/C][C]4392.65222983531[/C][C]4406.13917931098[/C][C]-13.4869494756749[/C][/ROW]
[ROW][C]9[/C][C]4380.55771833127[/C][C]4379.91426758942[/C][C]0.64345074184379[/C][/ROW]
[ROW][C]10[/C][C]4348.39248482402[/C][C]4353.68935586786[/C][C]-5.29687104384352[/C][/ROW]
[ROW][C]11[/C][C]4328.65652711967[/C][C]4327.46444414631[/C][C]1.19208297336104[/C][/ROW]
[ROW][C]12[/C][C]4304.34984740604[/C][C]4301.23953242475[/C][C]3.11031498129171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300316&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
14597.412651653744589.71356136197.69909029183754
24571.359182399884563.488649640347.87053275954274
34531.338246261864537.26373791878-5.92549165691865
44505.683172778534511.03882619722-5.35565341868948
54522.011411120324484.8139144756637.197496644652
64453.129074946634458.5890027541-5.4599278074704
74410.176016042614432.36409103254-22.1880749899319
84392.652229835314406.13917931098-13.4869494756749
94380.557718331274379.914267589420.64345074184379
104348.392484824024353.68935586786-5.29687104384352
114328.656527119674327.464444146311.19208297336104
124304.349847406044301.239532424753.11031498129171



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
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')