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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationFri, 16 Dec 2016 12:55:49 +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/t1481889432l47xdk21tafujgn.htm/, Retrieved Fri, 01 Nov 2024 03:33:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300196, Retrieved Fri, 01 Nov 2024 03:33:48 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Structural Time S...] [2016-12-16 11:55:49] [d5bfc1731fe289380efec318f4354749] [Current]
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Dataseries X:
3280
3444
3855
3811
3785
4075
3547
3863
4064
4176
4191
4307
4179
4622
4798
4673
4635
4875
4097
4262
4135
4238
3891
3573
3963
4192
4306
4316
4249
4408
3731
4096
4102
3962
3845
3734
3933
4176
4150
4137
4016
4113
3611
3474
3654
3712
3394
3348
3476
3908
4009
4102
4253
4532
4080
4402
4597
4844
4877
4735
4768
5251
5553
5548
5519
5798
4918
5271
5492
5547
5244
5149
5453
5584
5773
5811
5687
5647
4892
5235
5311
5378
4994
4559
4895
5104
5477
5302
5360
5540
4877
5241
5233
5561
5049
4482
4846
4636
4431
4702
4775
4834
4344
4800
4981
5069
4655
4254
4753
4888
5048
4991
4962
5150
4444
4815




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=300196&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=300196&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300196&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
132803280000
234443426.342042207677.6969687355955517.65795779233140.621455104965411
338553757.7627833855916.13510375087397.23721661440782.14066603277092
438113813.4320384592516.4500587875064-2.432038459245380.271060900880603
537853784.9229178775316.22493569130760.0770821224691147-0.308005305517161
640753999.4477725985817.316241416684775.55222740142081.35795573042547
735473650.7975408634815.1755766644975-103.797540863481-2.5058544738632
838633779.7744573384815.845173088137483.22554266151960.779219879940483
940644002.2997526924817.052212730165961.70024730751621.4151787592357
1041764144.8471676279717.779856629438731.15283237203280.859282686708887
1141914180.7380982132917.884233473481110.26190178671090.124007615332627
1243074270.9180662261618.298508761632136.08193377383580.495007789173913
1341794327.7127565843216.8498831080341-148.7127565843230.301176433433779
1446224615.0326577811120.85956111118376.967342218887651.69790454609622
1547984706.1443938902822.125545150588491.85560610971520.459689455403435
1646734688.6835604904421.7674489693476-15.6835604904444-0.270192066432189
1746354681.8246687376921.645831273857-46.8246687376913-0.1960200944159
1848754705.4909913182721.6525810795656169.5090086817310.013828244318075
1940974350.1215882390620.305882324031-253.121588239062-2.5795297282651
2042624226.5302964637719.757297378820835.4697035362322-0.984406459389993
2141354120.1646242524219.254991055698414.8353757475771-0.862872805102431
2242384175.1285147617319.404673994764162.87148523827140.244378413492362
2338913971.6060021951218.5860422407416-80.6060021951243-1.52549491763458
2435733646.2507463816418.9058266574896-73.2507463816369-2.35271877258874
2539634000.6247572669414.9145013357298-37.62475726693942.38870576800965
2641924167.5767389278715.852077723254224.42326107213211.0099755997238
2743064218.1121833483616.285582429351987.88781665164070.229081139139522
2843164318.3911279278217.038120214117-2.391127927823580.570651401070606
2942494319.6471628881616.9605712577279-70.6471628881583-0.108000141367448
3044084199.1060939598316.5184429448679208.893906040173-0.941067682044893
3137314016.169173976215.9215264073639-285.169173976203-1.36462562925085
3240964022.2846686517315.889700505881673.7153313482661-0.0670807218170409
3341024079.378159548416.035713895668122.62184045159770.281903295538236
3439623904.6698263718915.367484024542357.3301736281085-1.30524347045623
3538453846.0610807475515.211689665378-1.06108074754484-0.505813859398624
3637343879.3963771264115.1798951237489-145.3963771264110.1241437774807
3739333977.6293019908614.7799801906781-44.62930199086380.576502005260219
3841764122.7654466369415.264060110856553.23455336306420.878107567221847
3941504113.3517274369615.041029405441536.6482725630443-0.164527663620481
4041374135.9555701202815.10215621813671.044429879716770.0512627840724952
4140164077.8655034677914.7171454069316-61.8655034677939-0.500286804359621
4241133917.2271060710814.1110127311875195.77289392892-1.20003800082299
4336113898.0710421344314.0143345845251-287.071042134426-0.227630176207319
4434743546.8985367360512.9204528691456-72.8985367360517-2.49856271053367
4536543547.2285491786512.8807785505812106.771450821348-0.0861471911790493
4637123606.2683204451413.0094257194827105.7316795548640.315762319075734
4733943462.0255283000212.8156693035427-68.0255283000153-1.07485049771063
4833483495.7624599510712.7877504706758-147.762459951070.143299368273438
4934763539.8554909430912.7265417074435-63.85549094309320.215263113120108
5039083767.133412705113.3542119957057140.86658729491.45176772783557
5140093935.9354737112714.430136990734973.06452628873121.04307078825363
5241024055.5863280214615.175422483687746.41367197854290.712805358644724
5342534222.2403356818615.975595954221630.75966431814221.0341897553609
5445324303.6823522769516.21738246629228.317647723050.447910704317659
5540804286.0524246791116.1166981843585-206.052424679106-0.231623714094846
5644024422.7796509350816.4595385462823-20.77965093508050.825327170794099
5745974483.5772792800316.5822469359121113.4227207199720.303369117260714
5848444636.7830341531916.8834013014623207.2169658468120.934321484065063
5948774871.6013069739417.06361172195425.398693026061341.48949559070223
6047354911.7058202151217.0459248181516-176.7058202151230.157715843709848
6147684916.5869836224117.0528511221962-148.586983622406-0.083301946952573
6252515100.8075688968217.4913111178002150.1924311031751.1333382630104
6355535415.9755979693119.1582182203338137.0244020306872.00580380428179
6455485530.3338930387619.748451574563917.66610696123960.64510706398632
6555195521.5763023868919.6025301454014-2.57630238688763-0.194447621185018
6657985554.1546383138119.6522202777732243.8453616861850.0887491798619997
6749185275.1623885912718.7405181727475-357.162388591271-2.04374179994965
6852715285.0942475419818.7165122716212-14.0942475419789-0.0602809738964148
6954925383.9156470789518.9122560092204108.0843529210490.54804159831293
7055475399.2170195821918.9057833907424147.782980417811-0.0246881938630739
7152445288.5739674331918.8189080692405-44.5739674331877-0.885375693104905
7251495315.199372494618.8166477285888-166.1993724945980.053398460800208
7354535570.8268255725818.8607506159166-117.8268255725751.61832914273399
7455845557.0330516133418.780020057995826.9669483866572-0.221630073616271
7557735639.7689193627219.0830584832602133.2310806372830.432139712889378
7658115756.0923161500619.615728613002554.90768384994290.659338659795146
7756875714.2680631237319.3165762975738-27.2680631237305-0.418860412720062
7856475436.116892548418.1678146883633210.883107451604-2.03383532873996
7948925294.7495076863717.6744211084543-402.749507686373-1.09169833033577
8052355272.980927172717.5708850057621-37.9809271726954-0.269917887344761
8153115216.4047987581217.408205778273694.5952012418798-0.50721574533774
8253785197.0196312142617.3521208364811180.980368785742-0.251525303344691
8349945092.5694939969817.274377527857-98.5694939969779-0.832384892529019
8445594873.7430763459517.2563046468454-314.743076345946-1.61404561648789
8548954960.045385615217.2999916249027-65.04538561519750.471342702224288
8651045068.0036124270917.515163399645135.99638757291130.615777376393319
8754775293.8910865095218.3793695861412183.1089134904761.41063204706293
8853025255.9516026974818.103461256337746.0483973025182-0.382135866230738
8953605290.2551088507318.177802468518369.74489114927390.110406747278353
9055405293.9361245533818.1225062367465246.063875446619-0.0990835005762069
9148775280.7339681925618.0257895105539-403.73396819256-0.214325835555119
9252415268.0498993223517.9479390481524-27.0498993223528-0.210136060112048
9352335166.4754705906817.707490196071966.5245294093173-0.817501204689123
9455615282.8959791662617.8418264930181278.104020833740.674746855571926
9550495147.9759561145417.7401296283485-98.9759561145373-1.04387741220645
9644824911.1506493376117.650584171341-429.150649337611-1.73948966326716
9748464928.116970391917.6499602454394-82.1169703918982-0.00466839057021965
9846364736.9941555164717.170885169027-100.994155516474-1.41888666035063
9944314367.191782531915.730967447569263.8082174681019-2.62335456338873
10047024560.1456436558316.5166174563562141.8543563441651.20330529585605
10147754671.3985585432116.924729591196103.6014414567860.645554397761698
10248344613.9976721920316.6487019642257220.002327807969-0.507854001020762
10343444703.5089439076316.8705612335164-359.5089439076290.498439520448425
10448004783.1163222255717.024429046690316.8836777744250.429225829128558
10549814903.7136228555317.21944150601577.28637714446630.708313773673208
10650694797.8349332638317.0632145018131271.165066736166-0.841358209134463
10746554716.0633493883516.9920012152984-61.0633493883493-0.675312681665176
10842544684.7845636256416.9649620201977-430.784563625636-0.329731545893819
10947534737.2462322989817.003778100583615.75376770101460.242099803003226
11048884849.2677583229517.215251384965138.73224167705510.646087791895641
11150484994.3254723178717.649727777215153.67452768213110.867577386104295
11249914918.4626004897217.270733323234472.5373995102789-0.635320481066621
11349624864.2961766108716.982155116831797.7038233891252-0.486773476054871
11451504931.0514808277417.1604198530897218.9485191722590.340005746730031
11544444864.3837736180616.9109962454569-420.383773618058-0.573331683099562
11648154834.782137208716.8004784027643-19.782137208701-0.318172662769019

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3280 & 3280 & 0 & 0 & 0 \tabularnewline
2 & 3444 & 3426.34204220767 & 7.69696873559555 & 17.6579577923314 & 0.621455104965411 \tabularnewline
3 & 3855 & 3757.76278338559 & 16.135103750873 & 97.2372166144078 & 2.14066603277092 \tabularnewline
4 & 3811 & 3813.43203845925 & 16.4500587875064 & -2.43203845924538 & 0.271060900880603 \tabularnewline
5 & 3785 & 3784.92291787753 & 16.2249356913076 & 0.0770821224691147 & -0.308005305517161 \tabularnewline
6 & 4075 & 3999.44777259858 & 17.3162414166847 & 75.5522274014208 & 1.35795573042547 \tabularnewline
7 & 3547 & 3650.79754086348 & 15.1755766644975 & -103.797540863481 & -2.5058544738632 \tabularnewline
8 & 3863 & 3779.77445733848 & 15.8451730881374 & 83.2255426615196 & 0.779219879940483 \tabularnewline
9 & 4064 & 4002.29975269248 & 17.0522127301659 & 61.7002473075162 & 1.4151787592357 \tabularnewline
10 & 4176 & 4144.84716762797 & 17.7798566294387 & 31.1528323720328 & 0.859282686708887 \tabularnewline
11 & 4191 & 4180.73809821329 & 17.8842334734811 & 10.2619017867109 & 0.124007615332627 \tabularnewline
12 & 4307 & 4270.91806622616 & 18.2985087616321 & 36.0819337738358 & 0.495007789173913 \tabularnewline
13 & 4179 & 4327.71275658432 & 16.8498831080341 & -148.712756584323 & 0.301176433433779 \tabularnewline
14 & 4622 & 4615.03265778111 & 20.8595611111837 & 6.96734221888765 & 1.69790454609622 \tabularnewline
15 & 4798 & 4706.14439389028 & 22.1255451505884 & 91.8556061097152 & 0.459689455403435 \tabularnewline
16 & 4673 & 4688.68356049044 & 21.7674489693476 & -15.6835604904444 & -0.270192066432189 \tabularnewline
17 & 4635 & 4681.82466873769 & 21.645831273857 & -46.8246687376913 & -0.1960200944159 \tabularnewline
18 & 4875 & 4705.49099131827 & 21.6525810795656 & 169.509008681731 & 0.013828244318075 \tabularnewline
19 & 4097 & 4350.12158823906 & 20.305882324031 & -253.121588239062 & -2.5795297282651 \tabularnewline
20 & 4262 & 4226.53029646377 & 19.7572973788208 & 35.4697035362322 & -0.984406459389993 \tabularnewline
21 & 4135 & 4120.16462425242 & 19.2549910556984 & 14.8353757475771 & -0.862872805102431 \tabularnewline
22 & 4238 & 4175.12851476173 & 19.4046739947641 & 62.8714852382714 & 0.244378413492362 \tabularnewline
23 & 3891 & 3971.60600219512 & 18.5860422407416 & -80.6060021951243 & -1.52549491763458 \tabularnewline
24 & 3573 & 3646.25074638164 & 18.9058266574896 & -73.2507463816369 & -2.35271877258874 \tabularnewline
25 & 3963 & 4000.62475726694 & 14.9145013357298 & -37.6247572669394 & 2.38870576800965 \tabularnewline
26 & 4192 & 4167.57673892787 & 15.8520777232542 & 24.4232610721321 & 1.0099755997238 \tabularnewline
27 & 4306 & 4218.11218334836 & 16.2855824293519 & 87.8878166516407 & 0.229081139139522 \tabularnewline
28 & 4316 & 4318.39112792782 & 17.038120214117 & -2.39112792782358 & 0.570651401070606 \tabularnewline
29 & 4249 & 4319.64716288816 & 16.9605712577279 & -70.6471628881583 & -0.108000141367448 \tabularnewline
30 & 4408 & 4199.10609395983 & 16.5184429448679 & 208.893906040173 & -0.941067682044893 \tabularnewline
31 & 3731 & 4016.1691739762 & 15.9215264073639 & -285.169173976203 & -1.36462562925085 \tabularnewline
32 & 4096 & 4022.28466865173 & 15.8897005058816 & 73.7153313482661 & -0.0670807218170409 \tabularnewline
33 & 4102 & 4079.3781595484 & 16.0357138956681 & 22.6218404515977 & 0.281903295538236 \tabularnewline
34 & 3962 & 3904.66982637189 & 15.3674840245423 & 57.3301736281085 & -1.30524347045623 \tabularnewline
35 & 3845 & 3846.06108074755 & 15.211689665378 & -1.06108074754484 & -0.505813859398624 \tabularnewline
36 & 3734 & 3879.39637712641 & 15.1798951237489 & -145.396377126411 & 0.1241437774807 \tabularnewline
37 & 3933 & 3977.62930199086 & 14.7799801906781 & -44.6293019908638 & 0.576502005260219 \tabularnewline
38 & 4176 & 4122.76544663694 & 15.2640601108565 & 53.2345533630642 & 0.878107567221847 \tabularnewline
39 & 4150 & 4113.35172743696 & 15.0410294054415 & 36.6482725630443 & -0.164527663620481 \tabularnewline
40 & 4137 & 4135.95557012028 & 15.1021562181367 & 1.04442987971677 & 0.0512627840724952 \tabularnewline
41 & 4016 & 4077.86550346779 & 14.7171454069316 & -61.8655034677939 & -0.500286804359621 \tabularnewline
42 & 4113 & 3917.22710607108 & 14.1110127311875 & 195.77289392892 & -1.20003800082299 \tabularnewline
43 & 3611 & 3898.07104213443 & 14.0143345845251 & -287.071042134426 & -0.227630176207319 \tabularnewline
44 & 3474 & 3546.89853673605 & 12.9204528691456 & -72.8985367360517 & -2.49856271053367 \tabularnewline
45 & 3654 & 3547.22854917865 & 12.8807785505812 & 106.771450821348 & -0.0861471911790493 \tabularnewline
46 & 3712 & 3606.26832044514 & 13.0094257194827 & 105.731679554864 & 0.315762319075734 \tabularnewline
47 & 3394 & 3462.02552830002 & 12.8156693035427 & -68.0255283000153 & -1.07485049771063 \tabularnewline
48 & 3348 & 3495.76245995107 & 12.7877504706758 & -147.76245995107 & 0.143299368273438 \tabularnewline
49 & 3476 & 3539.85549094309 & 12.7265417074435 & -63.8554909430932 & 0.215263113120108 \tabularnewline
50 & 3908 & 3767.1334127051 & 13.3542119957057 & 140.8665872949 & 1.45176772783557 \tabularnewline
51 & 4009 & 3935.93547371127 & 14.4301369907349 & 73.0645262887312 & 1.04307078825363 \tabularnewline
52 & 4102 & 4055.58632802146 & 15.1754224836877 & 46.4136719785429 & 0.712805358644724 \tabularnewline
53 & 4253 & 4222.24033568186 & 15.9755959542216 & 30.7596643181422 & 1.0341897553609 \tabularnewline
54 & 4532 & 4303.68235227695 & 16.21738246629 & 228.31764772305 & 0.447910704317659 \tabularnewline
55 & 4080 & 4286.05242467911 & 16.1166981843585 & -206.052424679106 & -0.231623714094846 \tabularnewline
56 & 4402 & 4422.77965093508 & 16.4595385462823 & -20.7796509350805 & 0.825327170794099 \tabularnewline
57 & 4597 & 4483.57727928003 & 16.5822469359121 & 113.422720719972 & 0.303369117260714 \tabularnewline
58 & 4844 & 4636.78303415319 & 16.8834013014623 & 207.216965846812 & 0.934321484065063 \tabularnewline
59 & 4877 & 4871.60130697394 & 17.0636117219542 & 5.39869302606134 & 1.48949559070223 \tabularnewline
60 & 4735 & 4911.70582021512 & 17.0459248181516 & -176.705820215123 & 0.157715843709848 \tabularnewline
61 & 4768 & 4916.58698362241 & 17.0528511221962 & -148.586983622406 & -0.083301946952573 \tabularnewline
62 & 5251 & 5100.80756889682 & 17.4913111178002 & 150.192431103175 & 1.1333382630104 \tabularnewline
63 & 5553 & 5415.97559796931 & 19.1582182203338 & 137.024402030687 & 2.00580380428179 \tabularnewline
64 & 5548 & 5530.33389303876 & 19.7484515745639 & 17.6661069612396 & 0.64510706398632 \tabularnewline
65 & 5519 & 5521.57630238689 & 19.6025301454014 & -2.57630238688763 & -0.194447621185018 \tabularnewline
66 & 5798 & 5554.15463831381 & 19.6522202777732 & 243.845361686185 & 0.0887491798619997 \tabularnewline
67 & 4918 & 5275.16238859127 & 18.7405181727475 & -357.162388591271 & -2.04374179994965 \tabularnewline
68 & 5271 & 5285.09424754198 & 18.7165122716212 & -14.0942475419789 & -0.0602809738964148 \tabularnewline
69 & 5492 & 5383.91564707895 & 18.9122560092204 & 108.084352921049 & 0.54804159831293 \tabularnewline
70 & 5547 & 5399.21701958219 & 18.9057833907424 & 147.782980417811 & -0.0246881938630739 \tabularnewline
71 & 5244 & 5288.57396743319 & 18.8189080692405 & -44.5739674331877 & -0.885375693104905 \tabularnewline
72 & 5149 & 5315.1993724946 & 18.8166477285888 & -166.199372494598 & 0.053398460800208 \tabularnewline
73 & 5453 & 5570.82682557258 & 18.8607506159166 & -117.826825572575 & 1.61832914273399 \tabularnewline
74 & 5584 & 5557.03305161334 & 18.7800200579958 & 26.9669483866572 & -0.221630073616271 \tabularnewline
75 & 5773 & 5639.76891936272 & 19.0830584832602 & 133.231080637283 & 0.432139712889378 \tabularnewline
76 & 5811 & 5756.09231615006 & 19.6157286130025 & 54.9076838499429 & 0.659338659795146 \tabularnewline
77 & 5687 & 5714.26806312373 & 19.3165762975738 & -27.2680631237305 & -0.418860412720062 \tabularnewline
78 & 5647 & 5436.1168925484 & 18.1678146883633 & 210.883107451604 & -2.03383532873996 \tabularnewline
79 & 4892 & 5294.74950768637 & 17.6744211084543 & -402.749507686373 & -1.09169833033577 \tabularnewline
80 & 5235 & 5272.9809271727 & 17.5708850057621 & -37.9809271726954 & -0.269917887344761 \tabularnewline
81 & 5311 & 5216.40479875812 & 17.4082057782736 & 94.5952012418798 & -0.50721574533774 \tabularnewline
82 & 5378 & 5197.01963121426 & 17.3521208364811 & 180.980368785742 & -0.251525303344691 \tabularnewline
83 & 4994 & 5092.56949399698 & 17.274377527857 & -98.5694939969779 & -0.832384892529019 \tabularnewline
84 & 4559 & 4873.74307634595 & 17.2563046468454 & -314.743076345946 & -1.61404561648789 \tabularnewline
85 & 4895 & 4960.0453856152 & 17.2999916249027 & -65.0453856151975 & 0.471342702224288 \tabularnewline
86 & 5104 & 5068.00361242709 & 17.5151633996451 & 35.9963875729113 & 0.615777376393319 \tabularnewline
87 & 5477 & 5293.89108650952 & 18.3793695861412 & 183.108913490476 & 1.41063204706293 \tabularnewline
88 & 5302 & 5255.95160269748 & 18.1034612563377 & 46.0483973025182 & -0.382135866230738 \tabularnewline
89 & 5360 & 5290.25510885073 & 18.1778024685183 & 69.7448911492739 & 0.110406747278353 \tabularnewline
90 & 5540 & 5293.93612455338 & 18.1225062367465 & 246.063875446619 & -0.0990835005762069 \tabularnewline
91 & 4877 & 5280.73396819256 & 18.0257895105539 & -403.73396819256 & -0.214325835555119 \tabularnewline
92 & 5241 & 5268.04989932235 & 17.9479390481524 & -27.0498993223528 & -0.210136060112048 \tabularnewline
93 & 5233 & 5166.47547059068 & 17.7074901960719 & 66.5245294093173 & -0.817501204689123 \tabularnewline
94 & 5561 & 5282.89597916626 & 17.8418264930181 & 278.10402083374 & 0.674746855571926 \tabularnewline
95 & 5049 & 5147.97595611454 & 17.7401296283485 & -98.9759561145373 & -1.04387741220645 \tabularnewline
96 & 4482 & 4911.15064933761 & 17.650584171341 & -429.150649337611 & -1.73948966326716 \tabularnewline
97 & 4846 & 4928.1169703919 & 17.6499602454394 & -82.1169703918982 & -0.00466839057021965 \tabularnewline
98 & 4636 & 4736.99415551647 & 17.170885169027 & -100.994155516474 & -1.41888666035063 \tabularnewline
99 & 4431 & 4367.1917825319 & 15.7309674475692 & 63.8082174681019 & -2.62335456338873 \tabularnewline
100 & 4702 & 4560.14564365583 & 16.5166174563562 & 141.854356344165 & 1.20330529585605 \tabularnewline
101 & 4775 & 4671.39855854321 & 16.924729591196 & 103.601441456786 & 0.645554397761698 \tabularnewline
102 & 4834 & 4613.99767219203 & 16.6487019642257 & 220.002327807969 & -0.507854001020762 \tabularnewline
103 & 4344 & 4703.50894390763 & 16.8705612335164 & -359.508943907629 & 0.498439520448425 \tabularnewline
104 & 4800 & 4783.11632222557 & 17.0244290466903 & 16.883677774425 & 0.429225829128558 \tabularnewline
105 & 4981 & 4903.71362285553 & 17.219441506015 & 77.2863771444663 & 0.708313773673208 \tabularnewline
106 & 5069 & 4797.83493326383 & 17.0632145018131 & 271.165066736166 & -0.841358209134463 \tabularnewline
107 & 4655 & 4716.06334938835 & 16.9920012152984 & -61.0633493883493 & -0.675312681665176 \tabularnewline
108 & 4254 & 4684.78456362564 & 16.9649620201977 & -430.784563625636 & -0.329731545893819 \tabularnewline
109 & 4753 & 4737.24623229898 & 17.0037781005836 & 15.7537677010146 & 0.242099803003226 \tabularnewline
110 & 4888 & 4849.26775832295 & 17.2152513849651 & 38.7322416770551 & 0.646087791895641 \tabularnewline
111 & 5048 & 4994.32547231787 & 17.6497277772151 & 53.6745276821311 & 0.867577386104295 \tabularnewline
112 & 4991 & 4918.46260048972 & 17.2707333232344 & 72.5373995102789 & -0.635320481066621 \tabularnewline
113 & 4962 & 4864.29617661087 & 16.9821551168317 & 97.7038233891252 & -0.486773476054871 \tabularnewline
114 & 5150 & 4931.05148082774 & 17.1604198530897 & 218.948519172259 & 0.340005746730031 \tabularnewline
115 & 4444 & 4864.38377361806 & 16.9109962454569 & -420.383773618058 & -0.573331683099562 \tabularnewline
116 & 4815 & 4834.7821372087 & 16.8004784027643 & -19.782137208701 & -0.318172662769019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300196&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]3280[/C][C]3280[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3444[/C][C]3426.34204220767[/C][C]7.69696873559555[/C][C]17.6579577923314[/C][C]0.621455104965411[/C][/ROW]
[ROW][C]3[/C][C]3855[/C][C]3757.76278338559[/C][C]16.135103750873[/C][C]97.2372166144078[/C][C]2.14066603277092[/C][/ROW]
[ROW][C]4[/C][C]3811[/C][C]3813.43203845925[/C][C]16.4500587875064[/C][C]-2.43203845924538[/C][C]0.271060900880603[/C][/ROW]
[ROW][C]5[/C][C]3785[/C][C]3784.92291787753[/C][C]16.2249356913076[/C][C]0.0770821224691147[/C][C]-0.308005305517161[/C][/ROW]
[ROW][C]6[/C][C]4075[/C][C]3999.44777259858[/C][C]17.3162414166847[/C][C]75.5522274014208[/C][C]1.35795573042547[/C][/ROW]
[ROW][C]7[/C][C]3547[/C][C]3650.79754086348[/C][C]15.1755766644975[/C][C]-103.797540863481[/C][C]-2.5058544738632[/C][/ROW]
[ROW][C]8[/C][C]3863[/C][C]3779.77445733848[/C][C]15.8451730881374[/C][C]83.2255426615196[/C][C]0.779219879940483[/C][/ROW]
[ROW][C]9[/C][C]4064[/C][C]4002.29975269248[/C][C]17.0522127301659[/C][C]61.7002473075162[/C][C]1.4151787592357[/C][/ROW]
[ROW][C]10[/C][C]4176[/C][C]4144.84716762797[/C][C]17.7798566294387[/C][C]31.1528323720328[/C][C]0.859282686708887[/C][/ROW]
[ROW][C]11[/C][C]4191[/C][C]4180.73809821329[/C][C]17.8842334734811[/C][C]10.2619017867109[/C][C]0.124007615332627[/C][/ROW]
[ROW][C]12[/C][C]4307[/C][C]4270.91806622616[/C][C]18.2985087616321[/C][C]36.0819337738358[/C][C]0.495007789173913[/C][/ROW]
[ROW][C]13[/C][C]4179[/C][C]4327.71275658432[/C][C]16.8498831080341[/C][C]-148.712756584323[/C][C]0.301176433433779[/C][/ROW]
[ROW][C]14[/C][C]4622[/C][C]4615.03265778111[/C][C]20.8595611111837[/C][C]6.96734221888765[/C][C]1.69790454609622[/C][/ROW]
[ROW][C]15[/C][C]4798[/C][C]4706.14439389028[/C][C]22.1255451505884[/C][C]91.8556061097152[/C][C]0.459689455403435[/C][/ROW]
[ROW][C]16[/C][C]4673[/C][C]4688.68356049044[/C][C]21.7674489693476[/C][C]-15.6835604904444[/C][C]-0.270192066432189[/C][/ROW]
[ROW][C]17[/C][C]4635[/C][C]4681.82466873769[/C][C]21.645831273857[/C][C]-46.8246687376913[/C][C]-0.1960200944159[/C][/ROW]
[ROW][C]18[/C][C]4875[/C][C]4705.49099131827[/C][C]21.6525810795656[/C][C]169.509008681731[/C][C]0.013828244318075[/C][/ROW]
[ROW][C]19[/C][C]4097[/C][C]4350.12158823906[/C][C]20.305882324031[/C][C]-253.121588239062[/C][C]-2.5795297282651[/C][/ROW]
[ROW][C]20[/C][C]4262[/C][C]4226.53029646377[/C][C]19.7572973788208[/C][C]35.4697035362322[/C][C]-0.984406459389993[/C][/ROW]
[ROW][C]21[/C][C]4135[/C][C]4120.16462425242[/C][C]19.2549910556984[/C][C]14.8353757475771[/C][C]-0.862872805102431[/C][/ROW]
[ROW][C]22[/C][C]4238[/C][C]4175.12851476173[/C][C]19.4046739947641[/C][C]62.8714852382714[/C][C]0.244378413492362[/C][/ROW]
[ROW][C]23[/C][C]3891[/C][C]3971.60600219512[/C][C]18.5860422407416[/C][C]-80.6060021951243[/C][C]-1.52549491763458[/C][/ROW]
[ROW][C]24[/C][C]3573[/C][C]3646.25074638164[/C][C]18.9058266574896[/C][C]-73.2507463816369[/C][C]-2.35271877258874[/C][/ROW]
[ROW][C]25[/C][C]3963[/C][C]4000.62475726694[/C][C]14.9145013357298[/C][C]-37.6247572669394[/C][C]2.38870576800965[/C][/ROW]
[ROW][C]26[/C][C]4192[/C][C]4167.57673892787[/C][C]15.8520777232542[/C][C]24.4232610721321[/C][C]1.0099755997238[/C][/ROW]
[ROW][C]27[/C][C]4306[/C][C]4218.11218334836[/C][C]16.2855824293519[/C][C]87.8878166516407[/C][C]0.229081139139522[/C][/ROW]
[ROW][C]28[/C][C]4316[/C][C]4318.39112792782[/C][C]17.038120214117[/C][C]-2.39112792782358[/C][C]0.570651401070606[/C][/ROW]
[ROW][C]29[/C][C]4249[/C][C]4319.64716288816[/C][C]16.9605712577279[/C][C]-70.6471628881583[/C][C]-0.108000141367448[/C][/ROW]
[ROW][C]30[/C][C]4408[/C][C]4199.10609395983[/C][C]16.5184429448679[/C][C]208.893906040173[/C][C]-0.941067682044893[/C][/ROW]
[ROW][C]31[/C][C]3731[/C][C]4016.1691739762[/C][C]15.9215264073639[/C][C]-285.169173976203[/C][C]-1.36462562925085[/C][/ROW]
[ROW][C]32[/C][C]4096[/C][C]4022.28466865173[/C][C]15.8897005058816[/C][C]73.7153313482661[/C][C]-0.0670807218170409[/C][/ROW]
[ROW][C]33[/C][C]4102[/C][C]4079.3781595484[/C][C]16.0357138956681[/C][C]22.6218404515977[/C][C]0.281903295538236[/C][/ROW]
[ROW][C]34[/C][C]3962[/C][C]3904.66982637189[/C][C]15.3674840245423[/C][C]57.3301736281085[/C][C]-1.30524347045623[/C][/ROW]
[ROW][C]35[/C][C]3845[/C][C]3846.06108074755[/C][C]15.211689665378[/C][C]-1.06108074754484[/C][C]-0.505813859398624[/C][/ROW]
[ROW][C]36[/C][C]3734[/C][C]3879.39637712641[/C][C]15.1798951237489[/C][C]-145.396377126411[/C][C]0.1241437774807[/C][/ROW]
[ROW][C]37[/C][C]3933[/C][C]3977.62930199086[/C][C]14.7799801906781[/C][C]-44.6293019908638[/C][C]0.576502005260219[/C][/ROW]
[ROW][C]38[/C][C]4176[/C][C]4122.76544663694[/C][C]15.2640601108565[/C][C]53.2345533630642[/C][C]0.878107567221847[/C][/ROW]
[ROW][C]39[/C][C]4150[/C][C]4113.35172743696[/C][C]15.0410294054415[/C][C]36.6482725630443[/C][C]-0.164527663620481[/C][/ROW]
[ROW][C]40[/C][C]4137[/C][C]4135.95557012028[/C][C]15.1021562181367[/C][C]1.04442987971677[/C][C]0.0512627840724952[/C][/ROW]
[ROW][C]41[/C][C]4016[/C][C]4077.86550346779[/C][C]14.7171454069316[/C][C]-61.8655034677939[/C][C]-0.500286804359621[/C][/ROW]
[ROW][C]42[/C][C]4113[/C][C]3917.22710607108[/C][C]14.1110127311875[/C][C]195.77289392892[/C][C]-1.20003800082299[/C][/ROW]
[ROW][C]43[/C][C]3611[/C][C]3898.07104213443[/C][C]14.0143345845251[/C][C]-287.071042134426[/C][C]-0.227630176207319[/C][/ROW]
[ROW][C]44[/C][C]3474[/C][C]3546.89853673605[/C][C]12.9204528691456[/C][C]-72.8985367360517[/C][C]-2.49856271053367[/C][/ROW]
[ROW][C]45[/C][C]3654[/C][C]3547.22854917865[/C][C]12.8807785505812[/C][C]106.771450821348[/C][C]-0.0861471911790493[/C][/ROW]
[ROW][C]46[/C][C]3712[/C][C]3606.26832044514[/C][C]13.0094257194827[/C][C]105.731679554864[/C][C]0.315762319075734[/C][/ROW]
[ROW][C]47[/C][C]3394[/C][C]3462.02552830002[/C][C]12.8156693035427[/C][C]-68.0255283000153[/C][C]-1.07485049771063[/C][/ROW]
[ROW][C]48[/C][C]3348[/C][C]3495.76245995107[/C][C]12.7877504706758[/C][C]-147.76245995107[/C][C]0.143299368273438[/C][/ROW]
[ROW][C]49[/C][C]3476[/C][C]3539.85549094309[/C][C]12.7265417074435[/C][C]-63.8554909430932[/C][C]0.215263113120108[/C][/ROW]
[ROW][C]50[/C][C]3908[/C][C]3767.1334127051[/C][C]13.3542119957057[/C][C]140.8665872949[/C][C]1.45176772783557[/C][/ROW]
[ROW][C]51[/C][C]4009[/C][C]3935.93547371127[/C][C]14.4301369907349[/C][C]73.0645262887312[/C][C]1.04307078825363[/C][/ROW]
[ROW][C]52[/C][C]4102[/C][C]4055.58632802146[/C][C]15.1754224836877[/C][C]46.4136719785429[/C][C]0.712805358644724[/C][/ROW]
[ROW][C]53[/C][C]4253[/C][C]4222.24033568186[/C][C]15.9755959542216[/C][C]30.7596643181422[/C][C]1.0341897553609[/C][/ROW]
[ROW][C]54[/C][C]4532[/C][C]4303.68235227695[/C][C]16.21738246629[/C][C]228.31764772305[/C][C]0.447910704317659[/C][/ROW]
[ROW][C]55[/C][C]4080[/C][C]4286.05242467911[/C][C]16.1166981843585[/C][C]-206.052424679106[/C][C]-0.231623714094846[/C][/ROW]
[ROW][C]56[/C][C]4402[/C][C]4422.77965093508[/C][C]16.4595385462823[/C][C]-20.7796509350805[/C][C]0.825327170794099[/C][/ROW]
[ROW][C]57[/C][C]4597[/C][C]4483.57727928003[/C][C]16.5822469359121[/C][C]113.422720719972[/C][C]0.303369117260714[/C][/ROW]
[ROW][C]58[/C][C]4844[/C][C]4636.78303415319[/C][C]16.8834013014623[/C][C]207.216965846812[/C][C]0.934321484065063[/C][/ROW]
[ROW][C]59[/C][C]4877[/C][C]4871.60130697394[/C][C]17.0636117219542[/C][C]5.39869302606134[/C][C]1.48949559070223[/C][/ROW]
[ROW][C]60[/C][C]4735[/C][C]4911.70582021512[/C][C]17.0459248181516[/C][C]-176.705820215123[/C][C]0.157715843709848[/C][/ROW]
[ROW][C]61[/C][C]4768[/C][C]4916.58698362241[/C][C]17.0528511221962[/C][C]-148.586983622406[/C][C]-0.083301946952573[/C][/ROW]
[ROW][C]62[/C][C]5251[/C][C]5100.80756889682[/C][C]17.4913111178002[/C][C]150.192431103175[/C][C]1.1333382630104[/C][/ROW]
[ROW][C]63[/C][C]5553[/C][C]5415.97559796931[/C][C]19.1582182203338[/C][C]137.024402030687[/C][C]2.00580380428179[/C][/ROW]
[ROW][C]64[/C][C]5548[/C][C]5530.33389303876[/C][C]19.7484515745639[/C][C]17.6661069612396[/C][C]0.64510706398632[/C][/ROW]
[ROW][C]65[/C][C]5519[/C][C]5521.57630238689[/C][C]19.6025301454014[/C][C]-2.57630238688763[/C][C]-0.194447621185018[/C][/ROW]
[ROW][C]66[/C][C]5798[/C][C]5554.15463831381[/C][C]19.6522202777732[/C][C]243.845361686185[/C][C]0.0887491798619997[/C][/ROW]
[ROW][C]67[/C][C]4918[/C][C]5275.16238859127[/C][C]18.7405181727475[/C][C]-357.162388591271[/C][C]-2.04374179994965[/C][/ROW]
[ROW][C]68[/C][C]5271[/C][C]5285.09424754198[/C][C]18.7165122716212[/C][C]-14.0942475419789[/C][C]-0.0602809738964148[/C][/ROW]
[ROW][C]69[/C][C]5492[/C][C]5383.91564707895[/C][C]18.9122560092204[/C][C]108.084352921049[/C][C]0.54804159831293[/C][/ROW]
[ROW][C]70[/C][C]5547[/C][C]5399.21701958219[/C][C]18.9057833907424[/C][C]147.782980417811[/C][C]-0.0246881938630739[/C][/ROW]
[ROW][C]71[/C][C]5244[/C][C]5288.57396743319[/C][C]18.8189080692405[/C][C]-44.5739674331877[/C][C]-0.885375693104905[/C][/ROW]
[ROW][C]72[/C][C]5149[/C][C]5315.1993724946[/C][C]18.8166477285888[/C][C]-166.199372494598[/C][C]0.053398460800208[/C][/ROW]
[ROW][C]73[/C][C]5453[/C][C]5570.82682557258[/C][C]18.8607506159166[/C][C]-117.826825572575[/C][C]1.61832914273399[/C][/ROW]
[ROW][C]74[/C][C]5584[/C][C]5557.03305161334[/C][C]18.7800200579958[/C][C]26.9669483866572[/C][C]-0.221630073616271[/C][/ROW]
[ROW][C]75[/C][C]5773[/C][C]5639.76891936272[/C][C]19.0830584832602[/C][C]133.231080637283[/C][C]0.432139712889378[/C][/ROW]
[ROW][C]76[/C][C]5811[/C][C]5756.09231615006[/C][C]19.6157286130025[/C][C]54.9076838499429[/C][C]0.659338659795146[/C][/ROW]
[ROW][C]77[/C][C]5687[/C][C]5714.26806312373[/C][C]19.3165762975738[/C][C]-27.2680631237305[/C][C]-0.418860412720062[/C][/ROW]
[ROW][C]78[/C][C]5647[/C][C]5436.1168925484[/C][C]18.1678146883633[/C][C]210.883107451604[/C][C]-2.03383532873996[/C][/ROW]
[ROW][C]79[/C][C]4892[/C][C]5294.74950768637[/C][C]17.6744211084543[/C][C]-402.749507686373[/C][C]-1.09169833033577[/C][/ROW]
[ROW][C]80[/C][C]5235[/C][C]5272.9809271727[/C][C]17.5708850057621[/C][C]-37.9809271726954[/C][C]-0.269917887344761[/C][/ROW]
[ROW][C]81[/C][C]5311[/C][C]5216.40479875812[/C][C]17.4082057782736[/C][C]94.5952012418798[/C][C]-0.50721574533774[/C][/ROW]
[ROW][C]82[/C][C]5378[/C][C]5197.01963121426[/C][C]17.3521208364811[/C][C]180.980368785742[/C][C]-0.251525303344691[/C][/ROW]
[ROW][C]83[/C][C]4994[/C][C]5092.56949399698[/C][C]17.274377527857[/C][C]-98.5694939969779[/C][C]-0.832384892529019[/C][/ROW]
[ROW][C]84[/C][C]4559[/C][C]4873.74307634595[/C][C]17.2563046468454[/C][C]-314.743076345946[/C][C]-1.61404561648789[/C][/ROW]
[ROW][C]85[/C][C]4895[/C][C]4960.0453856152[/C][C]17.2999916249027[/C][C]-65.0453856151975[/C][C]0.471342702224288[/C][/ROW]
[ROW][C]86[/C][C]5104[/C][C]5068.00361242709[/C][C]17.5151633996451[/C][C]35.9963875729113[/C][C]0.615777376393319[/C][/ROW]
[ROW][C]87[/C][C]5477[/C][C]5293.89108650952[/C][C]18.3793695861412[/C][C]183.108913490476[/C][C]1.41063204706293[/C][/ROW]
[ROW][C]88[/C][C]5302[/C][C]5255.95160269748[/C][C]18.1034612563377[/C][C]46.0483973025182[/C][C]-0.382135866230738[/C][/ROW]
[ROW][C]89[/C][C]5360[/C][C]5290.25510885073[/C][C]18.1778024685183[/C][C]69.7448911492739[/C][C]0.110406747278353[/C][/ROW]
[ROW][C]90[/C][C]5540[/C][C]5293.93612455338[/C][C]18.1225062367465[/C][C]246.063875446619[/C][C]-0.0990835005762069[/C][/ROW]
[ROW][C]91[/C][C]4877[/C][C]5280.73396819256[/C][C]18.0257895105539[/C][C]-403.73396819256[/C][C]-0.214325835555119[/C][/ROW]
[ROW][C]92[/C][C]5241[/C][C]5268.04989932235[/C][C]17.9479390481524[/C][C]-27.0498993223528[/C][C]-0.210136060112048[/C][/ROW]
[ROW][C]93[/C][C]5233[/C][C]5166.47547059068[/C][C]17.7074901960719[/C][C]66.5245294093173[/C][C]-0.817501204689123[/C][/ROW]
[ROW][C]94[/C][C]5561[/C][C]5282.89597916626[/C][C]17.8418264930181[/C][C]278.10402083374[/C][C]0.674746855571926[/C][/ROW]
[ROW][C]95[/C][C]5049[/C][C]5147.97595611454[/C][C]17.7401296283485[/C][C]-98.9759561145373[/C][C]-1.04387741220645[/C][/ROW]
[ROW][C]96[/C][C]4482[/C][C]4911.15064933761[/C][C]17.650584171341[/C][C]-429.150649337611[/C][C]-1.73948966326716[/C][/ROW]
[ROW][C]97[/C][C]4846[/C][C]4928.1169703919[/C][C]17.6499602454394[/C][C]-82.1169703918982[/C][C]-0.00466839057021965[/C][/ROW]
[ROW][C]98[/C][C]4636[/C][C]4736.99415551647[/C][C]17.170885169027[/C][C]-100.994155516474[/C][C]-1.41888666035063[/C][/ROW]
[ROW][C]99[/C][C]4431[/C][C]4367.1917825319[/C][C]15.7309674475692[/C][C]63.8082174681019[/C][C]-2.62335456338873[/C][/ROW]
[ROW][C]100[/C][C]4702[/C][C]4560.14564365583[/C][C]16.5166174563562[/C][C]141.854356344165[/C][C]1.20330529585605[/C][/ROW]
[ROW][C]101[/C][C]4775[/C][C]4671.39855854321[/C][C]16.924729591196[/C][C]103.601441456786[/C][C]0.645554397761698[/C][/ROW]
[ROW][C]102[/C][C]4834[/C][C]4613.99767219203[/C][C]16.6487019642257[/C][C]220.002327807969[/C][C]-0.507854001020762[/C][/ROW]
[ROW][C]103[/C][C]4344[/C][C]4703.50894390763[/C][C]16.8705612335164[/C][C]-359.508943907629[/C][C]0.498439520448425[/C][/ROW]
[ROW][C]104[/C][C]4800[/C][C]4783.11632222557[/C][C]17.0244290466903[/C][C]16.883677774425[/C][C]0.429225829128558[/C][/ROW]
[ROW][C]105[/C][C]4981[/C][C]4903.71362285553[/C][C]17.219441506015[/C][C]77.2863771444663[/C][C]0.708313773673208[/C][/ROW]
[ROW][C]106[/C][C]5069[/C][C]4797.83493326383[/C][C]17.0632145018131[/C][C]271.165066736166[/C][C]-0.841358209134463[/C][/ROW]
[ROW][C]107[/C][C]4655[/C][C]4716.06334938835[/C][C]16.9920012152984[/C][C]-61.0633493883493[/C][C]-0.675312681665176[/C][/ROW]
[ROW][C]108[/C][C]4254[/C][C]4684.78456362564[/C][C]16.9649620201977[/C][C]-430.784563625636[/C][C]-0.329731545893819[/C][/ROW]
[ROW][C]109[/C][C]4753[/C][C]4737.24623229898[/C][C]17.0037781005836[/C][C]15.7537677010146[/C][C]0.242099803003226[/C][/ROW]
[ROW][C]110[/C][C]4888[/C][C]4849.26775832295[/C][C]17.2152513849651[/C][C]38.7322416770551[/C][C]0.646087791895641[/C][/ROW]
[ROW][C]111[/C][C]5048[/C][C]4994.32547231787[/C][C]17.6497277772151[/C][C]53.6745276821311[/C][C]0.867577386104295[/C][/ROW]
[ROW][C]112[/C][C]4991[/C][C]4918.46260048972[/C][C]17.2707333232344[/C][C]72.5373995102789[/C][C]-0.635320481066621[/C][/ROW]
[ROW][C]113[/C][C]4962[/C][C]4864.29617661087[/C][C]16.9821551168317[/C][C]97.7038233891252[/C][C]-0.486773476054871[/C][/ROW]
[ROW][C]114[/C][C]5150[/C][C]4931.05148082774[/C][C]17.1604198530897[/C][C]218.948519172259[/C][C]0.340005746730031[/C][/ROW]
[ROW][C]115[/C][C]4444[/C][C]4864.38377361806[/C][C]16.9109962454569[/C][C]-420.383773618058[/C][C]-0.573331683099562[/C][/ROW]
[ROW][C]116[/C][C]4815[/C][C]4834.7821372087[/C][C]16.8004784027643[/C][C]-19.782137208701[/C][C]-0.318172662769019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300196&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300196&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
132803280000
234443426.342042207677.6969687355955517.65795779233140.621455104965411
338553757.7627833855916.13510375087397.23721661440782.14066603277092
438113813.4320384592516.4500587875064-2.432038459245380.271060900880603
537853784.9229178775316.22493569130760.0770821224691147-0.308005305517161
640753999.4477725985817.316241416684775.55222740142081.35795573042547
735473650.7975408634815.1755766644975-103.797540863481-2.5058544738632
838633779.7744573384815.845173088137483.22554266151960.779219879940483
940644002.2997526924817.052212730165961.70024730751621.4151787592357
1041764144.8471676279717.779856629438731.15283237203280.859282686708887
1141914180.7380982132917.884233473481110.26190178671090.124007615332627
1243074270.9180662261618.298508761632136.08193377383580.495007789173913
1341794327.7127565843216.8498831080341-148.7127565843230.301176433433779
1446224615.0326577811120.85956111118376.967342218887651.69790454609622
1547984706.1443938902822.125545150588491.85560610971520.459689455403435
1646734688.6835604904421.7674489693476-15.6835604904444-0.270192066432189
1746354681.8246687376921.645831273857-46.8246687376913-0.1960200944159
1848754705.4909913182721.6525810795656169.5090086817310.013828244318075
1940974350.1215882390620.305882324031-253.121588239062-2.5795297282651
2042624226.5302964637719.757297378820835.4697035362322-0.984406459389993
2141354120.1646242524219.254991055698414.8353757475771-0.862872805102431
2242384175.1285147617319.404673994764162.87148523827140.244378413492362
2338913971.6060021951218.5860422407416-80.6060021951243-1.52549491763458
2435733646.2507463816418.9058266574896-73.2507463816369-2.35271877258874
2539634000.6247572669414.9145013357298-37.62475726693942.38870576800965
2641924167.5767389278715.852077723254224.42326107213211.0099755997238
2743064218.1121833483616.285582429351987.88781665164070.229081139139522
2843164318.3911279278217.038120214117-2.391127927823580.570651401070606
2942494319.6471628881616.9605712577279-70.6471628881583-0.108000141367448
3044084199.1060939598316.5184429448679208.893906040173-0.941067682044893
3137314016.169173976215.9215264073639-285.169173976203-1.36462562925085
3240964022.2846686517315.889700505881673.7153313482661-0.0670807218170409
3341024079.378159548416.035713895668122.62184045159770.281903295538236
3439623904.6698263718915.367484024542357.3301736281085-1.30524347045623
3538453846.0610807475515.211689665378-1.06108074754484-0.505813859398624
3637343879.3963771264115.1798951237489-145.3963771264110.1241437774807
3739333977.6293019908614.7799801906781-44.62930199086380.576502005260219
3841764122.7654466369415.264060110856553.23455336306420.878107567221847
3941504113.3517274369615.041029405441536.6482725630443-0.164527663620481
4041374135.9555701202815.10215621813671.044429879716770.0512627840724952
4140164077.8655034677914.7171454069316-61.8655034677939-0.500286804359621
4241133917.2271060710814.1110127311875195.77289392892-1.20003800082299
4336113898.0710421344314.0143345845251-287.071042134426-0.227630176207319
4434743546.8985367360512.9204528691456-72.8985367360517-2.49856271053367
4536543547.2285491786512.8807785505812106.771450821348-0.0861471911790493
4637123606.2683204451413.0094257194827105.7316795548640.315762319075734
4733943462.0255283000212.8156693035427-68.0255283000153-1.07485049771063
4833483495.7624599510712.7877504706758-147.762459951070.143299368273438
4934763539.8554909430912.7265417074435-63.85549094309320.215263113120108
5039083767.133412705113.3542119957057140.86658729491.45176772783557
5140093935.9354737112714.430136990734973.06452628873121.04307078825363
5241024055.5863280214615.175422483687746.41367197854290.712805358644724
5342534222.2403356818615.975595954221630.75966431814221.0341897553609
5445324303.6823522769516.21738246629228.317647723050.447910704317659
5540804286.0524246791116.1166981843585-206.052424679106-0.231623714094846
5644024422.7796509350816.4595385462823-20.77965093508050.825327170794099
5745974483.5772792800316.5822469359121113.4227207199720.303369117260714
5848444636.7830341531916.8834013014623207.2169658468120.934321484065063
5948774871.6013069739417.06361172195425.398693026061341.48949559070223
6047354911.7058202151217.0459248181516-176.7058202151230.157715843709848
6147684916.5869836224117.0528511221962-148.586983622406-0.083301946952573
6252515100.8075688968217.4913111178002150.1924311031751.1333382630104
6355535415.9755979693119.1582182203338137.0244020306872.00580380428179
6455485530.3338930387619.748451574563917.66610696123960.64510706398632
6555195521.5763023868919.6025301454014-2.57630238688763-0.194447621185018
6657985554.1546383138119.6522202777732243.8453616861850.0887491798619997
6749185275.1623885912718.7405181727475-357.162388591271-2.04374179994965
6852715285.0942475419818.7165122716212-14.0942475419789-0.0602809738964148
6954925383.9156470789518.9122560092204108.0843529210490.54804159831293
7055475399.2170195821918.9057833907424147.782980417811-0.0246881938630739
7152445288.5739674331918.8189080692405-44.5739674331877-0.885375693104905
7251495315.199372494618.8166477285888-166.1993724945980.053398460800208
7354535570.8268255725818.8607506159166-117.8268255725751.61832914273399
7455845557.0330516133418.780020057995826.9669483866572-0.221630073616271
7557735639.7689193627219.0830584832602133.2310806372830.432139712889378
7658115756.0923161500619.615728613002554.90768384994290.659338659795146
7756875714.2680631237319.3165762975738-27.2680631237305-0.418860412720062
7856475436.116892548418.1678146883633210.883107451604-2.03383532873996
7948925294.7495076863717.6744211084543-402.749507686373-1.09169833033577
8052355272.980927172717.5708850057621-37.9809271726954-0.269917887344761
8153115216.4047987581217.408205778273694.5952012418798-0.50721574533774
8253785197.0196312142617.3521208364811180.980368785742-0.251525303344691
8349945092.5694939969817.274377527857-98.5694939969779-0.832384892529019
8445594873.7430763459517.2563046468454-314.743076345946-1.61404561648789
8548954960.045385615217.2999916249027-65.04538561519750.471342702224288
8651045068.0036124270917.515163399645135.99638757291130.615777376393319
8754775293.8910865095218.3793695861412183.1089134904761.41063204706293
8853025255.9516026974818.103461256337746.0483973025182-0.382135866230738
8953605290.2551088507318.177802468518369.74489114927390.110406747278353
9055405293.9361245533818.1225062367465246.063875446619-0.0990835005762069
9148775280.7339681925618.0257895105539-403.73396819256-0.214325835555119
9252415268.0498993223517.9479390481524-27.0498993223528-0.210136060112048
9352335166.4754705906817.707490196071966.5245294093173-0.817501204689123
9455615282.8959791662617.8418264930181278.104020833740.674746855571926
9550495147.9759561145417.7401296283485-98.9759561145373-1.04387741220645
9644824911.1506493376117.650584171341-429.150649337611-1.73948966326716
9748464928.116970391917.6499602454394-82.1169703918982-0.00466839057021965
9846364736.9941555164717.170885169027-100.994155516474-1.41888666035063
9944314367.191782531915.730967447569263.8082174681019-2.62335456338873
10047024560.1456436558316.5166174563562141.8543563441651.20330529585605
10147754671.3985585432116.924729591196103.6014414567860.645554397761698
10248344613.9976721920316.6487019642257220.002327807969-0.507854001020762
10343444703.5089439076316.8705612335164-359.5089439076290.498439520448425
10448004783.1163222255717.024429046690316.8836777744250.429225829128558
10549814903.7136228555317.21944150601577.28637714446630.708313773673208
10650694797.8349332638317.0632145018131271.165066736166-0.841358209134463
10746554716.0633493883516.9920012152984-61.0633493883493-0.675312681665176
10842544684.7845636256416.9649620201977-430.784563625636-0.329731545893819
10947534737.2462322989817.003778100583615.75376770101460.242099803003226
11048884849.2677583229517.215251384965138.73224167705510.646087791895641
11150484994.3254723178717.649727777215153.67452768213110.867577386104295
11249914918.4626004897217.270733323234472.5373995102789-0.635320481066621
11349624864.2961766108716.982155116831797.7038233891252-0.486773476054871
11451504931.0514808277417.1604198530897218.9485191722590.340005746730031
11544444864.3837736180616.9109962454569-420.383773618058-0.573331683099562
11648154834.782137208716.8004784027643-19.782137208701-0.318172662769019







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14904.321823258014861.0857090915543.2361141664563
25079.062958697314872.85734376052206.20561493679
34738.164299615074884.62897842948-146.464678814412
44375.79061342154896.40061309844-520.609999676937
54859.998120862524908.1722477674-48.174126904887
64954.156438658754919.9438824363734.2125562223823
75093.498476179224931.71551710533161.78295907389
85138.22668793024943.48715177429194.739536155909
95140.917577618524955.25878644326185.658791175268
105277.033449205454967.03042111222310.003028093233
114592.526335776084978.80205578118-386.275720005103
124956.259616027564990.57369045015-34.3140744225898

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4904.32182325801 & 4861.08570909155 & 43.2361141664563 \tabularnewline
2 & 5079.06295869731 & 4872.85734376052 & 206.20561493679 \tabularnewline
3 & 4738.16429961507 & 4884.62897842948 & -146.464678814412 \tabularnewline
4 & 4375.7906134215 & 4896.40061309844 & -520.609999676937 \tabularnewline
5 & 4859.99812086252 & 4908.1722477674 & -48.174126904887 \tabularnewline
6 & 4954.15643865875 & 4919.94388243637 & 34.2125562223823 \tabularnewline
7 & 5093.49847617922 & 4931.71551710533 & 161.78295907389 \tabularnewline
8 & 5138.2266879302 & 4943.48715177429 & 194.739536155909 \tabularnewline
9 & 5140.91757761852 & 4955.25878644326 & 185.658791175268 \tabularnewline
10 & 5277.03344920545 & 4967.03042111222 & 310.003028093233 \tabularnewline
11 & 4592.52633577608 & 4978.80205578118 & -386.275720005103 \tabularnewline
12 & 4956.25961602756 & 4990.57369045015 & -34.3140744225898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300196&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]4904.32182325801[/C][C]4861.08570909155[/C][C]43.2361141664563[/C][/ROW]
[ROW][C]2[/C][C]5079.06295869731[/C][C]4872.85734376052[/C][C]206.20561493679[/C][/ROW]
[ROW][C]3[/C][C]4738.16429961507[/C][C]4884.62897842948[/C][C]-146.464678814412[/C][/ROW]
[ROW][C]4[/C][C]4375.7906134215[/C][C]4896.40061309844[/C][C]-520.609999676937[/C][/ROW]
[ROW][C]5[/C][C]4859.99812086252[/C][C]4908.1722477674[/C][C]-48.174126904887[/C][/ROW]
[ROW][C]6[/C][C]4954.15643865875[/C][C]4919.94388243637[/C][C]34.2125562223823[/C][/ROW]
[ROW][C]7[/C][C]5093.49847617922[/C][C]4931.71551710533[/C][C]161.78295907389[/C][/ROW]
[ROW][C]8[/C][C]5138.2266879302[/C][C]4943.48715177429[/C][C]194.739536155909[/C][/ROW]
[ROW][C]9[/C][C]5140.91757761852[/C][C]4955.25878644326[/C][C]185.658791175268[/C][/ROW]
[ROW][C]10[/C][C]5277.03344920545[/C][C]4967.03042111222[/C][C]310.003028093233[/C][/ROW]
[ROW][C]11[/C][C]4592.52633577608[/C][C]4978.80205578118[/C][C]-386.275720005103[/C][/ROW]
[ROW][C]12[/C][C]4956.25961602756[/C][C]4990.57369045015[/C][C]-34.3140744225898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300196&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300196&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
14904.321823258014861.0857090915543.2361141664563
25079.062958697314872.85734376052206.20561493679
34738.164299615074884.62897842948-146.464678814412
44375.79061342154896.40061309844-520.609999676937
54859.998120862524908.1722477674-48.174126904887
64954.156438658754919.9438824363734.2125562223823
75093.498476179224931.71551710533161.78295907389
85138.22668793024943.48715177429194.739536155909
95140.917577618524955.25878644326185.658791175268
105277.033449205454967.03042111222310.003028093233
114592.526335776084978.80205578118-386.275720005103
124956.259616027564990.57369045015-34.3140744225898



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')