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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, 09 Dec 2016 15:20:19 +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/09/t14812935761jtgncniofzk2ob.htm/, Retrieved Sat, 18 May 2024 04:05:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298558, Retrieved Sat, 18 May 2024 04:05:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
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...] [2016-12-09 14:20:19] [b7b12d6257d20c3ae3b596da588d7d29] [Current]
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Dataseries X:
3655
3390
4000
3810
3790
3790
3350
3900
3725
3945
3840
3625
4000
3915
4200
3900
4140
3945
3735
3970
3745
4140
3840
3570
4085
3865
4280
4280
4240
4065
4060
4265
4085
4450
4195
4160
4580
4130
4645
4375
4480
4485
4465
4515
4465
4790
4270
4495
4490
4275
4695
4630
4560
4665
4725
4840
4745
4940
4635
4910
4690
4585
5065
4705
4580
4660
4510
4885
4765
4700
4590
4655
4845
4495
5020
4535
4700
4435
4285
4780
4450
4875
4670
4325
5000
4675
4950
4790
4785
4520
4735
5055
4640
5045
4710
4650
4915
4260
4505
4575
4785
4610
5220
5285
4870
5440
4615
4645
4845
4780
5005
4905
4630
4785
5160




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298558&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298558&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
136553655000
233903540.9981510932-9.16126786762411-48.7221426425625-1.49662393602543
340003727.099985988696.06373000605504121.7977778969442.37550433094227
438103776.858866587838.65356413494005-5.626274012954980.58917195560992
537903787.64308480978.750564547730210.311850872009530.0304162512362876
637903790.790218529148.541953453426494.79500061445341-0.0821919978403404
733503624.899861616332.89408162470009-97.7551834579426-2.59297078780385
839003713.000501061945.4046128429702399.61490451210481.27545559836107
937253727.055157665.64340252000359-10.975128508660.129982776920065
1039453811.429889891547.7158845098879452.11398196390911.1857935967074
1138403831.722668610218.03484587035678-4.762807157769950.189702617412001
1236253757.11249016576.00336095656343-46.2922161369861-1.24785559547408
1340003826.433113865611.1905180404631998.03831734752281.21823560157543
1439153915.059488322293.01908750253466-78.51213654546881.22504670692601
1542003997.882537118245.83587005945717135.9311689373671.06715933138907
1639003978.684760328935.03399037148718-56.6694772927243-0.352046062638954
1741404035.354232503116.3876183297181756.88175183672820.755050737617969
1839453993.387442278945.33942270124118-2.41245134163116-0.72171472648387
1937353943.781018870954.30761051057763-155.81938413736-0.828343188082648
2039703916.117505827963.7621752152979184.910175257594-0.484370944112234
2137453867.908124771972.92820364764486-72.2912637589292-0.78939233035939
2241403941.287677814114.00787694779584129.9528550236451.07163908453872
2338403911.220576717243.52739517623774-37.8870787850365-0.518927005914856
2435703817.943903924472.67456785077298-152.50280736811-1.4800753875362
2540853878.691844550861.42512786047841145.5882845648380.961539047618774
2638653919.962539921331.8018116340243-92.39218520708990.5928273555201
2742804006.405203718363.65247158633176199.2052141197851.20140773683817
2842804143.239707960156.6979704087850918.17085279934531.91951444960756
2942404169.175635037197.0867701253147153.19675568908550.283914404412746
3040654133.093662395866.3426966797976-27.7110004102407-0.647395927674757
3140604154.375971844466.56637561827763-108.5195392710470.226066149367431
3242654162.239246025136.58385360753615101.5249866330130.0197180402187332
3340854172.171254883186.62562248555326-90.3730175928390.0510344538726507
3444504217.806659707697.07403001232306194.7986591690970.595484238842496
3541954219.073716872947.01829412352457-18.4905617451282-0.0887598795511357
3641604267.056764883477.20763269436802-146.7373129612180.629154004138561
3745804349.563287283036.70966946465841155.5730210068131.19079682965437
3841304341.85160614946.61628636440617-198.205846229957-0.217780827815648
3946454403.193274115047.44867883842863192.250407351030.799908481580837
4043754399.526891237787.25453289595196-14.4807862485189-0.16283469694367
4144804406.880277304367.2561673734624573.02897786459010.00146854786857454
4244854449.593339474847.776835851098172.362216209556920.533238956279511
4344654500.622800311118.33673059228589-76.35105980044830.655690260881504
4445154483.224079409218.0386251234993256.1621959442399-0.391961851552988
4544654515.951136011718.2971933598008-74.43474848336450.377004790262942
4647904551.930767286818.55287596111832211.6664597608360.423363264543802
4742704481.353621142057.98069270938422-135.659772165605-1.21178987713797
4844954543.454213863498.17740759195633-100.5100733284340.831949863332028
4944904485.992035992858.2315489780861467.8049228393359-1.01946383226956
5042754488.151030971268.19739591215255-207.401424292149-0.0921347913708803
5146954495.934552750428.1926258859694199.44641353862-0.00614690701089863
5246304553.984097483628.8853870002832930.39801662799020.738893247696421
5345604549.060793735838.6941142295436723.6757157038914-0.206299598413475
5446654597.974501180119.2075779201978129.52895904585360.606363774423097
5547254674.424321576199.97797264553142-12.6562134404941.02072240390085
5648404729.423221152510.438772450354367.99165195103680.686417521314267
5747454773.1808981363210.7413515545402-59.81844783878220.509323747114912
5849404759.0335482505910.5479676214026204.663730173204-0.381025897297502
5946354772.9184696110510.5679004395905-141.103915122820.0511492226058295
6049104850.431938820110.8059086916457-4.569720016707361.02866403165115
6146904790.0253655007110.6815678521856-31.5735273918785-1.09735272469553
6245854793.7394433476310.6444458449294-202.144860727334-0.105930888644338
6350654831.9923031687510.9020115768589207.3534736808760.413905057845348
6447054788.8551613037910.2845916771881-33.9590057889485-0.807532849898458
6545804720.617904612039.35838369065077-67.8314608760997-1.17875040932016
6646604700.105018018649.0238714862526-12.2075326928408-0.451406305981761
6745104650.548782540418.4250974237562-85.4560120753427-0.890285618754408
6848854709.757981973368.88989859138412127.2295812596290.774868833076073
6947654756.607855321079.19511481373908-27.6272013081420.580622370178042
7047004682.475514106298.629245373139496.7965553284956-1.27637858493354
7145904702.763183595338.69094694116852-123.8783314735020.178770515095441
7246554683.305458521538.58714436109726-1.40965236845186-0.432212106386254
7348454748.441762920418.7551885367316542.5121769822960.868258106975528
7444954742.055620077958.67700194989408-232.728250548479-0.230503774695896
7550204757.392487888958.72979996007161256.3830399708880.100435991275051
7645354685.924010910357.95495122686873-76.3828976914033-1.20565911477876
7747004704.365360638.06178816304613-14.12894511574260.158050994228792
7844354617.473650707927.12278652551744-93.6040193613939-1.43803941816525
7942854537.400438676876.32392173350715-170.336552799262-1.32665023809721
8047804572.561782688636.56176356551414180.1743243744570.440269154740131
8144504535.470241729366.24601351999607-44.0616252610156-0.667966645293633
8248754617.573947691946.70976255950521185.2992900204821.16230331284822
8346704686.92592183587.0168895678911-76.5930381711670.960659432503069
8443254585.384477610416.60148391425881-156.854732292641-1.66581801595541
8550004699.301750485176.98498399846316198.4505258912141.64497653254427
8646754781.168175123227.36083246872366-177.0245646496171.14115621278935
8749504751.209258732487.10063692993256233.804194890448-0.56505048086905
8847904787.332332348037.34336968806766-24.43880867041580.438245846793909
8947854781.175091328637.2230083674158616.4419067228959-0.204152318009021
9045204716.330266448826.58942782838085-128.734952728784-1.09359085216492
9147354780.197333801917.06192345815503-99.15555560737540.872362538171847
9250554819.579242670687.30371860962301204.8563478946470.493700599561587
9346404795.757126197287.09862821026686-126.235400310129-0.476413350086079
9450454825.343809997177.22504737977775198.282404582390.344623143186729
9547104809.585349993977.11801790578046-77.7093761783348-0.352463522067859
9646504830.448161917077.17188992433914-193.5388557760830.210817266930104
9749154808.176716734287.05817254841019134.82819746838-0.450988222807783
9842604680.096495910946.40021694713792-292.194959718004-2.06135431336247
9945054534.467390057585.44561488371271113.550736013823-2.30835775795951
10045754538.320993285255.4338646366328938.1713338107493-0.0241200393015078
10147854610.230850479845.95875335167952112.4523210782011.00793720363307
10246104673.525639771216.41003407333792-117.4107565150330.871555513889959
10352204904.328844162898.0851557847587104.0625970538123.42092181270307
10452854988.501819307268.60468791175713224.5148134042961.16284887912595
10548705008.515344553458.67385410058358-149.336271832070.174667242499435
10654405090.169996751949.05663979271563280.4836440047051.11853603142049
10746154968.878002051018.47277334090425-229.878618186293-1.99888557235507
10846454904.527310779618.18432528651697-190.231998644131-1.11665401551063
10948454809.837679090287.77460516322638132.919874895272-1.5753425453299
11047804871.109163964698.02660098866662-141.7588170483030.816706872429899
11150054894.163332358568.1129950984128996.67145639187950.228654263741819
11249054909.62318683988.16160564062113-11.52922760868340.111594906084088
11346304805.100365042617.36485533647389-69.1983108083781-1.71232184962499
11447854868.690886486077.76392500947757-136.6270052948230.855971219610596
11551604953.921933910568.29012101614477132.9489604118351.18206187487103

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3655 & 3655 & 0 & 0 & 0 \tabularnewline
2 & 3390 & 3540.9981510932 & -9.16126786762411 & -48.7221426425625 & -1.49662393602543 \tabularnewline
3 & 4000 & 3727.09998598869 & 6.06373000605504 & 121.797777896944 & 2.37550433094227 \tabularnewline
4 & 3810 & 3776.85886658783 & 8.65356413494005 & -5.62627401295498 & 0.58917195560992 \tabularnewline
5 & 3790 & 3787.6430848097 & 8.75056454773021 & 0.31185087200953 & 0.0304162512362876 \tabularnewline
6 & 3790 & 3790.79021852914 & 8.54195345342649 & 4.79500061445341 & -0.0821919978403404 \tabularnewline
7 & 3350 & 3624.89986161633 & 2.89408162470009 & -97.7551834579426 & -2.59297078780385 \tabularnewline
8 & 3900 & 3713.00050106194 & 5.40461284297023 & 99.6149045121048 & 1.27545559836107 \tabularnewline
9 & 3725 & 3727.05515766 & 5.64340252000359 & -10.97512850866 & 0.129982776920065 \tabularnewline
10 & 3945 & 3811.42988989154 & 7.71588450988794 & 52.1139819639091 & 1.1857935967074 \tabularnewline
11 & 3840 & 3831.72266861021 & 8.03484587035678 & -4.76280715776995 & 0.189702617412001 \tabularnewline
12 & 3625 & 3757.1124901657 & 6.00336095656343 & -46.2922161369861 & -1.24785559547408 \tabularnewline
13 & 4000 & 3826.43311386561 & 1.19051804046319 & 98.0383173475228 & 1.21823560157543 \tabularnewline
14 & 3915 & 3915.05948832229 & 3.01908750253466 & -78.5121365454688 & 1.22504670692601 \tabularnewline
15 & 4200 & 3997.88253711824 & 5.83587005945717 & 135.931168937367 & 1.06715933138907 \tabularnewline
16 & 3900 & 3978.68476032893 & 5.03399037148718 & -56.6694772927243 & -0.352046062638954 \tabularnewline
17 & 4140 & 4035.35423250311 & 6.38761832971817 & 56.8817518367282 & 0.755050737617969 \tabularnewline
18 & 3945 & 3993.38744227894 & 5.33942270124118 & -2.41245134163116 & -0.72171472648387 \tabularnewline
19 & 3735 & 3943.78101887095 & 4.30761051057763 & -155.81938413736 & -0.828343188082648 \tabularnewline
20 & 3970 & 3916.11750582796 & 3.76217521529791 & 84.910175257594 & -0.484370944112234 \tabularnewline
21 & 3745 & 3867.90812477197 & 2.92820364764486 & -72.2912637589292 & -0.78939233035939 \tabularnewline
22 & 4140 & 3941.28767781411 & 4.00787694779584 & 129.952855023645 & 1.07163908453872 \tabularnewline
23 & 3840 & 3911.22057671724 & 3.52739517623774 & -37.8870787850365 & -0.518927005914856 \tabularnewline
24 & 3570 & 3817.94390392447 & 2.67456785077298 & -152.50280736811 & -1.4800753875362 \tabularnewline
25 & 4085 & 3878.69184455086 & 1.42512786047841 & 145.588284564838 & 0.961539047618774 \tabularnewline
26 & 3865 & 3919.96253992133 & 1.8018116340243 & -92.3921852070899 & 0.5928273555201 \tabularnewline
27 & 4280 & 4006.40520371836 & 3.65247158633176 & 199.205214119785 & 1.20140773683817 \tabularnewline
28 & 4280 & 4143.23970796015 & 6.69797040878509 & 18.1708527993453 & 1.91951444960756 \tabularnewline
29 & 4240 & 4169.17563503719 & 7.08677012531471 & 53.1967556890855 & 0.283914404412746 \tabularnewline
30 & 4065 & 4133.09366239586 & 6.3426966797976 & -27.7110004102407 & -0.647395927674757 \tabularnewline
31 & 4060 & 4154.37597184446 & 6.56637561827763 & -108.519539271047 & 0.226066149367431 \tabularnewline
32 & 4265 & 4162.23924602513 & 6.58385360753615 & 101.524986633013 & 0.0197180402187332 \tabularnewline
33 & 4085 & 4172.17125488318 & 6.62562248555326 & -90.373017592839 & 0.0510344538726507 \tabularnewline
34 & 4450 & 4217.80665970769 & 7.07403001232306 & 194.798659169097 & 0.595484238842496 \tabularnewline
35 & 4195 & 4219.07371687294 & 7.01829412352457 & -18.4905617451282 & -0.0887598795511357 \tabularnewline
36 & 4160 & 4267.05676488347 & 7.20763269436802 & -146.737312961218 & 0.629154004138561 \tabularnewline
37 & 4580 & 4349.56328728303 & 6.70966946465841 & 155.573021006813 & 1.19079682965437 \tabularnewline
38 & 4130 & 4341.8516061494 & 6.61628636440617 & -198.205846229957 & -0.217780827815648 \tabularnewline
39 & 4645 & 4403.19327411504 & 7.44867883842863 & 192.25040735103 & 0.799908481580837 \tabularnewline
40 & 4375 & 4399.52689123778 & 7.25453289595196 & -14.4807862485189 & -0.16283469694367 \tabularnewline
41 & 4480 & 4406.88027730436 & 7.25616737346245 & 73.0289778645901 & 0.00146854786857454 \tabularnewline
42 & 4485 & 4449.59333947484 & 7.77683585109817 & 2.36221620955692 & 0.533238956279511 \tabularnewline
43 & 4465 & 4500.62280031111 & 8.33673059228589 & -76.3510598004483 & 0.655690260881504 \tabularnewline
44 & 4515 & 4483.22407940921 & 8.03862512349932 & 56.1621959442399 & -0.391961851552988 \tabularnewline
45 & 4465 & 4515.95113601171 & 8.2971933598008 & -74.4347484833645 & 0.377004790262942 \tabularnewline
46 & 4790 & 4551.93076728681 & 8.55287596111832 & 211.666459760836 & 0.423363264543802 \tabularnewline
47 & 4270 & 4481.35362114205 & 7.98069270938422 & -135.659772165605 & -1.21178987713797 \tabularnewline
48 & 4495 & 4543.45421386349 & 8.17740759195633 & -100.510073328434 & 0.831949863332028 \tabularnewline
49 & 4490 & 4485.99203599285 & 8.23154897808614 & 67.8049228393359 & -1.01946383226956 \tabularnewline
50 & 4275 & 4488.15103097126 & 8.19739591215255 & -207.401424292149 & -0.0921347913708803 \tabularnewline
51 & 4695 & 4495.93455275042 & 8.1926258859694 & 199.44641353862 & -0.00614690701089863 \tabularnewline
52 & 4630 & 4553.98409748362 & 8.88538700028329 & 30.3980166279902 & 0.738893247696421 \tabularnewline
53 & 4560 & 4549.06079373583 & 8.69411422954367 & 23.6757157038914 & -0.206299598413475 \tabularnewline
54 & 4665 & 4597.97450118011 & 9.20757792019781 & 29.5289590458536 & 0.606363774423097 \tabularnewline
55 & 4725 & 4674.42432157619 & 9.97797264553142 & -12.656213440494 & 1.02072240390085 \tabularnewline
56 & 4840 & 4729.4232211525 & 10.4387724503543 & 67.9916519510368 & 0.686417521314267 \tabularnewline
57 & 4745 & 4773.18089813632 & 10.7413515545402 & -59.8184478387822 & 0.509323747114912 \tabularnewline
58 & 4940 & 4759.03354825059 & 10.5479676214026 & 204.663730173204 & -0.381025897297502 \tabularnewline
59 & 4635 & 4772.91846961105 & 10.5679004395905 & -141.10391512282 & 0.0511492226058295 \tabularnewline
60 & 4910 & 4850.4319388201 & 10.8059086916457 & -4.56972001670736 & 1.02866403165115 \tabularnewline
61 & 4690 & 4790.02536550071 & 10.6815678521856 & -31.5735273918785 & -1.09735272469553 \tabularnewline
62 & 4585 & 4793.73944334763 & 10.6444458449294 & -202.144860727334 & -0.105930888644338 \tabularnewline
63 & 5065 & 4831.99230316875 & 10.9020115768589 & 207.353473680876 & 0.413905057845348 \tabularnewline
64 & 4705 & 4788.85516130379 & 10.2845916771881 & -33.9590057889485 & -0.807532849898458 \tabularnewline
65 & 4580 & 4720.61790461203 & 9.35838369065077 & -67.8314608760997 & -1.17875040932016 \tabularnewline
66 & 4660 & 4700.10501801864 & 9.0238714862526 & -12.2075326928408 & -0.451406305981761 \tabularnewline
67 & 4510 & 4650.54878254041 & 8.4250974237562 & -85.4560120753427 & -0.890285618754408 \tabularnewline
68 & 4885 & 4709.75798197336 & 8.88989859138412 & 127.229581259629 & 0.774868833076073 \tabularnewline
69 & 4765 & 4756.60785532107 & 9.19511481373908 & -27.627201308142 & 0.580622370178042 \tabularnewline
70 & 4700 & 4682.47551410629 & 8.6292453731394 & 96.7965553284956 & -1.27637858493354 \tabularnewline
71 & 4590 & 4702.76318359533 & 8.69094694116852 & -123.878331473502 & 0.178770515095441 \tabularnewline
72 & 4655 & 4683.30545852153 & 8.58714436109726 & -1.40965236845186 & -0.432212106386254 \tabularnewline
73 & 4845 & 4748.44176292041 & 8.75518853673165 & 42.512176982296 & 0.868258106975528 \tabularnewline
74 & 4495 & 4742.05562007795 & 8.67700194989408 & -232.728250548479 & -0.230503774695896 \tabularnewline
75 & 5020 & 4757.39248788895 & 8.72979996007161 & 256.383039970888 & 0.100435991275051 \tabularnewline
76 & 4535 & 4685.92401091035 & 7.95495122686873 & -76.3828976914033 & -1.20565911477876 \tabularnewline
77 & 4700 & 4704.36536063 & 8.06178816304613 & -14.1289451157426 & 0.158050994228792 \tabularnewline
78 & 4435 & 4617.47365070792 & 7.12278652551744 & -93.6040193613939 & -1.43803941816525 \tabularnewline
79 & 4285 & 4537.40043867687 & 6.32392173350715 & -170.336552799262 & -1.32665023809721 \tabularnewline
80 & 4780 & 4572.56178268863 & 6.56176356551414 & 180.174324374457 & 0.440269154740131 \tabularnewline
81 & 4450 & 4535.47024172936 & 6.24601351999607 & -44.0616252610156 & -0.667966645293633 \tabularnewline
82 & 4875 & 4617.57394769194 & 6.70976255950521 & 185.299290020482 & 1.16230331284822 \tabularnewline
83 & 4670 & 4686.9259218358 & 7.0168895678911 & -76.593038171167 & 0.960659432503069 \tabularnewline
84 & 4325 & 4585.38447761041 & 6.60148391425881 & -156.854732292641 & -1.66581801595541 \tabularnewline
85 & 5000 & 4699.30175048517 & 6.98498399846316 & 198.450525891214 & 1.64497653254427 \tabularnewline
86 & 4675 & 4781.16817512322 & 7.36083246872366 & -177.024564649617 & 1.14115621278935 \tabularnewline
87 & 4950 & 4751.20925873248 & 7.10063692993256 & 233.804194890448 & -0.56505048086905 \tabularnewline
88 & 4790 & 4787.33233234803 & 7.34336968806766 & -24.4388086704158 & 0.438245846793909 \tabularnewline
89 & 4785 & 4781.17509132863 & 7.22300836741586 & 16.4419067228959 & -0.204152318009021 \tabularnewline
90 & 4520 & 4716.33026644882 & 6.58942782838085 & -128.734952728784 & -1.09359085216492 \tabularnewline
91 & 4735 & 4780.19733380191 & 7.06192345815503 & -99.1555556073754 & 0.872362538171847 \tabularnewline
92 & 5055 & 4819.57924267068 & 7.30371860962301 & 204.856347894647 & 0.493700599561587 \tabularnewline
93 & 4640 & 4795.75712619728 & 7.09862821026686 & -126.235400310129 & -0.476413350086079 \tabularnewline
94 & 5045 & 4825.34380999717 & 7.22504737977775 & 198.28240458239 & 0.344623143186729 \tabularnewline
95 & 4710 & 4809.58534999397 & 7.11801790578046 & -77.7093761783348 & -0.352463522067859 \tabularnewline
96 & 4650 & 4830.44816191707 & 7.17188992433914 & -193.538855776083 & 0.210817266930104 \tabularnewline
97 & 4915 & 4808.17671673428 & 7.05817254841019 & 134.82819746838 & -0.450988222807783 \tabularnewline
98 & 4260 & 4680.09649591094 & 6.40021694713792 & -292.194959718004 & -2.06135431336247 \tabularnewline
99 & 4505 & 4534.46739005758 & 5.44561488371271 & 113.550736013823 & -2.30835775795951 \tabularnewline
100 & 4575 & 4538.32099328525 & 5.43386463663289 & 38.1713338107493 & -0.0241200393015078 \tabularnewline
101 & 4785 & 4610.23085047984 & 5.95875335167952 & 112.452321078201 & 1.00793720363307 \tabularnewline
102 & 4610 & 4673.52563977121 & 6.41003407333792 & -117.410756515033 & 0.871555513889959 \tabularnewline
103 & 5220 & 4904.32884416289 & 8.0851557847587 & 104.062597053812 & 3.42092181270307 \tabularnewline
104 & 5285 & 4988.50181930726 & 8.60468791175713 & 224.514813404296 & 1.16284887912595 \tabularnewline
105 & 4870 & 5008.51534455345 & 8.67385410058358 & -149.33627183207 & 0.174667242499435 \tabularnewline
106 & 5440 & 5090.16999675194 & 9.05663979271563 & 280.483644004705 & 1.11853603142049 \tabularnewline
107 & 4615 & 4968.87800205101 & 8.47277334090425 & -229.878618186293 & -1.99888557235507 \tabularnewline
108 & 4645 & 4904.52731077961 & 8.18432528651697 & -190.231998644131 & -1.11665401551063 \tabularnewline
109 & 4845 & 4809.83767909028 & 7.77460516322638 & 132.919874895272 & -1.5753425453299 \tabularnewline
110 & 4780 & 4871.10916396469 & 8.02660098866662 & -141.758817048303 & 0.816706872429899 \tabularnewline
111 & 5005 & 4894.16333235856 & 8.11299509841289 & 96.6714563918795 & 0.228654263741819 \tabularnewline
112 & 4905 & 4909.6231868398 & 8.16160564062113 & -11.5292276086834 & 0.111594906084088 \tabularnewline
113 & 4630 & 4805.10036504261 & 7.36485533647389 & -69.1983108083781 & -1.71232184962499 \tabularnewline
114 & 4785 & 4868.69088648607 & 7.76392500947757 & -136.627005294823 & 0.855971219610596 \tabularnewline
115 & 5160 & 4953.92193391056 & 8.29012101614477 & 132.948960411835 & 1.18206187487103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298558&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]3655[/C][C]3655[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3390[/C][C]3540.9981510932[/C][C]-9.16126786762411[/C][C]-48.7221426425625[/C][C]-1.49662393602543[/C][/ROW]
[ROW][C]3[/C][C]4000[/C][C]3727.09998598869[/C][C]6.06373000605504[/C][C]121.797777896944[/C][C]2.37550433094227[/C][/ROW]
[ROW][C]4[/C][C]3810[/C][C]3776.85886658783[/C][C]8.65356413494005[/C][C]-5.62627401295498[/C][C]0.58917195560992[/C][/ROW]
[ROW][C]5[/C][C]3790[/C][C]3787.6430848097[/C][C]8.75056454773021[/C][C]0.31185087200953[/C][C]0.0304162512362876[/C][/ROW]
[ROW][C]6[/C][C]3790[/C][C]3790.79021852914[/C][C]8.54195345342649[/C][C]4.79500061445341[/C][C]-0.0821919978403404[/C][/ROW]
[ROW][C]7[/C][C]3350[/C][C]3624.89986161633[/C][C]2.89408162470009[/C][C]-97.7551834579426[/C][C]-2.59297078780385[/C][/ROW]
[ROW][C]8[/C][C]3900[/C][C]3713.00050106194[/C][C]5.40461284297023[/C][C]99.6149045121048[/C][C]1.27545559836107[/C][/ROW]
[ROW][C]9[/C][C]3725[/C][C]3727.05515766[/C][C]5.64340252000359[/C][C]-10.97512850866[/C][C]0.129982776920065[/C][/ROW]
[ROW][C]10[/C][C]3945[/C][C]3811.42988989154[/C][C]7.71588450988794[/C][C]52.1139819639091[/C][C]1.1857935967074[/C][/ROW]
[ROW][C]11[/C][C]3840[/C][C]3831.72266861021[/C][C]8.03484587035678[/C][C]-4.76280715776995[/C][C]0.189702617412001[/C][/ROW]
[ROW][C]12[/C][C]3625[/C][C]3757.1124901657[/C][C]6.00336095656343[/C][C]-46.2922161369861[/C][C]-1.24785559547408[/C][/ROW]
[ROW][C]13[/C][C]4000[/C][C]3826.43311386561[/C][C]1.19051804046319[/C][C]98.0383173475228[/C][C]1.21823560157543[/C][/ROW]
[ROW][C]14[/C][C]3915[/C][C]3915.05948832229[/C][C]3.01908750253466[/C][C]-78.5121365454688[/C][C]1.22504670692601[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]3997.88253711824[/C][C]5.83587005945717[/C][C]135.931168937367[/C][C]1.06715933138907[/C][/ROW]
[ROW][C]16[/C][C]3900[/C][C]3978.68476032893[/C][C]5.03399037148718[/C][C]-56.6694772927243[/C][C]-0.352046062638954[/C][/ROW]
[ROW][C]17[/C][C]4140[/C][C]4035.35423250311[/C][C]6.38761832971817[/C][C]56.8817518367282[/C][C]0.755050737617969[/C][/ROW]
[ROW][C]18[/C][C]3945[/C][C]3993.38744227894[/C][C]5.33942270124118[/C][C]-2.41245134163116[/C][C]-0.72171472648387[/C][/ROW]
[ROW][C]19[/C][C]3735[/C][C]3943.78101887095[/C][C]4.30761051057763[/C][C]-155.81938413736[/C][C]-0.828343188082648[/C][/ROW]
[ROW][C]20[/C][C]3970[/C][C]3916.11750582796[/C][C]3.76217521529791[/C][C]84.910175257594[/C][C]-0.484370944112234[/C][/ROW]
[ROW][C]21[/C][C]3745[/C][C]3867.90812477197[/C][C]2.92820364764486[/C][C]-72.2912637589292[/C][C]-0.78939233035939[/C][/ROW]
[ROW][C]22[/C][C]4140[/C][C]3941.28767781411[/C][C]4.00787694779584[/C][C]129.952855023645[/C][C]1.07163908453872[/C][/ROW]
[ROW][C]23[/C][C]3840[/C][C]3911.22057671724[/C][C]3.52739517623774[/C][C]-37.8870787850365[/C][C]-0.518927005914856[/C][/ROW]
[ROW][C]24[/C][C]3570[/C][C]3817.94390392447[/C][C]2.67456785077298[/C][C]-152.50280736811[/C][C]-1.4800753875362[/C][/ROW]
[ROW][C]25[/C][C]4085[/C][C]3878.69184455086[/C][C]1.42512786047841[/C][C]145.588284564838[/C][C]0.961539047618774[/C][/ROW]
[ROW][C]26[/C][C]3865[/C][C]3919.96253992133[/C][C]1.8018116340243[/C][C]-92.3921852070899[/C][C]0.5928273555201[/C][/ROW]
[ROW][C]27[/C][C]4280[/C][C]4006.40520371836[/C][C]3.65247158633176[/C][C]199.205214119785[/C][C]1.20140773683817[/C][/ROW]
[ROW][C]28[/C][C]4280[/C][C]4143.23970796015[/C][C]6.69797040878509[/C][C]18.1708527993453[/C][C]1.91951444960756[/C][/ROW]
[ROW][C]29[/C][C]4240[/C][C]4169.17563503719[/C][C]7.08677012531471[/C][C]53.1967556890855[/C][C]0.283914404412746[/C][/ROW]
[ROW][C]30[/C][C]4065[/C][C]4133.09366239586[/C][C]6.3426966797976[/C][C]-27.7110004102407[/C][C]-0.647395927674757[/C][/ROW]
[ROW][C]31[/C][C]4060[/C][C]4154.37597184446[/C][C]6.56637561827763[/C][C]-108.519539271047[/C][C]0.226066149367431[/C][/ROW]
[ROW][C]32[/C][C]4265[/C][C]4162.23924602513[/C][C]6.58385360753615[/C][C]101.524986633013[/C][C]0.0197180402187332[/C][/ROW]
[ROW][C]33[/C][C]4085[/C][C]4172.17125488318[/C][C]6.62562248555326[/C][C]-90.373017592839[/C][C]0.0510344538726507[/C][/ROW]
[ROW][C]34[/C][C]4450[/C][C]4217.80665970769[/C][C]7.07403001232306[/C][C]194.798659169097[/C][C]0.595484238842496[/C][/ROW]
[ROW][C]35[/C][C]4195[/C][C]4219.07371687294[/C][C]7.01829412352457[/C][C]-18.4905617451282[/C][C]-0.0887598795511357[/C][/ROW]
[ROW][C]36[/C][C]4160[/C][C]4267.05676488347[/C][C]7.20763269436802[/C][C]-146.737312961218[/C][C]0.629154004138561[/C][/ROW]
[ROW][C]37[/C][C]4580[/C][C]4349.56328728303[/C][C]6.70966946465841[/C][C]155.573021006813[/C][C]1.19079682965437[/C][/ROW]
[ROW][C]38[/C][C]4130[/C][C]4341.8516061494[/C][C]6.61628636440617[/C][C]-198.205846229957[/C][C]-0.217780827815648[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4403.19327411504[/C][C]7.44867883842863[/C][C]192.25040735103[/C][C]0.799908481580837[/C][/ROW]
[ROW][C]40[/C][C]4375[/C][C]4399.52689123778[/C][C]7.25453289595196[/C][C]-14.4807862485189[/C][C]-0.16283469694367[/C][/ROW]
[ROW][C]41[/C][C]4480[/C][C]4406.88027730436[/C][C]7.25616737346245[/C][C]73.0289778645901[/C][C]0.00146854786857454[/C][/ROW]
[ROW][C]42[/C][C]4485[/C][C]4449.59333947484[/C][C]7.77683585109817[/C][C]2.36221620955692[/C][C]0.533238956279511[/C][/ROW]
[ROW][C]43[/C][C]4465[/C][C]4500.62280031111[/C][C]8.33673059228589[/C][C]-76.3510598004483[/C][C]0.655690260881504[/C][/ROW]
[ROW][C]44[/C][C]4515[/C][C]4483.22407940921[/C][C]8.03862512349932[/C][C]56.1621959442399[/C][C]-0.391961851552988[/C][/ROW]
[ROW][C]45[/C][C]4465[/C][C]4515.95113601171[/C][C]8.2971933598008[/C][C]-74.4347484833645[/C][C]0.377004790262942[/C][/ROW]
[ROW][C]46[/C][C]4790[/C][C]4551.93076728681[/C][C]8.55287596111832[/C][C]211.666459760836[/C][C]0.423363264543802[/C][/ROW]
[ROW][C]47[/C][C]4270[/C][C]4481.35362114205[/C][C]7.98069270938422[/C][C]-135.659772165605[/C][C]-1.21178987713797[/C][/ROW]
[ROW][C]48[/C][C]4495[/C][C]4543.45421386349[/C][C]8.17740759195633[/C][C]-100.510073328434[/C][C]0.831949863332028[/C][/ROW]
[ROW][C]49[/C][C]4490[/C][C]4485.99203599285[/C][C]8.23154897808614[/C][C]67.8049228393359[/C][C]-1.01946383226956[/C][/ROW]
[ROW][C]50[/C][C]4275[/C][C]4488.15103097126[/C][C]8.19739591215255[/C][C]-207.401424292149[/C][C]-0.0921347913708803[/C][/ROW]
[ROW][C]51[/C][C]4695[/C][C]4495.93455275042[/C][C]8.1926258859694[/C][C]199.44641353862[/C][C]-0.00614690701089863[/C][/ROW]
[ROW][C]52[/C][C]4630[/C][C]4553.98409748362[/C][C]8.88538700028329[/C][C]30.3980166279902[/C][C]0.738893247696421[/C][/ROW]
[ROW][C]53[/C][C]4560[/C][C]4549.06079373583[/C][C]8.69411422954367[/C][C]23.6757157038914[/C][C]-0.206299598413475[/C][/ROW]
[ROW][C]54[/C][C]4665[/C][C]4597.97450118011[/C][C]9.20757792019781[/C][C]29.5289590458536[/C][C]0.606363774423097[/C][/ROW]
[ROW][C]55[/C][C]4725[/C][C]4674.42432157619[/C][C]9.97797264553142[/C][C]-12.656213440494[/C][C]1.02072240390085[/C][/ROW]
[ROW][C]56[/C][C]4840[/C][C]4729.4232211525[/C][C]10.4387724503543[/C][C]67.9916519510368[/C][C]0.686417521314267[/C][/ROW]
[ROW][C]57[/C][C]4745[/C][C]4773.18089813632[/C][C]10.7413515545402[/C][C]-59.8184478387822[/C][C]0.509323747114912[/C][/ROW]
[ROW][C]58[/C][C]4940[/C][C]4759.03354825059[/C][C]10.5479676214026[/C][C]204.663730173204[/C][C]-0.381025897297502[/C][/ROW]
[ROW][C]59[/C][C]4635[/C][C]4772.91846961105[/C][C]10.5679004395905[/C][C]-141.10391512282[/C][C]0.0511492226058295[/C][/ROW]
[ROW][C]60[/C][C]4910[/C][C]4850.4319388201[/C][C]10.8059086916457[/C][C]-4.56972001670736[/C][C]1.02866403165115[/C][/ROW]
[ROW][C]61[/C][C]4690[/C][C]4790.02536550071[/C][C]10.6815678521856[/C][C]-31.5735273918785[/C][C]-1.09735272469553[/C][/ROW]
[ROW][C]62[/C][C]4585[/C][C]4793.73944334763[/C][C]10.6444458449294[/C][C]-202.144860727334[/C][C]-0.105930888644338[/C][/ROW]
[ROW][C]63[/C][C]5065[/C][C]4831.99230316875[/C][C]10.9020115768589[/C][C]207.353473680876[/C][C]0.413905057845348[/C][/ROW]
[ROW][C]64[/C][C]4705[/C][C]4788.85516130379[/C][C]10.2845916771881[/C][C]-33.9590057889485[/C][C]-0.807532849898458[/C][/ROW]
[ROW][C]65[/C][C]4580[/C][C]4720.61790461203[/C][C]9.35838369065077[/C][C]-67.8314608760997[/C][C]-1.17875040932016[/C][/ROW]
[ROW][C]66[/C][C]4660[/C][C]4700.10501801864[/C][C]9.0238714862526[/C][C]-12.2075326928408[/C][C]-0.451406305981761[/C][/ROW]
[ROW][C]67[/C][C]4510[/C][C]4650.54878254041[/C][C]8.4250974237562[/C][C]-85.4560120753427[/C][C]-0.890285618754408[/C][/ROW]
[ROW][C]68[/C][C]4885[/C][C]4709.75798197336[/C][C]8.88989859138412[/C][C]127.229581259629[/C][C]0.774868833076073[/C][/ROW]
[ROW][C]69[/C][C]4765[/C][C]4756.60785532107[/C][C]9.19511481373908[/C][C]-27.627201308142[/C][C]0.580622370178042[/C][/ROW]
[ROW][C]70[/C][C]4700[/C][C]4682.47551410629[/C][C]8.6292453731394[/C][C]96.7965553284956[/C][C]-1.27637858493354[/C][/ROW]
[ROW][C]71[/C][C]4590[/C][C]4702.76318359533[/C][C]8.69094694116852[/C][C]-123.878331473502[/C][C]0.178770515095441[/C][/ROW]
[ROW][C]72[/C][C]4655[/C][C]4683.30545852153[/C][C]8.58714436109726[/C][C]-1.40965236845186[/C][C]-0.432212106386254[/C][/ROW]
[ROW][C]73[/C][C]4845[/C][C]4748.44176292041[/C][C]8.75518853673165[/C][C]42.512176982296[/C][C]0.868258106975528[/C][/ROW]
[ROW][C]74[/C][C]4495[/C][C]4742.05562007795[/C][C]8.67700194989408[/C][C]-232.728250548479[/C][C]-0.230503774695896[/C][/ROW]
[ROW][C]75[/C][C]5020[/C][C]4757.39248788895[/C][C]8.72979996007161[/C][C]256.383039970888[/C][C]0.100435991275051[/C][/ROW]
[ROW][C]76[/C][C]4535[/C][C]4685.92401091035[/C][C]7.95495122686873[/C][C]-76.3828976914033[/C][C]-1.20565911477876[/C][/ROW]
[ROW][C]77[/C][C]4700[/C][C]4704.36536063[/C][C]8.06178816304613[/C][C]-14.1289451157426[/C][C]0.158050994228792[/C][/ROW]
[ROW][C]78[/C][C]4435[/C][C]4617.47365070792[/C][C]7.12278652551744[/C][C]-93.6040193613939[/C][C]-1.43803941816525[/C][/ROW]
[ROW][C]79[/C][C]4285[/C][C]4537.40043867687[/C][C]6.32392173350715[/C][C]-170.336552799262[/C][C]-1.32665023809721[/C][/ROW]
[ROW][C]80[/C][C]4780[/C][C]4572.56178268863[/C][C]6.56176356551414[/C][C]180.174324374457[/C][C]0.440269154740131[/C][/ROW]
[ROW][C]81[/C][C]4450[/C][C]4535.47024172936[/C][C]6.24601351999607[/C][C]-44.0616252610156[/C][C]-0.667966645293633[/C][/ROW]
[ROW][C]82[/C][C]4875[/C][C]4617.57394769194[/C][C]6.70976255950521[/C][C]185.299290020482[/C][C]1.16230331284822[/C][/ROW]
[ROW][C]83[/C][C]4670[/C][C]4686.9259218358[/C][C]7.0168895678911[/C][C]-76.593038171167[/C][C]0.960659432503069[/C][/ROW]
[ROW][C]84[/C][C]4325[/C][C]4585.38447761041[/C][C]6.60148391425881[/C][C]-156.854732292641[/C][C]-1.66581801595541[/C][/ROW]
[ROW][C]85[/C][C]5000[/C][C]4699.30175048517[/C][C]6.98498399846316[/C][C]198.450525891214[/C][C]1.64497653254427[/C][/ROW]
[ROW][C]86[/C][C]4675[/C][C]4781.16817512322[/C][C]7.36083246872366[/C][C]-177.024564649617[/C][C]1.14115621278935[/C][/ROW]
[ROW][C]87[/C][C]4950[/C][C]4751.20925873248[/C][C]7.10063692993256[/C][C]233.804194890448[/C][C]-0.56505048086905[/C][/ROW]
[ROW][C]88[/C][C]4790[/C][C]4787.33233234803[/C][C]7.34336968806766[/C][C]-24.4388086704158[/C][C]0.438245846793909[/C][/ROW]
[ROW][C]89[/C][C]4785[/C][C]4781.17509132863[/C][C]7.22300836741586[/C][C]16.4419067228959[/C][C]-0.204152318009021[/C][/ROW]
[ROW][C]90[/C][C]4520[/C][C]4716.33026644882[/C][C]6.58942782838085[/C][C]-128.734952728784[/C][C]-1.09359085216492[/C][/ROW]
[ROW][C]91[/C][C]4735[/C][C]4780.19733380191[/C][C]7.06192345815503[/C][C]-99.1555556073754[/C][C]0.872362538171847[/C][/ROW]
[ROW][C]92[/C][C]5055[/C][C]4819.57924267068[/C][C]7.30371860962301[/C][C]204.856347894647[/C][C]0.493700599561587[/C][/ROW]
[ROW][C]93[/C][C]4640[/C][C]4795.75712619728[/C][C]7.09862821026686[/C][C]-126.235400310129[/C][C]-0.476413350086079[/C][/ROW]
[ROW][C]94[/C][C]5045[/C][C]4825.34380999717[/C][C]7.22504737977775[/C][C]198.28240458239[/C][C]0.344623143186729[/C][/ROW]
[ROW][C]95[/C][C]4710[/C][C]4809.58534999397[/C][C]7.11801790578046[/C][C]-77.7093761783348[/C][C]-0.352463522067859[/C][/ROW]
[ROW][C]96[/C][C]4650[/C][C]4830.44816191707[/C][C]7.17188992433914[/C][C]-193.538855776083[/C][C]0.210817266930104[/C][/ROW]
[ROW][C]97[/C][C]4915[/C][C]4808.17671673428[/C][C]7.05817254841019[/C][C]134.82819746838[/C][C]-0.450988222807783[/C][/ROW]
[ROW][C]98[/C][C]4260[/C][C]4680.09649591094[/C][C]6.40021694713792[/C][C]-292.194959718004[/C][C]-2.06135431336247[/C][/ROW]
[ROW][C]99[/C][C]4505[/C][C]4534.46739005758[/C][C]5.44561488371271[/C][C]113.550736013823[/C][C]-2.30835775795951[/C][/ROW]
[ROW][C]100[/C][C]4575[/C][C]4538.32099328525[/C][C]5.43386463663289[/C][C]38.1713338107493[/C][C]-0.0241200393015078[/C][/ROW]
[ROW][C]101[/C][C]4785[/C][C]4610.23085047984[/C][C]5.95875335167952[/C][C]112.452321078201[/C][C]1.00793720363307[/C][/ROW]
[ROW][C]102[/C][C]4610[/C][C]4673.52563977121[/C][C]6.41003407333792[/C][C]-117.410756515033[/C][C]0.871555513889959[/C][/ROW]
[ROW][C]103[/C][C]5220[/C][C]4904.32884416289[/C][C]8.0851557847587[/C][C]104.062597053812[/C][C]3.42092181270307[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]4988.50181930726[/C][C]8.60468791175713[/C][C]224.514813404296[/C][C]1.16284887912595[/C][/ROW]
[ROW][C]105[/C][C]4870[/C][C]5008.51534455345[/C][C]8.67385410058358[/C][C]-149.33627183207[/C][C]0.174667242499435[/C][/ROW]
[ROW][C]106[/C][C]5440[/C][C]5090.16999675194[/C][C]9.05663979271563[/C][C]280.483644004705[/C][C]1.11853603142049[/C][/ROW]
[ROW][C]107[/C][C]4615[/C][C]4968.87800205101[/C][C]8.47277334090425[/C][C]-229.878618186293[/C][C]-1.99888557235507[/C][/ROW]
[ROW][C]108[/C][C]4645[/C][C]4904.52731077961[/C][C]8.18432528651697[/C][C]-190.231998644131[/C][C]-1.11665401551063[/C][/ROW]
[ROW][C]109[/C][C]4845[/C][C]4809.83767909028[/C][C]7.77460516322638[/C][C]132.919874895272[/C][C]-1.5753425453299[/C][/ROW]
[ROW][C]110[/C][C]4780[/C][C]4871.10916396469[/C][C]8.02660098866662[/C][C]-141.758817048303[/C][C]0.816706872429899[/C][/ROW]
[ROW][C]111[/C][C]5005[/C][C]4894.16333235856[/C][C]8.11299509841289[/C][C]96.6714563918795[/C][C]0.228654263741819[/C][/ROW]
[ROW][C]112[/C][C]4905[/C][C]4909.6231868398[/C][C]8.16160564062113[/C][C]-11.5292276086834[/C][C]0.111594906084088[/C][/ROW]
[ROW][C]113[/C][C]4630[/C][C]4805.10036504261[/C][C]7.36485533647389[/C][C]-69.1983108083781[/C][C]-1.71232184962499[/C][/ROW]
[ROW][C]114[/C][C]4785[/C][C]4868.69088648607[/C][C]7.76392500947757[/C][C]-136.627005294823[/C][C]0.855971219610596[/C][/ROW]
[ROW][C]115[/C][C]5160[/C][C]4953.92193391056[/C][C]8.29012101614477[/C][C]132.948960411835[/C][C]1.18206187487103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298558&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
136553655000
233903540.9981510932-9.16126786762411-48.7221426425625-1.49662393602543
340003727.099985988696.06373000605504121.7977778969442.37550433094227
438103776.858866587838.65356413494005-5.626274012954980.58917195560992
537903787.64308480978.750564547730210.311850872009530.0304162512362876
637903790.790218529148.541953453426494.79500061445341-0.0821919978403404
733503624.899861616332.89408162470009-97.7551834579426-2.59297078780385
839003713.000501061945.4046128429702399.61490451210481.27545559836107
937253727.055157665.64340252000359-10.975128508660.129982776920065
1039453811.429889891547.7158845098879452.11398196390911.1857935967074
1138403831.722668610218.03484587035678-4.762807157769950.189702617412001
1236253757.11249016576.00336095656343-46.2922161369861-1.24785559547408
1340003826.433113865611.1905180404631998.03831734752281.21823560157543
1439153915.059488322293.01908750253466-78.51213654546881.22504670692601
1542003997.882537118245.83587005945717135.9311689373671.06715933138907
1639003978.684760328935.03399037148718-56.6694772927243-0.352046062638954
1741404035.354232503116.3876183297181756.88175183672820.755050737617969
1839453993.387442278945.33942270124118-2.41245134163116-0.72171472648387
1937353943.781018870954.30761051057763-155.81938413736-0.828343188082648
2039703916.117505827963.7621752152979184.910175257594-0.484370944112234
2137453867.908124771972.92820364764486-72.2912637589292-0.78939233035939
2241403941.287677814114.00787694779584129.9528550236451.07163908453872
2338403911.220576717243.52739517623774-37.8870787850365-0.518927005914856
2435703817.943903924472.67456785077298-152.50280736811-1.4800753875362
2540853878.691844550861.42512786047841145.5882845648380.961539047618774
2638653919.962539921331.8018116340243-92.39218520708990.5928273555201
2742804006.405203718363.65247158633176199.2052141197851.20140773683817
2842804143.239707960156.6979704087850918.17085279934531.91951444960756
2942404169.175635037197.0867701253147153.19675568908550.283914404412746
3040654133.093662395866.3426966797976-27.7110004102407-0.647395927674757
3140604154.375971844466.56637561827763-108.5195392710470.226066149367431
3242654162.239246025136.58385360753615101.5249866330130.0197180402187332
3340854172.171254883186.62562248555326-90.3730175928390.0510344538726507
3444504217.806659707697.07403001232306194.7986591690970.595484238842496
3541954219.073716872947.01829412352457-18.4905617451282-0.0887598795511357
3641604267.056764883477.20763269436802-146.7373129612180.629154004138561
3745804349.563287283036.70966946465841155.5730210068131.19079682965437
3841304341.85160614946.61628636440617-198.205846229957-0.217780827815648
3946454403.193274115047.44867883842863192.250407351030.799908481580837
4043754399.526891237787.25453289595196-14.4807862485189-0.16283469694367
4144804406.880277304367.2561673734624573.02897786459010.00146854786857454
4244854449.593339474847.776835851098172.362216209556920.533238956279511
4344654500.622800311118.33673059228589-76.35105980044830.655690260881504
4445154483.224079409218.0386251234993256.1621959442399-0.391961851552988
4544654515.951136011718.2971933598008-74.43474848336450.377004790262942
4647904551.930767286818.55287596111832211.6664597608360.423363264543802
4742704481.353621142057.98069270938422-135.659772165605-1.21178987713797
4844954543.454213863498.17740759195633-100.5100733284340.831949863332028
4944904485.992035992858.2315489780861467.8049228393359-1.01946383226956
5042754488.151030971268.19739591215255-207.401424292149-0.0921347913708803
5146954495.934552750428.1926258859694199.44641353862-0.00614690701089863
5246304553.984097483628.8853870002832930.39801662799020.738893247696421
5345604549.060793735838.6941142295436723.6757157038914-0.206299598413475
5446654597.974501180119.2075779201978129.52895904585360.606363774423097
5547254674.424321576199.97797264553142-12.6562134404941.02072240390085
5648404729.423221152510.438772450354367.99165195103680.686417521314267
5747454773.1808981363210.7413515545402-59.81844783878220.509323747114912
5849404759.0335482505910.5479676214026204.663730173204-0.381025897297502
5946354772.9184696110510.5679004395905-141.103915122820.0511492226058295
6049104850.431938820110.8059086916457-4.569720016707361.02866403165115
6146904790.0253655007110.6815678521856-31.5735273918785-1.09735272469553
6245854793.7394433476310.6444458449294-202.144860727334-0.105930888644338
6350654831.9923031687510.9020115768589207.3534736808760.413905057845348
6447054788.8551613037910.2845916771881-33.9590057889485-0.807532849898458
6545804720.617904612039.35838369065077-67.8314608760997-1.17875040932016
6646604700.105018018649.0238714862526-12.2075326928408-0.451406305981761
6745104650.548782540418.4250974237562-85.4560120753427-0.890285618754408
6848854709.757981973368.88989859138412127.2295812596290.774868833076073
6947654756.607855321079.19511481373908-27.6272013081420.580622370178042
7047004682.475514106298.629245373139496.7965553284956-1.27637858493354
7145904702.763183595338.69094694116852-123.8783314735020.178770515095441
7246554683.305458521538.58714436109726-1.40965236845186-0.432212106386254
7348454748.441762920418.7551885367316542.5121769822960.868258106975528
7444954742.055620077958.67700194989408-232.728250548479-0.230503774695896
7550204757.392487888958.72979996007161256.3830399708880.100435991275051
7645354685.924010910357.95495122686873-76.3828976914033-1.20565911477876
7747004704.365360638.06178816304613-14.12894511574260.158050994228792
7844354617.473650707927.12278652551744-93.6040193613939-1.43803941816525
7942854537.400438676876.32392173350715-170.336552799262-1.32665023809721
8047804572.561782688636.56176356551414180.1743243744570.440269154740131
8144504535.470241729366.24601351999607-44.0616252610156-0.667966645293633
8248754617.573947691946.70976255950521185.2992900204821.16230331284822
8346704686.92592183587.0168895678911-76.5930381711670.960659432503069
8443254585.384477610416.60148391425881-156.854732292641-1.66581801595541
8550004699.301750485176.98498399846316198.4505258912141.64497653254427
8646754781.168175123227.36083246872366-177.0245646496171.14115621278935
8749504751.209258732487.10063692993256233.804194890448-0.56505048086905
8847904787.332332348037.34336968806766-24.43880867041580.438245846793909
8947854781.175091328637.2230083674158616.4419067228959-0.204152318009021
9045204716.330266448826.58942782838085-128.734952728784-1.09359085216492
9147354780.197333801917.06192345815503-99.15555560737540.872362538171847
9250554819.579242670687.30371860962301204.8563478946470.493700599561587
9346404795.757126197287.09862821026686-126.235400310129-0.476413350086079
9450454825.343809997177.22504737977775198.282404582390.344623143186729
9547104809.585349993977.11801790578046-77.7093761783348-0.352463522067859
9646504830.448161917077.17188992433914-193.5388557760830.210817266930104
9749154808.176716734287.05817254841019134.82819746838-0.450988222807783
9842604680.096495910946.40021694713792-292.194959718004-2.06135431336247
9945054534.467390057585.44561488371271113.550736013823-2.30835775795951
10045754538.320993285255.4338646366328938.1713338107493-0.0241200393015078
10147854610.230850479845.95875335167952112.4523210782011.00793720363307
10246104673.525639771216.41003407333792-117.4107565150330.871555513889959
10352204904.328844162898.0851557847587104.0625970538123.42092181270307
10452854988.501819307268.60468791175713224.5148134042961.16284887912595
10548705008.515344553458.67385410058358-149.336271832070.174667242499435
10654405090.169996751949.05663979271563280.4836440047051.11853603142049
10746154968.878002051018.47277334090425-229.878618186293-1.99888557235507
10846454904.527310779618.18432528651697-190.231998644131-1.11665401551063
10948454809.837679090287.77460516322638132.919874895272-1.5753425453299
11047804871.109163964698.02660098866662-141.7588170483030.816706872429899
11150054894.163332358568.1129950984128996.67145639187950.228654263741819
11249054909.62318683988.16160564062113-11.52922760868340.111594906084088
11346304805.100365042617.36485533647389-69.1983108083781-1.71232184962499
11447854868.690886486077.76392500947757-136.6270052948230.855971219610596
11551604953.921933910568.29012101614477132.9489604118351.18206187487103







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15179.454932013954948.01733247815231.437599535805
24812.351672621674959.58424719963-147.232574577967
35414.765116776074971.15116192112443.613954854947
44747.928218347954982.71807664261-234.789858294661
54829.234299148214994.2849913641-165.050692215891
65057.628091246575005.8519060855951.7761851609727
74892.59310393135017.41882080708-124.825716875778
85109.110873792155028.9857355285780.1251382635828
95049.916194447125040.552650250069.36354419705819
104844.881772591655052.11956497155-207.237792379904
114916.259159107985063.68647969304-147.427320585064
125285.500927331435075.25339441453210.247532916898
135318.257908671825086.82030913602231.437599535805
144951.154649279545098.38722385751-147.232574577967
155553.568093433945109.954138579443.613954854947
164886.731195005835121.52105330049-234.789858294661
174968.037275806095133.08796802198-165.050692215891
185196.431067904445144.6548827434751.7761851609726

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5179.45493201395 & 4948.01733247815 & 231.437599535805 \tabularnewline
2 & 4812.35167262167 & 4959.58424719963 & -147.232574577967 \tabularnewline
3 & 5414.76511677607 & 4971.15116192112 & 443.613954854947 \tabularnewline
4 & 4747.92821834795 & 4982.71807664261 & -234.789858294661 \tabularnewline
5 & 4829.23429914821 & 4994.2849913641 & -165.050692215891 \tabularnewline
6 & 5057.62809124657 & 5005.85190608559 & 51.7761851609727 \tabularnewline
7 & 4892.5931039313 & 5017.41882080708 & -124.825716875778 \tabularnewline
8 & 5109.11087379215 & 5028.98573552857 & 80.1251382635828 \tabularnewline
9 & 5049.91619444712 & 5040.55265025006 & 9.36354419705819 \tabularnewline
10 & 4844.88177259165 & 5052.11956497155 & -207.237792379904 \tabularnewline
11 & 4916.25915910798 & 5063.68647969304 & -147.427320585064 \tabularnewline
12 & 5285.50092733143 & 5075.25339441453 & 210.247532916898 \tabularnewline
13 & 5318.25790867182 & 5086.82030913602 & 231.437599535805 \tabularnewline
14 & 4951.15464927954 & 5098.38722385751 & -147.232574577967 \tabularnewline
15 & 5553.56809343394 & 5109.954138579 & 443.613954854947 \tabularnewline
16 & 4886.73119500583 & 5121.52105330049 & -234.789858294661 \tabularnewline
17 & 4968.03727580609 & 5133.08796802198 & -165.050692215891 \tabularnewline
18 & 5196.43106790444 & 5144.65488274347 & 51.7761851609726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298558&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]5179.45493201395[/C][C]4948.01733247815[/C][C]231.437599535805[/C][/ROW]
[ROW][C]2[/C][C]4812.35167262167[/C][C]4959.58424719963[/C][C]-147.232574577967[/C][/ROW]
[ROW][C]3[/C][C]5414.76511677607[/C][C]4971.15116192112[/C][C]443.613954854947[/C][/ROW]
[ROW][C]4[/C][C]4747.92821834795[/C][C]4982.71807664261[/C][C]-234.789858294661[/C][/ROW]
[ROW][C]5[/C][C]4829.23429914821[/C][C]4994.2849913641[/C][C]-165.050692215891[/C][/ROW]
[ROW][C]6[/C][C]5057.62809124657[/C][C]5005.85190608559[/C][C]51.7761851609727[/C][/ROW]
[ROW][C]7[/C][C]4892.5931039313[/C][C]5017.41882080708[/C][C]-124.825716875778[/C][/ROW]
[ROW][C]8[/C][C]5109.11087379215[/C][C]5028.98573552857[/C][C]80.1251382635828[/C][/ROW]
[ROW][C]9[/C][C]5049.91619444712[/C][C]5040.55265025006[/C][C]9.36354419705819[/C][/ROW]
[ROW][C]10[/C][C]4844.88177259165[/C][C]5052.11956497155[/C][C]-207.237792379904[/C][/ROW]
[ROW][C]11[/C][C]4916.25915910798[/C][C]5063.68647969304[/C][C]-147.427320585064[/C][/ROW]
[ROW][C]12[/C][C]5285.50092733143[/C][C]5075.25339441453[/C][C]210.247532916898[/C][/ROW]
[ROW][C]13[/C][C]5318.25790867182[/C][C]5086.82030913602[/C][C]231.437599535805[/C][/ROW]
[ROW][C]14[/C][C]4951.15464927954[/C][C]5098.38722385751[/C][C]-147.232574577967[/C][/ROW]
[ROW][C]15[/C][C]5553.56809343394[/C][C]5109.954138579[/C][C]443.613954854947[/C][/ROW]
[ROW][C]16[/C][C]4886.73119500583[/C][C]5121.52105330049[/C][C]-234.789858294661[/C][/ROW]
[ROW][C]17[/C][C]4968.03727580609[/C][C]5133.08796802198[/C][C]-165.050692215891[/C][/ROW]
[ROW][C]18[/C][C]5196.43106790444[/C][C]5144.65488274347[/C][C]51.7761851609726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298558&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298558&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
15179.454932013954948.01733247815231.437599535805
24812.351672621674959.58424719963-147.232574577967
35414.765116776074971.15116192112443.613954854947
44747.928218347954982.71807664261-234.789858294661
54829.234299148214994.2849913641-165.050692215891
65057.628091246575005.8519060855951.7761851609727
74892.59310393135017.41882080708-124.825716875778
85109.110873792155028.9857355285780.1251382635828
95049.916194447125040.552650250069.36354419705819
104844.881772591655052.11956497155-207.237792379904
114916.259159107985063.68647969304-147.427320585064
125285.500927331435075.25339441453210.247532916898
135318.257908671825086.82030913602231.437599535805
144951.154649279545098.38722385751-147.232574577967
155553.568093433945109.954138579443.613954854947
164886.731195005835121.52105330049-234.789858294661
174968.037275806095133.08796802198-165.050692215891
185196.431067904445144.6548827434751.7761851609726



Parameters (Session):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 18 ; 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')