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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 computationSat, 17 Dec 2016 10:30:24 +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/17/t1481967056g5nlq21u01t4lom.htm/, Retrieved Fri, 01 Nov 2024 03:28:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300635, Retrieved Fri, 01 Nov 2024 03:28:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-17 09:30:24] [57f1f1af0ba442a9c0352eeef9ded060] [Current]
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Dataseries X:
4393.9
4248
4346.2
4351.7
4424.4
4468.4
4519.1
4518.2
4574.5
4509.6
4337.9
4441.8
4414.1
4465.9
4426
4518.8
4606.3
4647.4
4650.8
4650.2
4720.1
4655
4520.8
4617.3
4488.1
4527.4
4618.3
4642.8
4667.3
4640.6
4716.9
4719.4
4817.3
4764.5
4514.1
4625
4617.7
4361.3
4474.9
4623.8
4692
4672.1
4721.5
4784.6
4858.7
4813.3
4628.2
4710.4
4698.4
4631
4727.4
4719.9
4890.6
4839.9
4867.5
4898.3
4675.7
4981.9
4771.1
4827.8
4685
4646.1
4815
4911.8
4958.4
5019.4
5024.3
5035.8
5082.4
5179.2
4963.2
4951.3
4876.4
4812.1
5004.1
5093.8
5063.1
5078.6
5251.5
5263.2
5280.5
5386.1
5227.3
5149.5
5128.6
5087.7
5188.5
5084
5258.6
5348.9
5280
5374.2
5458.4
5315
5294.5
5341.4
5068
5156.9
5184.7
5280.7
5339
5377.7
5388.6
5443.6
5528.7
5539
5292
5351.5
5163.7
5105
5248.1
5370.9
5484.9
5510.7
5484.9
5567.8
5275.6




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=300635&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=300635&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300635&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
14393.94393.9000
242484359.65235110047-2.17343659554694-58.9117385762458-1.7849689271686
34346.24341.86050999648-3.8403796052279516.1623757341549-0.472367286652765
44351.74341.04902647048-3.555573203401438.283170049071250.0957112761067133
54424.44365.24738553109-1.4028179435472934.55401614685790.968533435237428
64468.44399.158501158230.86313172958988635.03283495628441.31977092708012
74519.14439.611638349933.0244756271626739.02206765548861.54179876087262
84518.24470.215259475954.3489685760187618.87980524031521.10065555679162
94574.54505.98503405275.7157008921284734.70348842888921.27279358635038
104509.64515.9003270585.88485316659067-10.87566448079280.171729755545667
114337.94471.660331445563.98603292760348-78.6984249992488-2.06261712279895
124441.84455.316729783343.254060567230128.94575112512744-0.840263749922301
134414.14444.219578911443.91781004128107-11.3122705126686-0.740686970830514
144465.94463.140943678024.07381432043515-13.32018502165470.634409146915988
1544264456.326684559743.68197337592326-20.3950298922257-0.405529216745529
164518.84476.430307490874.3705763256498527.7035361142740.607028932628631
174606.34514.395293966755.7235660839964460.79208569543191.28427815894141
184647.44557.594358007147.083803930770453.64806643821991.48254207803017
194650.84589.716125663827.8913740282702736.16910465968221.01554558973141
204650.24615.818937131998.4177660947382715.88134589390750.750861086301673
214720.14641.119462221258.8613552531282261.59857827888490.703404343590753
2246554647.858929019658.810507330896179.34616550963506-0.089022844268724
234520.84637.815565334428.41461076459595-97.2550888502811-0.795520934204925
244617.34631.263945034178.191770803003691.94471602373579-0.637676728266749
254488.14609.45098925828.24998525733642-87.9462836288983-1.34044844737858
264527.44593.787922534938.03679036730101-41.0846692586027-1.0198427978051
274618.34611.359204690148.23147143689435-2.497211559496020.38533190434861
284642.84628.488835007758.462645418020745.740253559550220.353182935114405
294667.34639.420378811788.5297450336303325.4902193704530.0987055180876148
304640.64639.330623036838.304698730534699.7552695805958-0.35004697394025
314716.94658.344255188738.5633346436129547.8227673159780.441551249529563
324719.44680.178152708968.855326783415925.72577298496380.553723705070396
334817.34705.702321429139.1864910313630994.45749061957440.701526806746741
344764.54722.954893574879.3284123828322633.18005459106770.341578324427734
354514.14700.232491611448.85534898860044-152.638323271482-1.36433274813287
3646254675.823485651558.49574175053803-15.7378449613615-1.42559218651163
374617.74679.064505626078.46325866765449-55.754159409687-0.227599603749476
384361.34619.951556938147.82537048875288-187.852147849648-2.87813749424706
394474.94578.199374333347.09448769544753-52.8937650829979-2.06077628706543
404623.84582.569262315447.0442802621089943.9510349837698-0.111805366014015
4146924606.871237406467.3890119914880567.94166956748210.708226981495355
424672.14632.337859704377.7497377197316621.63247765149180.747201375248518
434721.54655.269453319528.038432012481250.84841300559890.633225993426952
444784.64691.791828784358.5399962707295163.65907091602671.19792385594012
454858.74719.49080539238.8455761260722119.4364425340920.811096683379602
464813.34736.005933774628.9535463530173169.32414853384580.326331061982009
474628.24746.742448832258.97486534146742-120.406094746470.0761721234002062
484710.44742.326114351058.84497397320113-17.8556273545272-0.574222500569508
494698.44734.627275086198.71073274417304-18.7961484245678-0.710732500400637
5046314750.361302546588.77685068001543-126.6945028081140.299312162487998
514727.44767.313783327248.87532947916211-48.3239998890380.344238195882442
524719.94758.824089063278.62668057602142-21.2561658956933-0.725338910497746
534890.64782.77612859778.8654966591173192.28360830859620.639200505465205
544839.94806.072411869249.094417783719419.15414607644290.603867696480136
554867.54824.657849958619.240723637245233.13474698367810.399303674979821
564898.34839.597444803929.3233189456545652.83495083947510.24110346994379
574675.74781.504015627318.42822985524351-35.96354998033-2.86605922949423
584981.94804.998952981698.60720251087347161.2112956220190.642998982142582
594771.14831.180415021038.79010513278354-78.45837165429990.752234418726198
604827.84842.436347346558.81251625567956-17.22253093394920.105753187231161
6146854818.578797214788.53755764762147-99.303894640053-1.40091391416415
624646.14808.735520716368.37146706839919-143.448146858763-0.784691886949534
6348154822.798790197658.43085031334565-13.69305179199830.241417456485117
644911.84860.002984135588.7708922946024522.19598670936261.21451515777782
654958.44876.046002919828.8634253076016174.89310270973110.306504894432978
665019.44914.183304903619.2449797927613975.1522257222651.2357142286281
675024.34942.137291981459.4848163745266462.88280743584490.79229649415922
685035.84952.858539701229.4999187714184881.66172180040370.0525558154362989
695082.45003.019851673299.9615125059655337.11136201991621.73433313022647
705179.25024.0610822878110.0762212525273143.577453332990.473929963557984
714963.25036.3862325131510.0972536025395-75.53988478070520.0963985474492846
724951.35022.948178236669.89619130609713-46.9740961855323-1.00993290295566
734876.45013.82939311699.74037741509264-117.499132936355-0.815556757076684
744812.15007.804830197369.60610958037021-179.229863736709-0.674388985274575
755004.15021.188468725399.64123054916371-21.01822401330760.160999491480456
765093.85045.369167665059.7887244327698933.36573259490180.617848080716573
775063.15049.018505546769.7226637027915220.4304390057036-0.260596419754109
785078.65049.178743996059.6173261286860139.3134134714483-0.406186731707974
795251.55090.921716710979.9678366778909127.2775118427321.36729047211537
805263.25133.1788188361810.307230070952496.45433939738611.37765352756799
815280.55174.3002910359410.612577117665674.06899969083081.31791707041008
825386.15202.6369366380210.7757905135226164.9315564528870.759613145461104
835227.35232.6101505722210.9394888840374-25.42373391940960.823972146847494
845149.55232.6110763029910.8519148981422-71.6378915694727-0.469808809459504
855128.65240.5314289588110.8290695833708-108.857399676184-0.125856780902166
865087.75256.4613157334310.8696958051563-174.1004155200660.218636381718228
875188.55257.4833528274310.7868240918782-58.7033699904892-0.421179734325209
8850845215.2598490356310.3130576980452-76.0579154741329-2.26310058443534
895258.65220.7902148799710.268365901435342.7836277728615-0.204019457695029
905348.95257.4701167850610.520139649448863.96048320982611.12706309032101
9152805254.0617525414110.388129198561240.4425596702901-0.595098628698724
925374.25271.8830955821710.456591027718694.56160224619970.318110831333852
935458.45311.5627801095310.7135301028611116.2835869208791.25275420037143
9453155289.5334839768310.441651142993859.7661371920506-1.40570564070563
955294.55296.0825785381310.411151776682.50100642190698-0.167288816026054
965341.45329.3051391713210.5819115468625-11.85377389837380.980795484509522
9750685304.3256010002410.3209055129043-198.99796397628-1.52855598321778
985156.95306.5232742224210.2605630417165-141.105983402472-0.34882119099357
995184.75289.1465083119910.0479484450155-75.515790973168-1.18520731875972
1005280.75308.1217421641810.1195094612293-36.75256491396220.382406440100218
10153395318.4182643675310.120975260220420.39688296808770.00757842530563099
1025377.75323.6013531359810.079444527607959.2552403309861-0.211445349942204
1035388.65338.2776677203610.117956753431645.5181121721540.196996357932421
1045443.65351.8453202165310.146229092752588.14475533563770.147999804536696
1055528.75368.6870773520710.199153800425152.9961379274020.287595096854997
10655395403.1883150529210.3829402698607110.3087797932521.04495106835757
10752925389.8093861232410.210975927901-72.8475229920227-1.02248706571142
1085351.55379.6468926464510.0684718337971-6.73325510127896-0.876964626707017
1095163.75376.305428535219.97612098178368-198.512139242089-0.577124922128635
11051055346.521055424349.70065323127821-199.762517266969-1.71014039612568
1115248.15342.215937168769.60144171738242-79.4211171603852-0.601911772689491
1125370.95361.850797369879.67451661584862-1.46778469817220.430890217283077
1135484.95394.817556786979.8481046247024665.68144247469620.999949991243736
1145510.75421.370457853649.9740226580312271.82979890073150.717228179323415
1155484.95437.6855382622610.021673462979840.56825681233390.272396306857326
1165567.85457.9687536299310.097480706953799.06650603676570.441147123640704
1175275.65390.127990487329.5376506310119-32.684124859085-3.3533924147242

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 4393.9 & 4393.9 & 0 & 0 & 0 \tabularnewline
2 & 4248 & 4359.65235110047 & -2.17343659554694 & -58.9117385762458 & -1.7849689271686 \tabularnewline
3 & 4346.2 & 4341.86050999648 & -3.84037960522795 & 16.1623757341549 & -0.472367286652765 \tabularnewline
4 & 4351.7 & 4341.04902647048 & -3.55557320340143 & 8.28317004907125 & 0.0957112761067133 \tabularnewline
5 & 4424.4 & 4365.24738553109 & -1.40281794354729 & 34.5540161468579 & 0.968533435237428 \tabularnewline
6 & 4468.4 & 4399.15850115823 & 0.863131729589886 & 35.0328349562844 & 1.31977092708012 \tabularnewline
7 & 4519.1 & 4439.61163834993 & 3.02447562716267 & 39.0220676554886 & 1.54179876087262 \tabularnewline
8 & 4518.2 & 4470.21525947595 & 4.34896857601876 & 18.8798052403152 & 1.10065555679162 \tabularnewline
9 & 4574.5 & 4505.9850340527 & 5.71570089212847 & 34.7034884288892 & 1.27279358635038 \tabularnewline
10 & 4509.6 & 4515.900327058 & 5.88485316659067 & -10.8756644807928 & 0.171729755545667 \tabularnewline
11 & 4337.9 & 4471.66033144556 & 3.98603292760348 & -78.6984249992488 & -2.06261712279895 \tabularnewline
12 & 4441.8 & 4455.31672978334 & 3.25406056723012 & 8.94575112512744 & -0.840263749922301 \tabularnewline
13 & 4414.1 & 4444.21957891144 & 3.91781004128107 & -11.3122705126686 & -0.740686970830514 \tabularnewline
14 & 4465.9 & 4463.14094367802 & 4.07381432043515 & -13.3201850216547 & 0.634409146915988 \tabularnewline
15 & 4426 & 4456.32668455974 & 3.68197337592326 & -20.3950298922257 & -0.405529216745529 \tabularnewline
16 & 4518.8 & 4476.43030749087 & 4.37057632564985 & 27.703536114274 & 0.607028932628631 \tabularnewline
17 & 4606.3 & 4514.39529396675 & 5.72356608399644 & 60.7920856954319 & 1.28427815894141 \tabularnewline
18 & 4647.4 & 4557.59435800714 & 7.0838039307704 & 53.6480664382199 & 1.48254207803017 \tabularnewline
19 & 4650.8 & 4589.71612566382 & 7.89137402827027 & 36.1691046596822 & 1.01554558973141 \tabularnewline
20 & 4650.2 & 4615.81893713199 & 8.41776609473827 & 15.8813458939075 & 0.750861086301673 \tabularnewline
21 & 4720.1 & 4641.11946222125 & 8.86135525312822 & 61.5985782788849 & 0.703404343590753 \tabularnewline
22 & 4655 & 4647.85892901965 & 8.81050733089617 & 9.34616550963506 & -0.089022844268724 \tabularnewline
23 & 4520.8 & 4637.81556533442 & 8.41461076459595 & -97.2550888502811 & -0.795520934204925 \tabularnewline
24 & 4617.3 & 4631.26394503417 & 8.19177080300369 & 1.94471602373579 & -0.637676728266749 \tabularnewline
25 & 4488.1 & 4609.4509892582 & 8.24998525733642 & -87.9462836288983 & -1.34044844737858 \tabularnewline
26 & 4527.4 & 4593.78792253493 & 8.03679036730101 & -41.0846692586027 & -1.0198427978051 \tabularnewline
27 & 4618.3 & 4611.35920469014 & 8.23147143689435 & -2.49721155949602 & 0.38533190434861 \tabularnewline
28 & 4642.8 & 4628.48883500775 & 8.46264541802074 & 5.74025355955022 & 0.353182935114405 \tabularnewline
29 & 4667.3 & 4639.42037881178 & 8.52974503363033 & 25.490219370453 & 0.0987055180876148 \tabularnewline
30 & 4640.6 & 4639.33062303683 & 8.30469873053469 & 9.7552695805958 & -0.35004697394025 \tabularnewline
31 & 4716.9 & 4658.34425518873 & 8.56333464361295 & 47.822767315978 & 0.441551249529563 \tabularnewline
32 & 4719.4 & 4680.17815270896 & 8.8553267834159 & 25.7257729849638 & 0.553723705070396 \tabularnewline
33 & 4817.3 & 4705.70232142913 & 9.18649103136309 & 94.4574906195744 & 0.701526806746741 \tabularnewline
34 & 4764.5 & 4722.95489357487 & 9.32841238283226 & 33.1800545910677 & 0.341578324427734 \tabularnewline
35 & 4514.1 & 4700.23249161144 & 8.85534898860044 & -152.638323271482 & -1.36433274813287 \tabularnewline
36 & 4625 & 4675.82348565155 & 8.49574175053803 & -15.7378449613615 & -1.42559218651163 \tabularnewline
37 & 4617.7 & 4679.06450562607 & 8.46325866765449 & -55.754159409687 & -0.227599603749476 \tabularnewline
38 & 4361.3 & 4619.95155693814 & 7.82537048875288 & -187.852147849648 & -2.87813749424706 \tabularnewline
39 & 4474.9 & 4578.19937433334 & 7.09448769544753 & -52.8937650829979 & -2.06077628706543 \tabularnewline
40 & 4623.8 & 4582.56926231544 & 7.04428026210899 & 43.9510349837698 & -0.111805366014015 \tabularnewline
41 & 4692 & 4606.87123740646 & 7.38901199148805 & 67.9416695674821 & 0.708226981495355 \tabularnewline
42 & 4672.1 & 4632.33785970437 & 7.74973771973166 & 21.6324776514918 & 0.747201375248518 \tabularnewline
43 & 4721.5 & 4655.26945331952 & 8.0384320124812 & 50.8484130055989 & 0.633225993426952 \tabularnewline
44 & 4784.6 & 4691.79182878435 & 8.53999627072951 & 63.6590709160267 & 1.19792385594012 \tabularnewline
45 & 4858.7 & 4719.4908053923 & 8.8455761260722 & 119.436442534092 & 0.811096683379602 \tabularnewline
46 & 4813.3 & 4736.00593377462 & 8.95354635301731 & 69.3241485338458 & 0.326331061982009 \tabularnewline
47 & 4628.2 & 4746.74244883225 & 8.97486534146742 & -120.40609474647 & 0.0761721234002062 \tabularnewline
48 & 4710.4 & 4742.32611435105 & 8.84497397320113 & -17.8556273545272 & -0.574222500569508 \tabularnewline
49 & 4698.4 & 4734.62727508619 & 8.71073274417304 & -18.7961484245678 & -0.710732500400637 \tabularnewline
50 & 4631 & 4750.36130254658 & 8.77685068001543 & -126.694502808114 & 0.299312162487998 \tabularnewline
51 & 4727.4 & 4767.31378332724 & 8.87532947916211 & -48.323999889038 & 0.344238195882442 \tabularnewline
52 & 4719.9 & 4758.82408906327 & 8.62668057602142 & -21.2561658956933 & -0.725338910497746 \tabularnewline
53 & 4890.6 & 4782.7761285977 & 8.86549665911731 & 92.2836083085962 & 0.639200505465205 \tabularnewline
54 & 4839.9 & 4806.07241186924 & 9.0944177837194 & 19.1541460764429 & 0.603867696480136 \tabularnewline
55 & 4867.5 & 4824.65784995861 & 9.2407236372452 & 33.1347469836781 & 0.399303674979821 \tabularnewline
56 & 4898.3 & 4839.59744480392 & 9.32331894565456 & 52.8349508394751 & 0.24110346994379 \tabularnewline
57 & 4675.7 & 4781.50401562731 & 8.42822985524351 & -35.96354998033 & -2.86605922949423 \tabularnewline
58 & 4981.9 & 4804.99895298169 & 8.60720251087347 & 161.211295622019 & 0.642998982142582 \tabularnewline
59 & 4771.1 & 4831.18041502103 & 8.79010513278354 & -78.4583716542999 & 0.752234418726198 \tabularnewline
60 & 4827.8 & 4842.43634734655 & 8.81251625567956 & -17.2225309339492 & 0.105753187231161 \tabularnewline
61 & 4685 & 4818.57879721478 & 8.53755764762147 & -99.303894640053 & -1.40091391416415 \tabularnewline
62 & 4646.1 & 4808.73552071636 & 8.37146706839919 & -143.448146858763 & -0.784691886949534 \tabularnewline
63 & 4815 & 4822.79879019765 & 8.43085031334565 & -13.6930517919983 & 0.241417456485117 \tabularnewline
64 & 4911.8 & 4860.00298413558 & 8.77089229460245 & 22.1959867093626 & 1.21451515777782 \tabularnewline
65 & 4958.4 & 4876.04600291982 & 8.86342530760161 & 74.8931027097311 & 0.306504894432978 \tabularnewline
66 & 5019.4 & 4914.18330490361 & 9.24497979276139 & 75.152225722265 & 1.2357142286281 \tabularnewline
67 & 5024.3 & 4942.13729198145 & 9.48481637452664 & 62.8828074358449 & 0.79229649415922 \tabularnewline
68 & 5035.8 & 4952.85853970122 & 9.49991877141848 & 81.6617218004037 & 0.0525558154362989 \tabularnewline
69 & 5082.4 & 5003.01985167329 & 9.96151250596553 & 37.1113620199162 & 1.73433313022647 \tabularnewline
70 & 5179.2 & 5024.06108228781 & 10.0762212525273 & 143.57745333299 & 0.473929963557984 \tabularnewline
71 & 4963.2 & 5036.38623251315 & 10.0972536025395 & -75.5398847807052 & 0.0963985474492846 \tabularnewline
72 & 4951.3 & 5022.94817823666 & 9.89619130609713 & -46.9740961855323 & -1.00993290295566 \tabularnewline
73 & 4876.4 & 5013.8293931169 & 9.74037741509264 & -117.499132936355 & -0.815556757076684 \tabularnewline
74 & 4812.1 & 5007.80483019736 & 9.60610958037021 & -179.229863736709 & -0.674388985274575 \tabularnewline
75 & 5004.1 & 5021.18846872539 & 9.64123054916371 & -21.0182240133076 & 0.160999491480456 \tabularnewline
76 & 5093.8 & 5045.36916766505 & 9.78872443276989 & 33.3657325949018 & 0.617848080716573 \tabularnewline
77 & 5063.1 & 5049.01850554676 & 9.72266370279152 & 20.4304390057036 & -0.260596419754109 \tabularnewline
78 & 5078.6 & 5049.17874399605 & 9.61732612868601 & 39.3134134714483 & -0.406186731707974 \tabularnewline
79 & 5251.5 & 5090.92171671097 & 9.9678366778909 & 127.277511842732 & 1.36729047211537 \tabularnewline
80 & 5263.2 & 5133.17881883618 & 10.3072300709524 & 96.4543393973861 & 1.37765352756799 \tabularnewline
81 & 5280.5 & 5174.30029103594 & 10.6125771176656 & 74.0689996908308 & 1.31791707041008 \tabularnewline
82 & 5386.1 & 5202.63693663802 & 10.7757905135226 & 164.931556452887 & 0.759613145461104 \tabularnewline
83 & 5227.3 & 5232.61015057222 & 10.9394888840374 & -25.4237339194096 & 0.823972146847494 \tabularnewline
84 & 5149.5 & 5232.61107630299 & 10.8519148981422 & -71.6378915694727 & -0.469808809459504 \tabularnewline
85 & 5128.6 & 5240.53142895881 & 10.8290695833708 & -108.857399676184 & -0.125856780902166 \tabularnewline
86 & 5087.7 & 5256.46131573343 & 10.8696958051563 & -174.100415520066 & 0.218636381718228 \tabularnewline
87 & 5188.5 & 5257.48335282743 & 10.7868240918782 & -58.7033699904892 & -0.421179734325209 \tabularnewline
88 & 5084 & 5215.25984903563 & 10.3130576980452 & -76.0579154741329 & -2.26310058443534 \tabularnewline
89 & 5258.6 & 5220.79021487997 & 10.2683659014353 & 42.7836277728615 & -0.204019457695029 \tabularnewline
90 & 5348.9 & 5257.47011678506 & 10.5201396494488 & 63.9604832098261 & 1.12706309032101 \tabularnewline
91 & 5280 & 5254.06175254141 & 10.3881291985612 & 40.4425596702901 & -0.595098628698724 \tabularnewline
92 & 5374.2 & 5271.88309558217 & 10.4565910277186 & 94.5616022461997 & 0.318110831333852 \tabularnewline
93 & 5458.4 & 5311.56278010953 & 10.7135301028611 & 116.283586920879 & 1.25275420037143 \tabularnewline
94 & 5315 & 5289.53348397683 & 10.4416511429938 & 59.7661371920506 & -1.40570564070563 \tabularnewline
95 & 5294.5 & 5296.08257853813 & 10.41115177668 & 2.50100642190698 & -0.167288816026054 \tabularnewline
96 & 5341.4 & 5329.30513917132 & 10.5819115468625 & -11.8537738983738 & 0.980795484509522 \tabularnewline
97 & 5068 & 5304.32560100024 & 10.3209055129043 & -198.99796397628 & -1.52855598321778 \tabularnewline
98 & 5156.9 & 5306.52327422242 & 10.2605630417165 & -141.105983402472 & -0.34882119099357 \tabularnewline
99 & 5184.7 & 5289.14650831199 & 10.0479484450155 & -75.515790973168 & -1.18520731875972 \tabularnewline
100 & 5280.7 & 5308.12174216418 & 10.1195094612293 & -36.7525649139622 & 0.382406440100218 \tabularnewline
101 & 5339 & 5318.41826436753 & 10.1209752602204 & 20.3968829680877 & 0.00757842530563099 \tabularnewline
102 & 5377.7 & 5323.60135313598 & 10.0794445276079 & 59.2552403309861 & -0.211445349942204 \tabularnewline
103 & 5388.6 & 5338.27766772036 & 10.1179567534316 & 45.518112172154 & 0.196996357932421 \tabularnewline
104 & 5443.6 & 5351.84532021653 & 10.1462290927525 & 88.1447553356377 & 0.147999804536696 \tabularnewline
105 & 5528.7 & 5368.68707735207 & 10.199153800425 & 152.996137927402 & 0.287595096854997 \tabularnewline
106 & 5539 & 5403.18831505292 & 10.3829402698607 & 110.308779793252 & 1.04495106835757 \tabularnewline
107 & 5292 & 5389.80938612324 & 10.210975927901 & -72.8475229920227 & -1.02248706571142 \tabularnewline
108 & 5351.5 & 5379.64689264645 & 10.0684718337971 & -6.73325510127896 & -0.876964626707017 \tabularnewline
109 & 5163.7 & 5376.30542853521 & 9.97612098178368 & -198.512139242089 & -0.577124922128635 \tabularnewline
110 & 5105 & 5346.52105542434 & 9.70065323127821 & -199.762517266969 & -1.71014039612568 \tabularnewline
111 & 5248.1 & 5342.21593716876 & 9.60144171738242 & -79.4211171603852 & -0.601911772689491 \tabularnewline
112 & 5370.9 & 5361.85079736987 & 9.67451661584862 & -1.4677846981722 & 0.430890217283077 \tabularnewline
113 & 5484.9 & 5394.81755678697 & 9.84810462470246 & 65.6814424746962 & 0.999949991243736 \tabularnewline
114 & 5510.7 & 5421.37045785364 & 9.97402265803122 & 71.8297989007315 & 0.717228179323415 \tabularnewline
115 & 5484.9 & 5437.68553826226 & 10.0216734629798 & 40.5682568123339 & 0.272396306857326 \tabularnewline
116 & 5567.8 & 5457.96875362993 & 10.0974807069537 & 99.0665060367657 & 0.441147123640704 \tabularnewline
117 & 5275.6 & 5390.12799048732 & 9.5376506310119 & -32.684124859085 & -3.3533924147242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300635&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]4393.9[/C][C]4393.9[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]4248[/C][C]4359.65235110047[/C][C]-2.17343659554694[/C][C]-58.9117385762458[/C][C]-1.7849689271686[/C][/ROW]
[ROW][C]3[/C][C]4346.2[/C][C]4341.86050999648[/C][C]-3.84037960522795[/C][C]16.1623757341549[/C][C]-0.472367286652765[/C][/ROW]
[ROW][C]4[/C][C]4351.7[/C][C]4341.04902647048[/C][C]-3.55557320340143[/C][C]8.28317004907125[/C][C]0.0957112761067133[/C][/ROW]
[ROW][C]5[/C][C]4424.4[/C][C]4365.24738553109[/C][C]-1.40281794354729[/C][C]34.5540161468579[/C][C]0.968533435237428[/C][/ROW]
[ROW][C]6[/C][C]4468.4[/C][C]4399.15850115823[/C][C]0.863131729589886[/C][C]35.0328349562844[/C][C]1.31977092708012[/C][/ROW]
[ROW][C]7[/C][C]4519.1[/C][C]4439.61163834993[/C][C]3.02447562716267[/C][C]39.0220676554886[/C][C]1.54179876087262[/C][/ROW]
[ROW][C]8[/C][C]4518.2[/C][C]4470.21525947595[/C][C]4.34896857601876[/C][C]18.8798052403152[/C][C]1.10065555679162[/C][/ROW]
[ROW][C]9[/C][C]4574.5[/C][C]4505.9850340527[/C][C]5.71570089212847[/C][C]34.7034884288892[/C][C]1.27279358635038[/C][/ROW]
[ROW][C]10[/C][C]4509.6[/C][C]4515.900327058[/C][C]5.88485316659067[/C][C]-10.8756644807928[/C][C]0.171729755545667[/C][/ROW]
[ROW][C]11[/C][C]4337.9[/C][C]4471.66033144556[/C][C]3.98603292760348[/C][C]-78.6984249992488[/C][C]-2.06261712279895[/C][/ROW]
[ROW][C]12[/C][C]4441.8[/C][C]4455.31672978334[/C][C]3.25406056723012[/C][C]8.94575112512744[/C][C]-0.840263749922301[/C][/ROW]
[ROW][C]13[/C][C]4414.1[/C][C]4444.21957891144[/C][C]3.91781004128107[/C][C]-11.3122705126686[/C][C]-0.740686970830514[/C][/ROW]
[ROW][C]14[/C][C]4465.9[/C][C]4463.14094367802[/C][C]4.07381432043515[/C][C]-13.3201850216547[/C][C]0.634409146915988[/C][/ROW]
[ROW][C]15[/C][C]4426[/C][C]4456.32668455974[/C][C]3.68197337592326[/C][C]-20.3950298922257[/C][C]-0.405529216745529[/C][/ROW]
[ROW][C]16[/C][C]4518.8[/C][C]4476.43030749087[/C][C]4.37057632564985[/C][C]27.703536114274[/C][C]0.607028932628631[/C][/ROW]
[ROW][C]17[/C][C]4606.3[/C][C]4514.39529396675[/C][C]5.72356608399644[/C][C]60.7920856954319[/C][C]1.28427815894141[/C][/ROW]
[ROW][C]18[/C][C]4647.4[/C][C]4557.59435800714[/C][C]7.0838039307704[/C][C]53.6480664382199[/C][C]1.48254207803017[/C][/ROW]
[ROW][C]19[/C][C]4650.8[/C][C]4589.71612566382[/C][C]7.89137402827027[/C][C]36.1691046596822[/C][C]1.01554558973141[/C][/ROW]
[ROW][C]20[/C][C]4650.2[/C][C]4615.81893713199[/C][C]8.41776609473827[/C][C]15.8813458939075[/C][C]0.750861086301673[/C][/ROW]
[ROW][C]21[/C][C]4720.1[/C][C]4641.11946222125[/C][C]8.86135525312822[/C][C]61.5985782788849[/C][C]0.703404343590753[/C][/ROW]
[ROW][C]22[/C][C]4655[/C][C]4647.85892901965[/C][C]8.81050733089617[/C][C]9.34616550963506[/C][C]-0.089022844268724[/C][/ROW]
[ROW][C]23[/C][C]4520.8[/C][C]4637.81556533442[/C][C]8.41461076459595[/C][C]-97.2550888502811[/C][C]-0.795520934204925[/C][/ROW]
[ROW][C]24[/C][C]4617.3[/C][C]4631.26394503417[/C][C]8.19177080300369[/C][C]1.94471602373579[/C][C]-0.637676728266749[/C][/ROW]
[ROW][C]25[/C][C]4488.1[/C][C]4609.4509892582[/C][C]8.24998525733642[/C][C]-87.9462836288983[/C][C]-1.34044844737858[/C][/ROW]
[ROW][C]26[/C][C]4527.4[/C][C]4593.78792253493[/C][C]8.03679036730101[/C][C]-41.0846692586027[/C][C]-1.0198427978051[/C][/ROW]
[ROW][C]27[/C][C]4618.3[/C][C]4611.35920469014[/C][C]8.23147143689435[/C][C]-2.49721155949602[/C][C]0.38533190434861[/C][/ROW]
[ROW][C]28[/C][C]4642.8[/C][C]4628.48883500775[/C][C]8.46264541802074[/C][C]5.74025355955022[/C][C]0.353182935114405[/C][/ROW]
[ROW][C]29[/C][C]4667.3[/C][C]4639.42037881178[/C][C]8.52974503363033[/C][C]25.490219370453[/C][C]0.0987055180876148[/C][/ROW]
[ROW][C]30[/C][C]4640.6[/C][C]4639.33062303683[/C][C]8.30469873053469[/C][C]9.7552695805958[/C][C]-0.35004697394025[/C][/ROW]
[ROW][C]31[/C][C]4716.9[/C][C]4658.34425518873[/C][C]8.56333464361295[/C][C]47.822767315978[/C][C]0.441551249529563[/C][/ROW]
[ROW][C]32[/C][C]4719.4[/C][C]4680.17815270896[/C][C]8.8553267834159[/C][C]25.7257729849638[/C][C]0.553723705070396[/C][/ROW]
[ROW][C]33[/C][C]4817.3[/C][C]4705.70232142913[/C][C]9.18649103136309[/C][C]94.4574906195744[/C][C]0.701526806746741[/C][/ROW]
[ROW][C]34[/C][C]4764.5[/C][C]4722.95489357487[/C][C]9.32841238283226[/C][C]33.1800545910677[/C][C]0.341578324427734[/C][/ROW]
[ROW][C]35[/C][C]4514.1[/C][C]4700.23249161144[/C][C]8.85534898860044[/C][C]-152.638323271482[/C][C]-1.36433274813287[/C][/ROW]
[ROW][C]36[/C][C]4625[/C][C]4675.82348565155[/C][C]8.49574175053803[/C][C]-15.7378449613615[/C][C]-1.42559218651163[/C][/ROW]
[ROW][C]37[/C][C]4617.7[/C][C]4679.06450562607[/C][C]8.46325866765449[/C][C]-55.754159409687[/C][C]-0.227599603749476[/C][/ROW]
[ROW][C]38[/C][C]4361.3[/C][C]4619.95155693814[/C][C]7.82537048875288[/C][C]-187.852147849648[/C][C]-2.87813749424706[/C][/ROW]
[ROW][C]39[/C][C]4474.9[/C][C]4578.19937433334[/C][C]7.09448769544753[/C][C]-52.8937650829979[/C][C]-2.06077628706543[/C][/ROW]
[ROW][C]40[/C][C]4623.8[/C][C]4582.56926231544[/C][C]7.04428026210899[/C][C]43.9510349837698[/C][C]-0.111805366014015[/C][/ROW]
[ROW][C]41[/C][C]4692[/C][C]4606.87123740646[/C][C]7.38901199148805[/C][C]67.9416695674821[/C][C]0.708226981495355[/C][/ROW]
[ROW][C]42[/C][C]4672.1[/C][C]4632.33785970437[/C][C]7.74973771973166[/C][C]21.6324776514918[/C][C]0.747201375248518[/C][/ROW]
[ROW][C]43[/C][C]4721.5[/C][C]4655.26945331952[/C][C]8.0384320124812[/C][C]50.8484130055989[/C][C]0.633225993426952[/C][/ROW]
[ROW][C]44[/C][C]4784.6[/C][C]4691.79182878435[/C][C]8.53999627072951[/C][C]63.6590709160267[/C][C]1.19792385594012[/C][/ROW]
[ROW][C]45[/C][C]4858.7[/C][C]4719.4908053923[/C][C]8.8455761260722[/C][C]119.436442534092[/C][C]0.811096683379602[/C][/ROW]
[ROW][C]46[/C][C]4813.3[/C][C]4736.00593377462[/C][C]8.95354635301731[/C][C]69.3241485338458[/C][C]0.326331061982009[/C][/ROW]
[ROW][C]47[/C][C]4628.2[/C][C]4746.74244883225[/C][C]8.97486534146742[/C][C]-120.40609474647[/C][C]0.0761721234002062[/C][/ROW]
[ROW][C]48[/C][C]4710.4[/C][C]4742.32611435105[/C][C]8.84497397320113[/C][C]-17.8556273545272[/C][C]-0.574222500569508[/C][/ROW]
[ROW][C]49[/C][C]4698.4[/C][C]4734.62727508619[/C][C]8.71073274417304[/C][C]-18.7961484245678[/C][C]-0.710732500400637[/C][/ROW]
[ROW][C]50[/C][C]4631[/C][C]4750.36130254658[/C][C]8.77685068001543[/C][C]-126.694502808114[/C][C]0.299312162487998[/C][/ROW]
[ROW][C]51[/C][C]4727.4[/C][C]4767.31378332724[/C][C]8.87532947916211[/C][C]-48.323999889038[/C][C]0.344238195882442[/C][/ROW]
[ROW][C]52[/C][C]4719.9[/C][C]4758.82408906327[/C][C]8.62668057602142[/C][C]-21.2561658956933[/C][C]-0.725338910497746[/C][/ROW]
[ROW][C]53[/C][C]4890.6[/C][C]4782.7761285977[/C][C]8.86549665911731[/C][C]92.2836083085962[/C][C]0.639200505465205[/C][/ROW]
[ROW][C]54[/C][C]4839.9[/C][C]4806.07241186924[/C][C]9.0944177837194[/C][C]19.1541460764429[/C][C]0.603867696480136[/C][/ROW]
[ROW][C]55[/C][C]4867.5[/C][C]4824.65784995861[/C][C]9.2407236372452[/C][C]33.1347469836781[/C][C]0.399303674979821[/C][/ROW]
[ROW][C]56[/C][C]4898.3[/C][C]4839.59744480392[/C][C]9.32331894565456[/C][C]52.8349508394751[/C][C]0.24110346994379[/C][/ROW]
[ROW][C]57[/C][C]4675.7[/C][C]4781.50401562731[/C][C]8.42822985524351[/C][C]-35.96354998033[/C][C]-2.86605922949423[/C][/ROW]
[ROW][C]58[/C][C]4981.9[/C][C]4804.99895298169[/C][C]8.60720251087347[/C][C]161.211295622019[/C][C]0.642998982142582[/C][/ROW]
[ROW][C]59[/C][C]4771.1[/C][C]4831.18041502103[/C][C]8.79010513278354[/C][C]-78.4583716542999[/C][C]0.752234418726198[/C][/ROW]
[ROW][C]60[/C][C]4827.8[/C][C]4842.43634734655[/C][C]8.81251625567956[/C][C]-17.2225309339492[/C][C]0.105753187231161[/C][/ROW]
[ROW][C]61[/C][C]4685[/C][C]4818.57879721478[/C][C]8.53755764762147[/C][C]-99.303894640053[/C][C]-1.40091391416415[/C][/ROW]
[ROW][C]62[/C][C]4646.1[/C][C]4808.73552071636[/C][C]8.37146706839919[/C][C]-143.448146858763[/C][C]-0.784691886949534[/C][/ROW]
[ROW][C]63[/C][C]4815[/C][C]4822.79879019765[/C][C]8.43085031334565[/C][C]-13.6930517919983[/C][C]0.241417456485117[/C][/ROW]
[ROW][C]64[/C][C]4911.8[/C][C]4860.00298413558[/C][C]8.77089229460245[/C][C]22.1959867093626[/C][C]1.21451515777782[/C][/ROW]
[ROW][C]65[/C][C]4958.4[/C][C]4876.04600291982[/C][C]8.86342530760161[/C][C]74.8931027097311[/C][C]0.306504894432978[/C][/ROW]
[ROW][C]66[/C][C]5019.4[/C][C]4914.18330490361[/C][C]9.24497979276139[/C][C]75.152225722265[/C][C]1.2357142286281[/C][/ROW]
[ROW][C]67[/C][C]5024.3[/C][C]4942.13729198145[/C][C]9.48481637452664[/C][C]62.8828074358449[/C][C]0.79229649415922[/C][/ROW]
[ROW][C]68[/C][C]5035.8[/C][C]4952.85853970122[/C][C]9.49991877141848[/C][C]81.6617218004037[/C][C]0.0525558154362989[/C][/ROW]
[ROW][C]69[/C][C]5082.4[/C][C]5003.01985167329[/C][C]9.96151250596553[/C][C]37.1113620199162[/C][C]1.73433313022647[/C][/ROW]
[ROW][C]70[/C][C]5179.2[/C][C]5024.06108228781[/C][C]10.0762212525273[/C][C]143.57745333299[/C][C]0.473929963557984[/C][/ROW]
[ROW][C]71[/C][C]4963.2[/C][C]5036.38623251315[/C][C]10.0972536025395[/C][C]-75.5398847807052[/C][C]0.0963985474492846[/C][/ROW]
[ROW][C]72[/C][C]4951.3[/C][C]5022.94817823666[/C][C]9.89619130609713[/C][C]-46.9740961855323[/C][C]-1.00993290295566[/C][/ROW]
[ROW][C]73[/C][C]4876.4[/C][C]5013.8293931169[/C][C]9.74037741509264[/C][C]-117.499132936355[/C][C]-0.815556757076684[/C][/ROW]
[ROW][C]74[/C][C]4812.1[/C][C]5007.80483019736[/C][C]9.60610958037021[/C][C]-179.229863736709[/C][C]-0.674388985274575[/C][/ROW]
[ROW][C]75[/C][C]5004.1[/C][C]5021.18846872539[/C][C]9.64123054916371[/C][C]-21.0182240133076[/C][C]0.160999491480456[/C][/ROW]
[ROW][C]76[/C][C]5093.8[/C][C]5045.36916766505[/C][C]9.78872443276989[/C][C]33.3657325949018[/C][C]0.617848080716573[/C][/ROW]
[ROW][C]77[/C][C]5063.1[/C][C]5049.01850554676[/C][C]9.72266370279152[/C][C]20.4304390057036[/C][C]-0.260596419754109[/C][/ROW]
[ROW][C]78[/C][C]5078.6[/C][C]5049.17874399605[/C][C]9.61732612868601[/C][C]39.3134134714483[/C][C]-0.406186731707974[/C][/ROW]
[ROW][C]79[/C][C]5251.5[/C][C]5090.92171671097[/C][C]9.9678366778909[/C][C]127.277511842732[/C][C]1.36729047211537[/C][/ROW]
[ROW][C]80[/C][C]5263.2[/C][C]5133.17881883618[/C][C]10.3072300709524[/C][C]96.4543393973861[/C][C]1.37765352756799[/C][/ROW]
[ROW][C]81[/C][C]5280.5[/C][C]5174.30029103594[/C][C]10.6125771176656[/C][C]74.0689996908308[/C][C]1.31791707041008[/C][/ROW]
[ROW][C]82[/C][C]5386.1[/C][C]5202.63693663802[/C][C]10.7757905135226[/C][C]164.931556452887[/C][C]0.759613145461104[/C][/ROW]
[ROW][C]83[/C][C]5227.3[/C][C]5232.61015057222[/C][C]10.9394888840374[/C][C]-25.4237339194096[/C][C]0.823972146847494[/C][/ROW]
[ROW][C]84[/C][C]5149.5[/C][C]5232.61107630299[/C][C]10.8519148981422[/C][C]-71.6378915694727[/C][C]-0.469808809459504[/C][/ROW]
[ROW][C]85[/C][C]5128.6[/C][C]5240.53142895881[/C][C]10.8290695833708[/C][C]-108.857399676184[/C][C]-0.125856780902166[/C][/ROW]
[ROW][C]86[/C][C]5087.7[/C][C]5256.46131573343[/C][C]10.8696958051563[/C][C]-174.100415520066[/C][C]0.218636381718228[/C][/ROW]
[ROW][C]87[/C][C]5188.5[/C][C]5257.48335282743[/C][C]10.7868240918782[/C][C]-58.7033699904892[/C][C]-0.421179734325209[/C][/ROW]
[ROW][C]88[/C][C]5084[/C][C]5215.25984903563[/C][C]10.3130576980452[/C][C]-76.0579154741329[/C][C]-2.26310058443534[/C][/ROW]
[ROW][C]89[/C][C]5258.6[/C][C]5220.79021487997[/C][C]10.2683659014353[/C][C]42.7836277728615[/C][C]-0.204019457695029[/C][/ROW]
[ROW][C]90[/C][C]5348.9[/C][C]5257.47011678506[/C][C]10.5201396494488[/C][C]63.9604832098261[/C][C]1.12706309032101[/C][/ROW]
[ROW][C]91[/C][C]5280[/C][C]5254.06175254141[/C][C]10.3881291985612[/C][C]40.4425596702901[/C][C]-0.595098628698724[/C][/ROW]
[ROW][C]92[/C][C]5374.2[/C][C]5271.88309558217[/C][C]10.4565910277186[/C][C]94.5616022461997[/C][C]0.318110831333852[/C][/ROW]
[ROW][C]93[/C][C]5458.4[/C][C]5311.56278010953[/C][C]10.7135301028611[/C][C]116.283586920879[/C][C]1.25275420037143[/C][/ROW]
[ROW][C]94[/C][C]5315[/C][C]5289.53348397683[/C][C]10.4416511429938[/C][C]59.7661371920506[/C][C]-1.40570564070563[/C][/ROW]
[ROW][C]95[/C][C]5294.5[/C][C]5296.08257853813[/C][C]10.41115177668[/C][C]2.50100642190698[/C][C]-0.167288816026054[/C][/ROW]
[ROW][C]96[/C][C]5341.4[/C][C]5329.30513917132[/C][C]10.5819115468625[/C][C]-11.8537738983738[/C][C]0.980795484509522[/C][/ROW]
[ROW][C]97[/C][C]5068[/C][C]5304.32560100024[/C][C]10.3209055129043[/C][C]-198.99796397628[/C][C]-1.52855598321778[/C][/ROW]
[ROW][C]98[/C][C]5156.9[/C][C]5306.52327422242[/C][C]10.2605630417165[/C][C]-141.105983402472[/C][C]-0.34882119099357[/C][/ROW]
[ROW][C]99[/C][C]5184.7[/C][C]5289.14650831199[/C][C]10.0479484450155[/C][C]-75.515790973168[/C][C]-1.18520731875972[/C][/ROW]
[ROW][C]100[/C][C]5280.7[/C][C]5308.12174216418[/C][C]10.1195094612293[/C][C]-36.7525649139622[/C][C]0.382406440100218[/C][/ROW]
[ROW][C]101[/C][C]5339[/C][C]5318.41826436753[/C][C]10.1209752602204[/C][C]20.3968829680877[/C][C]0.00757842530563099[/C][/ROW]
[ROW][C]102[/C][C]5377.7[/C][C]5323.60135313598[/C][C]10.0794445276079[/C][C]59.2552403309861[/C][C]-0.211445349942204[/C][/ROW]
[ROW][C]103[/C][C]5388.6[/C][C]5338.27766772036[/C][C]10.1179567534316[/C][C]45.518112172154[/C][C]0.196996357932421[/C][/ROW]
[ROW][C]104[/C][C]5443.6[/C][C]5351.84532021653[/C][C]10.1462290927525[/C][C]88.1447553356377[/C][C]0.147999804536696[/C][/ROW]
[ROW][C]105[/C][C]5528.7[/C][C]5368.68707735207[/C][C]10.199153800425[/C][C]152.996137927402[/C][C]0.287595096854997[/C][/ROW]
[ROW][C]106[/C][C]5539[/C][C]5403.18831505292[/C][C]10.3829402698607[/C][C]110.308779793252[/C][C]1.04495106835757[/C][/ROW]
[ROW][C]107[/C][C]5292[/C][C]5389.80938612324[/C][C]10.210975927901[/C][C]-72.8475229920227[/C][C]-1.02248706571142[/C][/ROW]
[ROW][C]108[/C][C]5351.5[/C][C]5379.64689264645[/C][C]10.0684718337971[/C][C]-6.73325510127896[/C][C]-0.876964626707017[/C][/ROW]
[ROW][C]109[/C][C]5163.7[/C][C]5376.30542853521[/C][C]9.97612098178368[/C][C]-198.512139242089[/C][C]-0.577124922128635[/C][/ROW]
[ROW][C]110[/C][C]5105[/C][C]5346.52105542434[/C][C]9.70065323127821[/C][C]-199.762517266969[/C][C]-1.71014039612568[/C][/ROW]
[ROW][C]111[/C][C]5248.1[/C][C]5342.21593716876[/C][C]9.60144171738242[/C][C]-79.4211171603852[/C][C]-0.601911772689491[/C][/ROW]
[ROW][C]112[/C][C]5370.9[/C][C]5361.85079736987[/C][C]9.67451661584862[/C][C]-1.4677846981722[/C][C]0.430890217283077[/C][/ROW]
[ROW][C]113[/C][C]5484.9[/C][C]5394.81755678697[/C][C]9.84810462470246[/C][C]65.6814424746962[/C][C]0.999949991243736[/C][/ROW]
[ROW][C]114[/C][C]5510.7[/C][C]5421.37045785364[/C][C]9.97402265803122[/C][C]71.8297989007315[/C][C]0.717228179323415[/C][/ROW]
[ROW][C]115[/C][C]5484.9[/C][C]5437.68553826226[/C][C]10.0216734629798[/C][C]40.5682568123339[/C][C]0.272396306857326[/C][/ROW]
[ROW][C]116[/C][C]5567.8[/C][C]5457.96875362993[/C][C]10.0974807069537[/C][C]99.0665060367657[/C][C]0.441147123640704[/C][/ROW]
[ROW][C]117[/C][C]5275.6[/C][C]5390.12799048732[/C][C]9.5376506310119[/C][C]-32.684124859085[/C][C]-3.3533924147242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300635&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300635&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
14393.94393.9000
242484359.65235110047-2.17343659554694-58.9117385762458-1.7849689271686
34346.24341.86050999648-3.8403796052279516.1623757341549-0.472367286652765
44351.74341.04902647048-3.555573203401438.283170049071250.0957112761067133
54424.44365.24738553109-1.4028179435472934.55401614685790.968533435237428
64468.44399.158501158230.86313172958988635.03283495628441.31977092708012
74519.14439.611638349933.0244756271626739.02206765548861.54179876087262
84518.24470.215259475954.3489685760187618.87980524031521.10065555679162
94574.54505.98503405275.7157008921284734.70348842888921.27279358635038
104509.64515.9003270585.88485316659067-10.87566448079280.171729755545667
114337.94471.660331445563.98603292760348-78.6984249992488-2.06261712279895
124441.84455.316729783343.254060567230128.94575112512744-0.840263749922301
134414.14444.219578911443.91781004128107-11.3122705126686-0.740686970830514
144465.94463.140943678024.07381432043515-13.32018502165470.634409146915988
1544264456.326684559743.68197337592326-20.3950298922257-0.405529216745529
164518.84476.430307490874.3705763256498527.7035361142740.607028932628631
174606.34514.395293966755.7235660839964460.79208569543191.28427815894141
184647.44557.594358007147.083803930770453.64806643821991.48254207803017
194650.84589.716125663827.8913740282702736.16910465968221.01554558973141
204650.24615.818937131998.4177660947382715.88134589390750.750861086301673
214720.14641.119462221258.8613552531282261.59857827888490.703404343590753
2246554647.858929019658.810507330896179.34616550963506-0.089022844268724
234520.84637.815565334428.41461076459595-97.2550888502811-0.795520934204925
244617.34631.263945034178.191770803003691.94471602373579-0.637676728266749
254488.14609.45098925828.24998525733642-87.9462836288983-1.34044844737858
264527.44593.787922534938.03679036730101-41.0846692586027-1.0198427978051
274618.34611.359204690148.23147143689435-2.497211559496020.38533190434861
284642.84628.488835007758.462645418020745.740253559550220.353182935114405
294667.34639.420378811788.5297450336303325.4902193704530.0987055180876148
304640.64639.330623036838.304698730534699.7552695805958-0.35004697394025
314716.94658.344255188738.5633346436129547.8227673159780.441551249529563
324719.44680.178152708968.855326783415925.72577298496380.553723705070396
334817.34705.702321429139.1864910313630994.45749061957440.701526806746741
344764.54722.954893574879.3284123828322633.18005459106770.341578324427734
354514.14700.232491611448.85534898860044-152.638323271482-1.36433274813287
3646254675.823485651558.49574175053803-15.7378449613615-1.42559218651163
374617.74679.064505626078.46325866765449-55.754159409687-0.227599603749476
384361.34619.951556938147.82537048875288-187.852147849648-2.87813749424706
394474.94578.199374333347.09448769544753-52.8937650829979-2.06077628706543
404623.84582.569262315447.0442802621089943.9510349837698-0.111805366014015
4146924606.871237406467.3890119914880567.94166956748210.708226981495355
424672.14632.337859704377.7497377197316621.63247765149180.747201375248518
434721.54655.269453319528.038432012481250.84841300559890.633225993426952
444784.64691.791828784358.5399962707295163.65907091602671.19792385594012
454858.74719.49080539238.8455761260722119.4364425340920.811096683379602
464813.34736.005933774628.9535463530173169.32414853384580.326331061982009
474628.24746.742448832258.97486534146742-120.406094746470.0761721234002062
484710.44742.326114351058.84497397320113-17.8556273545272-0.574222500569508
494698.44734.627275086198.71073274417304-18.7961484245678-0.710732500400637
5046314750.361302546588.77685068001543-126.6945028081140.299312162487998
514727.44767.313783327248.87532947916211-48.3239998890380.344238195882442
524719.94758.824089063278.62668057602142-21.2561658956933-0.725338910497746
534890.64782.77612859778.8654966591173192.28360830859620.639200505465205
544839.94806.072411869249.094417783719419.15414607644290.603867696480136
554867.54824.657849958619.240723637245233.13474698367810.399303674979821
564898.34839.597444803929.3233189456545652.83495083947510.24110346994379
574675.74781.504015627318.42822985524351-35.96354998033-2.86605922949423
584981.94804.998952981698.60720251087347161.2112956220190.642998982142582
594771.14831.180415021038.79010513278354-78.45837165429990.752234418726198
604827.84842.436347346558.81251625567956-17.22253093394920.105753187231161
6146854818.578797214788.53755764762147-99.303894640053-1.40091391416415
624646.14808.735520716368.37146706839919-143.448146858763-0.784691886949534
6348154822.798790197658.43085031334565-13.69305179199830.241417456485117
644911.84860.002984135588.7708922946024522.19598670936261.21451515777782
654958.44876.046002919828.8634253076016174.89310270973110.306504894432978
665019.44914.183304903619.2449797927613975.1522257222651.2357142286281
675024.34942.137291981459.4848163745266462.88280743584490.79229649415922
685035.84952.858539701229.4999187714184881.66172180040370.0525558154362989
695082.45003.019851673299.9615125059655337.11136201991621.73433313022647
705179.25024.0610822878110.0762212525273143.577453332990.473929963557984
714963.25036.3862325131510.0972536025395-75.53988478070520.0963985474492846
724951.35022.948178236669.89619130609713-46.9740961855323-1.00993290295566
734876.45013.82939311699.74037741509264-117.499132936355-0.815556757076684
744812.15007.804830197369.60610958037021-179.229863736709-0.674388985274575
755004.15021.188468725399.64123054916371-21.01822401330760.160999491480456
765093.85045.369167665059.7887244327698933.36573259490180.617848080716573
775063.15049.018505546769.7226637027915220.4304390057036-0.260596419754109
785078.65049.178743996059.6173261286860139.3134134714483-0.406186731707974
795251.55090.921716710979.9678366778909127.2775118427321.36729047211537
805263.25133.1788188361810.307230070952496.45433939738611.37765352756799
815280.55174.3002910359410.612577117665674.06899969083081.31791707041008
825386.15202.6369366380210.7757905135226164.9315564528870.759613145461104
835227.35232.6101505722210.9394888840374-25.42373391940960.823972146847494
845149.55232.6110763029910.8519148981422-71.6378915694727-0.469808809459504
855128.65240.5314289588110.8290695833708-108.857399676184-0.125856780902166
865087.75256.4613157334310.8696958051563-174.1004155200660.218636381718228
875188.55257.4833528274310.7868240918782-58.7033699904892-0.421179734325209
8850845215.2598490356310.3130576980452-76.0579154741329-2.26310058443534
895258.65220.7902148799710.268365901435342.7836277728615-0.204019457695029
905348.95257.4701167850610.520139649448863.96048320982611.12706309032101
9152805254.0617525414110.388129198561240.4425596702901-0.595098628698724
925374.25271.8830955821710.456591027718694.56160224619970.318110831333852
935458.45311.5627801095310.7135301028611116.2835869208791.25275420037143
9453155289.5334839768310.441651142993859.7661371920506-1.40570564070563
955294.55296.0825785381310.411151776682.50100642190698-0.167288816026054
965341.45329.3051391713210.5819115468625-11.85377389837380.980795484509522
9750685304.3256010002410.3209055129043-198.99796397628-1.52855598321778
985156.95306.5232742224210.2605630417165-141.105983402472-0.34882119099357
995184.75289.1465083119910.0479484450155-75.515790973168-1.18520731875972
1005280.75308.1217421641810.1195094612293-36.75256491396220.382406440100218
10153395318.4182643675310.120975260220420.39688296808770.00757842530563099
1025377.75323.6013531359810.079444527607959.2552403309861-0.211445349942204
1035388.65338.2776677203610.117956753431645.5181121721540.196996357932421
1045443.65351.8453202165310.146229092752588.14475533563770.147999804536696
1055528.75368.6870773520710.199153800425152.9961379274020.287595096854997
10655395403.1883150529210.3829402698607110.3087797932521.04495106835757
10752925389.8093861232410.210975927901-72.8475229920227-1.02248706571142
1085351.55379.6468926464510.0684718337971-6.73325510127896-0.876964626707017
1095163.75376.305428535219.97612098178368-198.512139242089-0.577124922128635
11051055346.521055424349.70065323127821-199.762517266969-1.71014039612568
1115248.15342.215937168769.60144171738242-79.4211171603852-0.601911772689491
1125370.95361.850797369879.67451661584862-1.46778469817220.430890217283077
1135484.95394.817556786979.8481046247024665.68144247469620.999949991243736
1145510.75421.370457853649.9740226580312271.82979890073150.717228179323415
1155484.95437.6855382622610.021673462979840.56825681233390.272396306857326
1165567.85457.9687536299310.097480706953799.06650603676570.441147123640704
1175275.65390.127990487329.5376506310119-32.684124859085-3.3533924147242







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15595.633584551745389.83789763932205.795686912423
25351.451842689395396.55786829506-45.1060256056615
35415.594278822825403.2778389507912.3164398720302
45234.571940952015409.99780960653-175.425868654525
55212.656500026835416.71778026227-204.061280235442
65321.447438807735423.43775091801-101.990312110277
75403.868510133095430.15772157374-26.2892114406555
85492.00646173875436.8776922294855.1287695092197
95521.842385763525443.5976628852278.2447228783041
105512.765952320735450.3176335409662.4483187797777
115619.140160868855457.03760419669162.102556672158
125440.593778275085463.75757485243-23.1637965773512

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5595.63358455174 & 5389.83789763932 & 205.795686912423 \tabularnewline
2 & 5351.45184268939 & 5396.55786829506 & -45.1060256056615 \tabularnewline
3 & 5415.59427882282 & 5403.27783895079 & 12.3164398720302 \tabularnewline
4 & 5234.57194095201 & 5409.99780960653 & -175.425868654525 \tabularnewline
5 & 5212.65650002683 & 5416.71778026227 & -204.061280235442 \tabularnewline
6 & 5321.44743880773 & 5423.43775091801 & -101.990312110277 \tabularnewline
7 & 5403.86851013309 & 5430.15772157374 & -26.2892114406555 \tabularnewline
8 & 5492.0064617387 & 5436.87769222948 & 55.1287695092197 \tabularnewline
9 & 5521.84238576352 & 5443.59766288522 & 78.2447228783041 \tabularnewline
10 & 5512.76595232073 & 5450.31763354096 & 62.4483187797777 \tabularnewline
11 & 5619.14016086885 & 5457.03760419669 & 162.102556672158 \tabularnewline
12 & 5440.59377827508 & 5463.75757485243 & -23.1637965773512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300635&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]5595.63358455174[/C][C]5389.83789763932[/C][C]205.795686912423[/C][/ROW]
[ROW][C]2[/C][C]5351.45184268939[/C][C]5396.55786829506[/C][C]-45.1060256056615[/C][/ROW]
[ROW][C]3[/C][C]5415.59427882282[/C][C]5403.27783895079[/C][C]12.3164398720302[/C][/ROW]
[ROW][C]4[/C][C]5234.57194095201[/C][C]5409.99780960653[/C][C]-175.425868654525[/C][/ROW]
[ROW][C]5[/C][C]5212.65650002683[/C][C]5416.71778026227[/C][C]-204.061280235442[/C][/ROW]
[ROW][C]6[/C][C]5321.44743880773[/C][C]5423.43775091801[/C][C]-101.990312110277[/C][/ROW]
[ROW][C]7[/C][C]5403.86851013309[/C][C]5430.15772157374[/C][C]-26.2892114406555[/C][/ROW]
[ROW][C]8[/C][C]5492.0064617387[/C][C]5436.87769222948[/C][C]55.1287695092197[/C][/ROW]
[ROW][C]9[/C][C]5521.84238576352[/C][C]5443.59766288522[/C][C]78.2447228783041[/C][/ROW]
[ROW][C]10[/C][C]5512.76595232073[/C][C]5450.31763354096[/C][C]62.4483187797777[/C][/ROW]
[ROW][C]11[/C][C]5619.14016086885[/C][C]5457.03760419669[/C][C]162.102556672158[/C][/ROW]
[ROW][C]12[/C][C]5440.59377827508[/C][C]5463.75757485243[/C][C]-23.1637965773512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300635&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300635&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
15595.633584551745389.83789763932205.795686912423
25351.451842689395396.55786829506-45.1060256056615
35415.594278822825403.2778389507912.3164398720302
45234.571940952015409.99780960653-175.425868654525
55212.656500026835416.71778026227-204.061280235442
65321.447438807735423.43775091801-101.990312110277
75403.868510133095430.15772157374-26.2892114406555
85492.00646173875436.8776922294855.1287695092197
95521.842385763525443.5976628852278.2447228783041
105512.765952320735450.3176335409662.4483187797777
115619.140160868855457.03760419669162.102556672158
125440.593778275085463.75757485243-23.1637965773512



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')