Free Statistics

of Irreproducible Research!

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 computationThu, 22 Dec 2016 20:50:16 +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/22/t14824365620uouycrncm7v56h.htm/, Retrieved Mon, 29 Apr 2024 05:32:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302661, Retrieved Mon, 29 Apr 2024 05:32:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-22 19:50:16] [2802fcbee976b89d2ab84425d3d65dcf] [Current]
Feedback Forum

Post a new message
Dataseries X:
5445.2
5403.6
5425.6
5424.4
5446
5449
5453.4
5407
5466
5499.6
5473.4
5497.2
5499.4
5504.4
5486.6
5540.8
5502.8
5519
5497.2
5451.2
5452
5426.4
5461.4
5470.8
5440.2
5418.8
5433.8
5416.2
5406.4
5423.2
5418.2
5426
5441.6
5417
5405.4
5418.6
5411.6
5398.2
5460.2
5462.8
5465.4
5431.6
5431.6
5454.8
5419.8
5417.8
5449.8
5435.4
5414
5433.6
5406.6
5373.6
5393.2
5370
5346.6
5390.4
5362.4
5362
5372
5359.2
5351.6
5357.8
5326.8
5364.2
5354.2
5337.6
5328.2
5302.6
5303.4
5346.4
5308.4
5322
5345.2
5293.2
5295.4
5311.2
5235.2
5239
5270.4
5255
5264.4
5281.8
5255.6
5241.4
5212.2
5225.2
5217
5240
5227.6
5231.8
5233
5171.2
5173.4
5088.4
5098.4
5128.4
5079
5083.8
5091.4
5081.6
5116.4
5155
5102.8
5121.6
5131.6
5109.4
5102.2
5117.2
5083.8
5140.8
5133.6
5088
5121.6
5087.2
5077.8
5136.8




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302661&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302661&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 time5 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
15445.25445.2000
25403.65417.69000588922-2.01727636011362-2.00692412481831-1.30292005455826
35425.65422.63636472309-1.72024797163078-1.718890003904820.434429061086157
45424.45423.87220930566-1.63542763401175-1.641085023623370.195216727863689
554465436.58320798005-1.30414420271748-1.359732616503660.96155748834909
654495443.78510562331-1.12441830242363-1.218910090775390.572435391812797
75453.45449.40652768074-0.984713177924671-1.1172575895860.454314953058851
854075425.67205612004-1.46093322048589-1.4415416012347-1.53146982757831
954665448.63027585286-0.93803982500581-1.106327568636891.64240989121815
105499.65477.66116745471-0.27914609068664-0.7070356777990162.01359626081904
115473.45475.52921200571-0.320983838568396-0.73107048287873-0.124354789401001
125497.25488.0735525269-0.0229193779167396-0.5684099030332410.862550012711987
135499.45489.93501267971-0.141977053333947.959604246560880.160974476376068
145504.45499.364644938850.270583440264524-0.4070512101218930.530831643106082
155486.65492.311618889130.0474159112494698-0.540940467226101-0.469598114943843
165540.85520.3503504860.750597520861854-0.2227806887892281.84925095757742
175502.85510.798798841380.511658456431514-0.30786258633034-0.685250013906202
1855195515.866862279980.615232797558652-0.2767396692470990.303477278419863
195497.25505.650047937060.367387996295227-0.343170411669312-0.721351684128991
205451.25474.95377128084-0.35558994431815-0.521852912173298-2.06738078050563
2154525462.00228676173-0.654812825497219-0.591249243273066-0.83765352785095
225426.45441.73433137438-1.13060821636995-0.695729762163739-1.30327108342774
235461.45452.87958247789-0.826700570297595-0.6322459095801270.815069186867978
245470.85463.1277740188-0.547205915684815-0.576560265710820.734762581421824
255440.25449.52207029371-0.4500300643782790.531631246666232-0.977675684796928
265418.85430.76317641077-1.13910391721839-0.434286961232774-1.08480048546843
275433.85432.29306530545-1.05647303301494-0.4046102337469280.172518257082832
285416.25422.83630436313-1.29386322866839-0.459667785606666-0.552471463408349
295406.45413.12372428416-1.52402629672584-0.497615261202891-0.55564147349728
305423.25418.53689009047-1.33555528709874-0.4728546762778170.458087627214349
315418.25418.04541061192-1.31250932733825-0.4702253896520920.0557238299809753
3254265422.32031249527-1.15853904691093-0.4541764791930280.368705953868757
335441.65433.15430368527-0.824555649414672-0.4215245699961330.790988569128313
3454175423.76937771009-1.06551244372226-0.443904892577078-0.564341112806844
355405.45413.01974517119-1.34091920279496-0.468357539260519-0.638124884239306
365418.65415.92453847625-1.21899421355729-0.45797781820380.279641322118082
375411.65410.71675859507-1.270685094207883.8203002431131-0.284209634571096
385398.25402.93308984864-1.50405250025397-0.446764201718231-0.397204023745211
395460.25435.70893112175-0.40261260134108-0.1833383404063032.22142408459879
405462.85451.242394085520.085947692286287-0.1156364112693921.04457026585283
415465.45459.492343198930.332133548012581-0.09346173842058460.536226339849777
425431.65443.63385209829-0.154516017155651-0.126181914932274-1.06362453332585
435431.65436.71320144312-0.358341226187323-0.137627863691971-0.444407151678705
445454.85447.05513522104-0.0346135097429262-0.1213349176602540.702619062676369
455419.85431.4132119183-0.509144567648178-0.1435641537585-1.02455532774192
465417.85423.43832865718-0.737278253124468-0.153697936215244-0.489967048993752
475449.85438.40224842347-0.255157201869922-0.1332102808331941.03019482465349
485435.45436.64090615473-0.301619187079886-0.13510693627599-0.0988014428132841
4954145424.21305621865-0.575383499653223-1.38640364234442-0.842754230528027
505433.65429.47054115622-0.3719946951868030.1955300560203660.361502389518849
515406.65415.96225483121-0.802497633800980.119932252032786-0.852496815408907
525373.65391.12319338467-1.570173330523790.0481085829619314-1.5727020565278
535393.25391.62794705147-1.504512250856420.0517638466175770.13593412602717
5453705378.48912346346-1.871889746317940.0376699543925818-0.762226470356493
555346.65359.28232402079-2.419682573475020.0210830863822799-1.13553369217666
565390.45376.1968113501-1.807574818105960.03716456225004331.26629271940232
575362.45367.45089607978-2.027728461808690.0318662529993498-0.454359894174743
5853625363.42967514141-2.091126927799330.030429406707232-0.130527006444723
5953725367.47298945674-1.895600737945370.03465818114392810.401611989167362
605359.25361.87713746284-2.013790147651930.0322037322591682-0.242221361924953
615351.65355.74270320928-2.12664864634109-1.15849868143616-0.282332092901822
625357.85356.0227425032-2.044287878900520.1288140801053670.150687174575831
635326.85338.17441013527-2.566021174341960.0566383073727775-1.02674929153457
645364.25352.07764308513-2.030270824444490.09363498118319611.07666530909195
655354.25352.3898772001-1.954479008999840.0964991034985720.153267161405934
665337.65342.97068335651-2.195641467226480.0907686179736853-0.488390749226638
675328.25333.4627720384-2.431907739709780.0866645450606621-0.478357691294307
685302.65314.56534241556-2.964325122515220.0790309932570598-1.07703619071424
695303.45306.81992632684-3.11907374578760.0770530853595456-0.312712483609957
705346.45328.31315463069-2.321636114416160.08652541138764981.60968075486103
715308.45315.78280186714-2.652730479591660.0827944878012157-0.667623481582373
7253225318.20466742011-2.487990847906150.08457267531415770.331846546018019
735345.25331.81502447331-2.007091304870221.748884010346971.09325101134806
745293.25308.37324444727-2.73093669903427-0.336487991527837-1.35143201573283
755295.45299.91043567826-2.92044907410384-0.358172362599543-0.372709019958955
765311.25305.40158352042-2.64471256224501-0.3431763822331520.549699691203877
775235.25263.94741484672-3.91279930194803-0.378234767859808-2.53766635925883
7852395248.10514389686-4.30219943067159-0.38438035205841-0.7799856582037
795270.45259.38737121042-3.79353902540884-0.3790565431322071.01884651770422
8052555255.46976849211-3.79758947519735-0.379089036295105-0.00811015606996152
815264.45259.24365170763-3.55029250384991-0.3773982150928590.494928013131486
825281.85270.99288464199-3.05035863548412-0.3742954214156971.0000521714362
835255.65261.02845047934-3.2763874483-0.375611243086266-0.451923536875996
845241.45248.52224279405-3.57825059197913-0.377285881088922-0.603270380542677
855212.25225.18961419973-4.194391585289241.28287583973141-1.3335545906429
865225.25223.53032147326-4.10956231689144-0.09836694279815720.160635424321502
8752175218.07717725583-4.15395895430895-0.102713900317264-0.0874244276685519
8852405229.04235921793-3.65688753955288-0.08038988286017710.987890210532655
895227.65226.71091558904-3.61339563738011-0.0794552630123170.0866412200994135
905231.85228.17055771777-3.44704332088791-0.07759722851160610.33158201824326
9152335229.54997736189-3.28879675769317-0.07655321442753030.315433815751205
925171.25194.49248805619-4.33049709444869-0.0812843547285804-2.07611650460001
935173.45180.52397885111-4.64658278673077-0.0824183464201137-0.629830845186514
945088.45125.38007834281-6.30300480688554-0.0875806580200943-3.29985239266699
955098.45107.18018468361-6.69332649550157-0.0886963226628638-0.777413624950201
965128.45116.66686959087-6.16237861466323-0.08726550093410451.0572836791368
9750795092.96886071487-6.72189500942282-1.29637643927191-1.17873694276591
985083.85084.74509763107-6.771844062731030.108266828291822-0.0955212178650831
995091.45085.67730001949-6.517551448764220.1300982052882170.501552635573553
1005081.65080.49406598754-6.473640116655660.1317844078054610.0871797197604084
1015116.45098.42444555726-5.67145890069350.1458482656685661.59498401882174
10251555128.63166628544-4.492591071610040.1557249472081742.34469978239041
1035102.85111.71918983018-4.900626680470490.153948511762305-0.811573240047816
1045121.65115.27092304144-4.622933334186120.1546627495995450.552287236824493
1055131.65122.66587643147-4.228072182405730.155362105613270.785240779064264
1065109.45113.12539507832-4.402631993058840.155117824504952-0.347103802782109
1075102.25104.86381708241-4.529443762939190.15496363641859-0.252134472303295
1085117.25109.99101561407-4.212082185715570.1553175814501240.630937815625883
1095083.85094.7537318667-4.56828159005398-2.98199814651071-0.73873764110092
1105140.85119.62315453489-3.593133448771670.4399887114104171.87769580808582
1115133.65125.93766364098-3.266431323075320.4650246302174980.645276662671968
11250885102.37541382925-3.934502453335550.442519880127454-1.32603142799529
1135121.65111.56404386397-3.50283127597210.448932212103920.857621220827507
1145087.25095.74844160278-3.907740931492630.446252498417767-0.804578912377338
1155077.85083.46945711318-4.183009675231220.44542250399405-0.546971540629106
1165136.85112.26472481919-3.098603706331240.4469809866732622.15467657824967

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5445.2 & 5445.2 & 0 & 0 & 0 \tabularnewline
2 & 5403.6 & 5417.69000588922 & -2.01727636011362 & -2.00692412481831 & -1.30292005455826 \tabularnewline
3 & 5425.6 & 5422.63636472309 & -1.72024797163078 & -1.71889000390482 & 0.434429061086157 \tabularnewline
4 & 5424.4 & 5423.87220930566 & -1.63542763401175 & -1.64108502362337 & 0.195216727863689 \tabularnewline
5 & 5446 & 5436.58320798005 & -1.30414420271748 & -1.35973261650366 & 0.96155748834909 \tabularnewline
6 & 5449 & 5443.78510562331 & -1.12441830242363 & -1.21891009077539 & 0.572435391812797 \tabularnewline
7 & 5453.4 & 5449.40652768074 & -0.984713177924671 & -1.117257589586 & 0.454314953058851 \tabularnewline
8 & 5407 & 5425.67205612004 & -1.46093322048589 & -1.4415416012347 & -1.53146982757831 \tabularnewline
9 & 5466 & 5448.63027585286 & -0.93803982500581 & -1.10632756863689 & 1.64240989121815 \tabularnewline
10 & 5499.6 & 5477.66116745471 & -0.27914609068664 & -0.707035677799016 & 2.01359626081904 \tabularnewline
11 & 5473.4 & 5475.52921200571 & -0.320983838568396 & -0.73107048287873 & -0.124354789401001 \tabularnewline
12 & 5497.2 & 5488.0735525269 & -0.0229193779167396 & -0.568409903033241 & 0.862550012711987 \tabularnewline
13 & 5499.4 & 5489.93501267971 & -0.14197705333394 & 7.95960424656088 & 0.160974476376068 \tabularnewline
14 & 5504.4 & 5499.36464493885 & 0.270583440264524 & -0.407051210121893 & 0.530831643106082 \tabularnewline
15 & 5486.6 & 5492.31161888913 & 0.0474159112494698 & -0.540940467226101 & -0.469598114943843 \tabularnewline
16 & 5540.8 & 5520.350350486 & 0.750597520861854 & -0.222780688789228 & 1.84925095757742 \tabularnewline
17 & 5502.8 & 5510.79879884138 & 0.511658456431514 & -0.30786258633034 & -0.685250013906202 \tabularnewline
18 & 5519 & 5515.86686227998 & 0.615232797558652 & -0.276739669247099 & 0.303477278419863 \tabularnewline
19 & 5497.2 & 5505.65004793706 & 0.367387996295227 & -0.343170411669312 & -0.721351684128991 \tabularnewline
20 & 5451.2 & 5474.95377128084 & -0.35558994431815 & -0.521852912173298 & -2.06738078050563 \tabularnewline
21 & 5452 & 5462.00228676173 & -0.654812825497219 & -0.591249243273066 & -0.83765352785095 \tabularnewline
22 & 5426.4 & 5441.73433137438 & -1.13060821636995 & -0.695729762163739 & -1.30327108342774 \tabularnewline
23 & 5461.4 & 5452.87958247789 & -0.826700570297595 & -0.632245909580127 & 0.815069186867978 \tabularnewline
24 & 5470.8 & 5463.1277740188 & -0.547205915684815 & -0.57656026571082 & 0.734762581421824 \tabularnewline
25 & 5440.2 & 5449.52207029371 & -0.450030064378279 & 0.531631246666232 & -0.977675684796928 \tabularnewline
26 & 5418.8 & 5430.76317641077 & -1.13910391721839 & -0.434286961232774 & -1.08480048546843 \tabularnewline
27 & 5433.8 & 5432.29306530545 & -1.05647303301494 & -0.404610233746928 & 0.172518257082832 \tabularnewline
28 & 5416.2 & 5422.83630436313 & -1.29386322866839 & -0.459667785606666 & -0.552471463408349 \tabularnewline
29 & 5406.4 & 5413.12372428416 & -1.52402629672584 & -0.497615261202891 & -0.55564147349728 \tabularnewline
30 & 5423.2 & 5418.53689009047 & -1.33555528709874 & -0.472854676277817 & 0.458087627214349 \tabularnewline
31 & 5418.2 & 5418.04541061192 & -1.31250932733825 & -0.470225389652092 & 0.0557238299809753 \tabularnewline
32 & 5426 & 5422.32031249527 & -1.15853904691093 & -0.454176479193028 & 0.368705953868757 \tabularnewline
33 & 5441.6 & 5433.15430368527 & -0.824555649414672 & -0.421524569996133 & 0.790988569128313 \tabularnewline
34 & 5417 & 5423.76937771009 & -1.06551244372226 & -0.443904892577078 & -0.564341112806844 \tabularnewline
35 & 5405.4 & 5413.01974517119 & -1.34091920279496 & -0.468357539260519 & -0.638124884239306 \tabularnewline
36 & 5418.6 & 5415.92453847625 & -1.21899421355729 & -0.4579778182038 & 0.279641322118082 \tabularnewline
37 & 5411.6 & 5410.71675859507 & -1.27068509420788 & 3.8203002431131 & -0.284209634571096 \tabularnewline
38 & 5398.2 & 5402.93308984864 & -1.50405250025397 & -0.446764201718231 & -0.397204023745211 \tabularnewline
39 & 5460.2 & 5435.70893112175 & -0.40261260134108 & -0.183338340406303 & 2.22142408459879 \tabularnewline
40 & 5462.8 & 5451.24239408552 & 0.085947692286287 & -0.115636411269392 & 1.04457026585283 \tabularnewline
41 & 5465.4 & 5459.49234319893 & 0.332133548012581 & -0.0934617384205846 & 0.536226339849777 \tabularnewline
42 & 5431.6 & 5443.63385209829 & -0.154516017155651 & -0.126181914932274 & -1.06362453332585 \tabularnewline
43 & 5431.6 & 5436.71320144312 & -0.358341226187323 & -0.137627863691971 & -0.444407151678705 \tabularnewline
44 & 5454.8 & 5447.05513522104 & -0.0346135097429262 & -0.121334917660254 & 0.702619062676369 \tabularnewline
45 & 5419.8 & 5431.4132119183 & -0.509144567648178 & -0.1435641537585 & -1.02455532774192 \tabularnewline
46 & 5417.8 & 5423.43832865718 & -0.737278253124468 & -0.153697936215244 & -0.489967048993752 \tabularnewline
47 & 5449.8 & 5438.40224842347 & -0.255157201869922 & -0.133210280833194 & 1.03019482465349 \tabularnewline
48 & 5435.4 & 5436.64090615473 & -0.301619187079886 & -0.13510693627599 & -0.0988014428132841 \tabularnewline
49 & 5414 & 5424.21305621865 & -0.575383499653223 & -1.38640364234442 & -0.842754230528027 \tabularnewline
50 & 5433.6 & 5429.47054115622 & -0.371994695186803 & 0.195530056020366 & 0.361502389518849 \tabularnewline
51 & 5406.6 & 5415.96225483121 & -0.80249763380098 & 0.119932252032786 & -0.852496815408907 \tabularnewline
52 & 5373.6 & 5391.12319338467 & -1.57017333052379 & 0.0481085829619314 & -1.5727020565278 \tabularnewline
53 & 5393.2 & 5391.62794705147 & -1.50451225085642 & 0.051763846617577 & 0.13593412602717 \tabularnewline
54 & 5370 & 5378.48912346346 & -1.87188974631794 & 0.0376699543925818 & -0.762226470356493 \tabularnewline
55 & 5346.6 & 5359.28232402079 & -2.41968257347502 & 0.0210830863822799 & -1.13553369217666 \tabularnewline
56 & 5390.4 & 5376.1968113501 & -1.80757481810596 & 0.0371645622500433 & 1.26629271940232 \tabularnewline
57 & 5362.4 & 5367.45089607978 & -2.02772846180869 & 0.0318662529993498 & -0.454359894174743 \tabularnewline
58 & 5362 & 5363.42967514141 & -2.09112692779933 & 0.030429406707232 & -0.130527006444723 \tabularnewline
59 & 5372 & 5367.47298945674 & -1.89560073794537 & 0.0346581811439281 & 0.401611989167362 \tabularnewline
60 & 5359.2 & 5361.87713746284 & -2.01379014765193 & 0.0322037322591682 & -0.242221361924953 \tabularnewline
61 & 5351.6 & 5355.74270320928 & -2.12664864634109 & -1.15849868143616 & -0.282332092901822 \tabularnewline
62 & 5357.8 & 5356.0227425032 & -2.04428787890052 & 0.128814080105367 & 0.150687174575831 \tabularnewline
63 & 5326.8 & 5338.17441013527 & -2.56602117434196 & 0.0566383073727775 & -1.02674929153457 \tabularnewline
64 & 5364.2 & 5352.07764308513 & -2.03027082444449 & 0.0936349811831961 & 1.07666530909195 \tabularnewline
65 & 5354.2 & 5352.3898772001 & -1.95447900899984 & 0.096499103498572 & 0.153267161405934 \tabularnewline
66 & 5337.6 & 5342.97068335651 & -2.19564146722648 & 0.0907686179736853 & -0.488390749226638 \tabularnewline
67 & 5328.2 & 5333.4627720384 & -2.43190773970978 & 0.0866645450606621 & -0.478357691294307 \tabularnewline
68 & 5302.6 & 5314.56534241556 & -2.96432512251522 & 0.0790309932570598 & -1.07703619071424 \tabularnewline
69 & 5303.4 & 5306.81992632684 & -3.1190737457876 & 0.0770530853595456 & -0.312712483609957 \tabularnewline
70 & 5346.4 & 5328.31315463069 & -2.32163611441616 & 0.0865254113876498 & 1.60968075486103 \tabularnewline
71 & 5308.4 & 5315.78280186714 & -2.65273047959166 & 0.0827944878012157 & -0.667623481582373 \tabularnewline
72 & 5322 & 5318.20466742011 & -2.48799084790615 & 0.0845726753141577 & 0.331846546018019 \tabularnewline
73 & 5345.2 & 5331.81502447331 & -2.00709130487022 & 1.74888401034697 & 1.09325101134806 \tabularnewline
74 & 5293.2 & 5308.37324444727 & -2.73093669903427 & -0.336487991527837 & -1.35143201573283 \tabularnewline
75 & 5295.4 & 5299.91043567826 & -2.92044907410384 & -0.358172362599543 & -0.372709019958955 \tabularnewline
76 & 5311.2 & 5305.40158352042 & -2.64471256224501 & -0.343176382233152 & 0.549699691203877 \tabularnewline
77 & 5235.2 & 5263.94741484672 & -3.91279930194803 & -0.378234767859808 & -2.53766635925883 \tabularnewline
78 & 5239 & 5248.10514389686 & -4.30219943067159 & -0.38438035205841 & -0.7799856582037 \tabularnewline
79 & 5270.4 & 5259.38737121042 & -3.79353902540884 & -0.379056543132207 & 1.01884651770422 \tabularnewline
80 & 5255 & 5255.46976849211 & -3.79758947519735 & -0.379089036295105 & -0.00811015606996152 \tabularnewline
81 & 5264.4 & 5259.24365170763 & -3.55029250384991 & -0.377398215092859 & 0.494928013131486 \tabularnewline
82 & 5281.8 & 5270.99288464199 & -3.05035863548412 & -0.374295421415697 & 1.0000521714362 \tabularnewline
83 & 5255.6 & 5261.02845047934 & -3.2763874483 & -0.375611243086266 & -0.451923536875996 \tabularnewline
84 & 5241.4 & 5248.52224279405 & -3.57825059197913 & -0.377285881088922 & -0.603270380542677 \tabularnewline
85 & 5212.2 & 5225.18961419973 & -4.19439158528924 & 1.28287583973141 & -1.3335545906429 \tabularnewline
86 & 5225.2 & 5223.53032147326 & -4.10956231689144 & -0.0983669427981572 & 0.160635424321502 \tabularnewline
87 & 5217 & 5218.07717725583 & -4.15395895430895 & -0.102713900317264 & -0.0874244276685519 \tabularnewline
88 & 5240 & 5229.04235921793 & -3.65688753955288 & -0.0803898828601771 & 0.987890210532655 \tabularnewline
89 & 5227.6 & 5226.71091558904 & -3.61339563738011 & -0.079455263012317 & 0.0866412200994135 \tabularnewline
90 & 5231.8 & 5228.17055771777 & -3.44704332088791 & -0.0775972285116061 & 0.33158201824326 \tabularnewline
91 & 5233 & 5229.54997736189 & -3.28879675769317 & -0.0765532144275303 & 0.315433815751205 \tabularnewline
92 & 5171.2 & 5194.49248805619 & -4.33049709444869 & -0.0812843547285804 & -2.07611650460001 \tabularnewline
93 & 5173.4 & 5180.52397885111 & -4.64658278673077 & -0.0824183464201137 & -0.629830845186514 \tabularnewline
94 & 5088.4 & 5125.38007834281 & -6.30300480688554 & -0.0875806580200943 & -3.29985239266699 \tabularnewline
95 & 5098.4 & 5107.18018468361 & -6.69332649550157 & -0.0886963226628638 & -0.777413624950201 \tabularnewline
96 & 5128.4 & 5116.66686959087 & -6.16237861466323 & -0.0872655009341045 & 1.0572836791368 \tabularnewline
97 & 5079 & 5092.96886071487 & -6.72189500942282 & -1.29637643927191 & -1.17873694276591 \tabularnewline
98 & 5083.8 & 5084.74509763107 & -6.77184406273103 & 0.108266828291822 & -0.0955212178650831 \tabularnewline
99 & 5091.4 & 5085.67730001949 & -6.51755144876422 & 0.130098205288217 & 0.501552635573553 \tabularnewline
100 & 5081.6 & 5080.49406598754 & -6.47364011665566 & 0.131784407805461 & 0.0871797197604084 \tabularnewline
101 & 5116.4 & 5098.42444555726 & -5.6714589006935 & 0.145848265668566 & 1.59498401882174 \tabularnewline
102 & 5155 & 5128.63166628544 & -4.49259107161004 & 0.155724947208174 & 2.34469978239041 \tabularnewline
103 & 5102.8 & 5111.71918983018 & -4.90062668047049 & 0.153948511762305 & -0.811573240047816 \tabularnewline
104 & 5121.6 & 5115.27092304144 & -4.62293333418612 & 0.154662749599545 & 0.552287236824493 \tabularnewline
105 & 5131.6 & 5122.66587643147 & -4.22807218240573 & 0.15536210561327 & 0.785240779064264 \tabularnewline
106 & 5109.4 & 5113.12539507832 & -4.40263199305884 & 0.155117824504952 & -0.347103802782109 \tabularnewline
107 & 5102.2 & 5104.86381708241 & -4.52944376293919 & 0.15496363641859 & -0.252134472303295 \tabularnewline
108 & 5117.2 & 5109.99101561407 & -4.21208218571557 & 0.155317581450124 & 0.630937815625883 \tabularnewline
109 & 5083.8 & 5094.7537318667 & -4.56828159005398 & -2.98199814651071 & -0.73873764110092 \tabularnewline
110 & 5140.8 & 5119.62315453489 & -3.59313344877167 & 0.439988711410417 & 1.87769580808582 \tabularnewline
111 & 5133.6 & 5125.93766364098 & -3.26643132307532 & 0.465024630217498 & 0.645276662671968 \tabularnewline
112 & 5088 & 5102.37541382925 & -3.93450245333555 & 0.442519880127454 & -1.32603142799529 \tabularnewline
113 & 5121.6 & 5111.56404386397 & -3.5028312759721 & 0.44893221210392 & 0.857621220827507 \tabularnewline
114 & 5087.2 & 5095.74844160278 & -3.90774093149263 & 0.446252498417767 & -0.804578912377338 \tabularnewline
115 & 5077.8 & 5083.46945711318 & -4.18300967523122 & 0.44542250399405 & -0.546971540629106 \tabularnewline
116 & 5136.8 & 5112.26472481919 & -3.09860370633124 & 0.446980986673262 & 2.15467657824967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302661&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]5445.2[/C][C]5445.2[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5403.6[/C][C]5417.69000588922[/C][C]-2.01727636011362[/C][C]-2.00692412481831[/C][C]-1.30292005455826[/C][/ROW]
[ROW][C]3[/C][C]5425.6[/C][C]5422.63636472309[/C][C]-1.72024797163078[/C][C]-1.71889000390482[/C][C]0.434429061086157[/C][/ROW]
[ROW][C]4[/C][C]5424.4[/C][C]5423.87220930566[/C][C]-1.63542763401175[/C][C]-1.64108502362337[/C][C]0.195216727863689[/C][/ROW]
[ROW][C]5[/C][C]5446[/C][C]5436.58320798005[/C][C]-1.30414420271748[/C][C]-1.35973261650366[/C][C]0.96155748834909[/C][/ROW]
[ROW][C]6[/C][C]5449[/C][C]5443.78510562331[/C][C]-1.12441830242363[/C][C]-1.21891009077539[/C][C]0.572435391812797[/C][/ROW]
[ROW][C]7[/C][C]5453.4[/C][C]5449.40652768074[/C][C]-0.984713177924671[/C][C]-1.117257589586[/C][C]0.454314953058851[/C][/ROW]
[ROW][C]8[/C][C]5407[/C][C]5425.67205612004[/C][C]-1.46093322048589[/C][C]-1.4415416012347[/C][C]-1.53146982757831[/C][/ROW]
[ROW][C]9[/C][C]5466[/C][C]5448.63027585286[/C][C]-0.93803982500581[/C][C]-1.10632756863689[/C][C]1.64240989121815[/C][/ROW]
[ROW][C]10[/C][C]5499.6[/C][C]5477.66116745471[/C][C]-0.27914609068664[/C][C]-0.707035677799016[/C][C]2.01359626081904[/C][/ROW]
[ROW][C]11[/C][C]5473.4[/C][C]5475.52921200571[/C][C]-0.320983838568396[/C][C]-0.73107048287873[/C][C]-0.124354789401001[/C][/ROW]
[ROW][C]12[/C][C]5497.2[/C][C]5488.0735525269[/C][C]-0.0229193779167396[/C][C]-0.568409903033241[/C][C]0.862550012711987[/C][/ROW]
[ROW][C]13[/C][C]5499.4[/C][C]5489.93501267971[/C][C]-0.14197705333394[/C][C]7.95960424656088[/C][C]0.160974476376068[/C][/ROW]
[ROW][C]14[/C][C]5504.4[/C][C]5499.36464493885[/C][C]0.270583440264524[/C][C]-0.407051210121893[/C][C]0.530831643106082[/C][/ROW]
[ROW][C]15[/C][C]5486.6[/C][C]5492.31161888913[/C][C]0.0474159112494698[/C][C]-0.540940467226101[/C][C]-0.469598114943843[/C][/ROW]
[ROW][C]16[/C][C]5540.8[/C][C]5520.350350486[/C][C]0.750597520861854[/C][C]-0.222780688789228[/C][C]1.84925095757742[/C][/ROW]
[ROW][C]17[/C][C]5502.8[/C][C]5510.79879884138[/C][C]0.511658456431514[/C][C]-0.30786258633034[/C][C]-0.685250013906202[/C][/ROW]
[ROW][C]18[/C][C]5519[/C][C]5515.86686227998[/C][C]0.615232797558652[/C][C]-0.276739669247099[/C][C]0.303477278419863[/C][/ROW]
[ROW][C]19[/C][C]5497.2[/C][C]5505.65004793706[/C][C]0.367387996295227[/C][C]-0.343170411669312[/C][C]-0.721351684128991[/C][/ROW]
[ROW][C]20[/C][C]5451.2[/C][C]5474.95377128084[/C][C]-0.35558994431815[/C][C]-0.521852912173298[/C][C]-2.06738078050563[/C][/ROW]
[ROW][C]21[/C][C]5452[/C][C]5462.00228676173[/C][C]-0.654812825497219[/C][C]-0.591249243273066[/C][C]-0.83765352785095[/C][/ROW]
[ROW][C]22[/C][C]5426.4[/C][C]5441.73433137438[/C][C]-1.13060821636995[/C][C]-0.695729762163739[/C][C]-1.30327108342774[/C][/ROW]
[ROW][C]23[/C][C]5461.4[/C][C]5452.87958247789[/C][C]-0.826700570297595[/C][C]-0.632245909580127[/C][C]0.815069186867978[/C][/ROW]
[ROW][C]24[/C][C]5470.8[/C][C]5463.1277740188[/C][C]-0.547205915684815[/C][C]-0.57656026571082[/C][C]0.734762581421824[/C][/ROW]
[ROW][C]25[/C][C]5440.2[/C][C]5449.52207029371[/C][C]-0.450030064378279[/C][C]0.531631246666232[/C][C]-0.977675684796928[/C][/ROW]
[ROW][C]26[/C][C]5418.8[/C][C]5430.76317641077[/C][C]-1.13910391721839[/C][C]-0.434286961232774[/C][C]-1.08480048546843[/C][/ROW]
[ROW][C]27[/C][C]5433.8[/C][C]5432.29306530545[/C][C]-1.05647303301494[/C][C]-0.404610233746928[/C][C]0.172518257082832[/C][/ROW]
[ROW][C]28[/C][C]5416.2[/C][C]5422.83630436313[/C][C]-1.29386322866839[/C][C]-0.459667785606666[/C][C]-0.552471463408349[/C][/ROW]
[ROW][C]29[/C][C]5406.4[/C][C]5413.12372428416[/C][C]-1.52402629672584[/C][C]-0.497615261202891[/C][C]-0.55564147349728[/C][/ROW]
[ROW][C]30[/C][C]5423.2[/C][C]5418.53689009047[/C][C]-1.33555528709874[/C][C]-0.472854676277817[/C][C]0.458087627214349[/C][/ROW]
[ROW][C]31[/C][C]5418.2[/C][C]5418.04541061192[/C][C]-1.31250932733825[/C][C]-0.470225389652092[/C][C]0.0557238299809753[/C][/ROW]
[ROW][C]32[/C][C]5426[/C][C]5422.32031249527[/C][C]-1.15853904691093[/C][C]-0.454176479193028[/C][C]0.368705953868757[/C][/ROW]
[ROW][C]33[/C][C]5441.6[/C][C]5433.15430368527[/C][C]-0.824555649414672[/C][C]-0.421524569996133[/C][C]0.790988569128313[/C][/ROW]
[ROW][C]34[/C][C]5417[/C][C]5423.76937771009[/C][C]-1.06551244372226[/C][C]-0.443904892577078[/C][C]-0.564341112806844[/C][/ROW]
[ROW][C]35[/C][C]5405.4[/C][C]5413.01974517119[/C][C]-1.34091920279496[/C][C]-0.468357539260519[/C][C]-0.638124884239306[/C][/ROW]
[ROW][C]36[/C][C]5418.6[/C][C]5415.92453847625[/C][C]-1.21899421355729[/C][C]-0.4579778182038[/C][C]0.279641322118082[/C][/ROW]
[ROW][C]37[/C][C]5411.6[/C][C]5410.71675859507[/C][C]-1.27068509420788[/C][C]3.8203002431131[/C][C]-0.284209634571096[/C][/ROW]
[ROW][C]38[/C][C]5398.2[/C][C]5402.93308984864[/C][C]-1.50405250025397[/C][C]-0.446764201718231[/C][C]-0.397204023745211[/C][/ROW]
[ROW][C]39[/C][C]5460.2[/C][C]5435.70893112175[/C][C]-0.40261260134108[/C][C]-0.183338340406303[/C][C]2.22142408459879[/C][/ROW]
[ROW][C]40[/C][C]5462.8[/C][C]5451.24239408552[/C][C]0.085947692286287[/C][C]-0.115636411269392[/C][C]1.04457026585283[/C][/ROW]
[ROW][C]41[/C][C]5465.4[/C][C]5459.49234319893[/C][C]0.332133548012581[/C][C]-0.0934617384205846[/C][C]0.536226339849777[/C][/ROW]
[ROW][C]42[/C][C]5431.6[/C][C]5443.63385209829[/C][C]-0.154516017155651[/C][C]-0.126181914932274[/C][C]-1.06362453332585[/C][/ROW]
[ROW][C]43[/C][C]5431.6[/C][C]5436.71320144312[/C][C]-0.358341226187323[/C][C]-0.137627863691971[/C][C]-0.444407151678705[/C][/ROW]
[ROW][C]44[/C][C]5454.8[/C][C]5447.05513522104[/C][C]-0.0346135097429262[/C][C]-0.121334917660254[/C][C]0.702619062676369[/C][/ROW]
[ROW][C]45[/C][C]5419.8[/C][C]5431.4132119183[/C][C]-0.509144567648178[/C][C]-0.1435641537585[/C][C]-1.02455532774192[/C][/ROW]
[ROW][C]46[/C][C]5417.8[/C][C]5423.43832865718[/C][C]-0.737278253124468[/C][C]-0.153697936215244[/C][C]-0.489967048993752[/C][/ROW]
[ROW][C]47[/C][C]5449.8[/C][C]5438.40224842347[/C][C]-0.255157201869922[/C][C]-0.133210280833194[/C][C]1.03019482465349[/C][/ROW]
[ROW][C]48[/C][C]5435.4[/C][C]5436.64090615473[/C][C]-0.301619187079886[/C][C]-0.13510693627599[/C][C]-0.0988014428132841[/C][/ROW]
[ROW][C]49[/C][C]5414[/C][C]5424.21305621865[/C][C]-0.575383499653223[/C][C]-1.38640364234442[/C][C]-0.842754230528027[/C][/ROW]
[ROW][C]50[/C][C]5433.6[/C][C]5429.47054115622[/C][C]-0.371994695186803[/C][C]0.195530056020366[/C][C]0.361502389518849[/C][/ROW]
[ROW][C]51[/C][C]5406.6[/C][C]5415.96225483121[/C][C]-0.80249763380098[/C][C]0.119932252032786[/C][C]-0.852496815408907[/C][/ROW]
[ROW][C]52[/C][C]5373.6[/C][C]5391.12319338467[/C][C]-1.57017333052379[/C][C]0.0481085829619314[/C][C]-1.5727020565278[/C][/ROW]
[ROW][C]53[/C][C]5393.2[/C][C]5391.62794705147[/C][C]-1.50451225085642[/C][C]0.051763846617577[/C][C]0.13593412602717[/C][/ROW]
[ROW][C]54[/C][C]5370[/C][C]5378.48912346346[/C][C]-1.87188974631794[/C][C]0.0376699543925818[/C][C]-0.762226470356493[/C][/ROW]
[ROW][C]55[/C][C]5346.6[/C][C]5359.28232402079[/C][C]-2.41968257347502[/C][C]0.0210830863822799[/C][C]-1.13553369217666[/C][/ROW]
[ROW][C]56[/C][C]5390.4[/C][C]5376.1968113501[/C][C]-1.80757481810596[/C][C]0.0371645622500433[/C][C]1.26629271940232[/C][/ROW]
[ROW][C]57[/C][C]5362.4[/C][C]5367.45089607978[/C][C]-2.02772846180869[/C][C]0.0318662529993498[/C][C]-0.454359894174743[/C][/ROW]
[ROW][C]58[/C][C]5362[/C][C]5363.42967514141[/C][C]-2.09112692779933[/C][C]0.030429406707232[/C][C]-0.130527006444723[/C][/ROW]
[ROW][C]59[/C][C]5372[/C][C]5367.47298945674[/C][C]-1.89560073794537[/C][C]0.0346581811439281[/C][C]0.401611989167362[/C][/ROW]
[ROW][C]60[/C][C]5359.2[/C][C]5361.87713746284[/C][C]-2.01379014765193[/C][C]0.0322037322591682[/C][C]-0.242221361924953[/C][/ROW]
[ROW][C]61[/C][C]5351.6[/C][C]5355.74270320928[/C][C]-2.12664864634109[/C][C]-1.15849868143616[/C][C]-0.282332092901822[/C][/ROW]
[ROW][C]62[/C][C]5357.8[/C][C]5356.0227425032[/C][C]-2.04428787890052[/C][C]0.128814080105367[/C][C]0.150687174575831[/C][/ROW]
[ROW][C]63[/C][C]5326.8[/C][C]5338.17441013527[/C][C]-2.56602117434196[/C][C]0.0566383073727775[/C][C]-1.02674929153457[/C][/ROW]
[ROW][C]64[/C][C]5364.2[/C][C]5352.07764308513[/C][C]-2.03027082444449[/C][C]0.0936349811831961[/C][C]1.07666530909195[/C][/ROW]
[ROW][C]65[/C][C]5354.2[/C][C]5352.3898772001[/C][C]-1.95447900899984[/C][C]0.096499103498572[/C][C]0.153267161405934[/C][/ROW]
[ROW][C]66[/C][C]5337.6[/C][C]5342.97068335651[/C][C]-2.19564146722648[/C][C]0.0907686179736853[/C][C]-0.488390749226638[/C][/ROW]
[ROW][C]67[/C][C]5328.2[/C][C]5333.4627720384[/C][C]-2.43190773970978[/C][C]0.0866645450606621[/C][C]-0.478357691294307[/C][/ROW]
[ROW][C]68[/C][C]5302.6[/C][C]5314.56534241556[/C][C]-2.96432512251522[/C][C]0.0790309932570598[/C][C]-1.07703619071424[/C][/ROW]
[ROW][C]69[/C][C]5303.4[/C][C]5306.81992632684[/C][C]-3.1190737457876[/C][C]0.0770530853595456[/C][C]-0.312712483609957[/C][/ROW]
[ROW][C]70[/C][C]5346.4[/C][C]5328.31315463069[/C][C]-2.32163611441616[/C][C]0.0865254113876498[/C][C]1.60968075486103[/C][/ROW]
[ROW][C]71[/C][C]5308.4[/C][C]5315.78280186714[/C][C]-2.65273047959166[/C][C]0.0827944878012157[/C][C]-0.667623481582373[/C][/ROW]
[ROW][C]72[/C][C]5322[/C][C]5318.20466742011[/C][C]-2.48799084790615[/C][C]0.0845726753141577[/C][C]0.331846546018019[/C][/ROW]
[ROW][C]73[/C][C]5345.2[/C][C]5331.81502447331[/C][C]-2.00709130487022[/C][C]1.74888401034697[/C][C]1.09325101134806[/C][/ROW]
[ROW][C]74[/C][C]5293.2[/C][C]5308.37324444727[/C][C]-2.73093669903427[/C][C]-0.336487991527837[/C][C]-1.35143201573283[/C][/ROW]
[ROW][C]75[/C][C]5295.4[/C][C]5299.91043567826[/C][C]-2.92044907410384[/C][C]-0.358172362599543[/C][C]-0.372709019958955[/C][/ROW]
[ROW][C]76[/C][C]5311.2[/C][C]5305.40158352042[/C][C]-2.64471256224501[/C][C]-0.343176382233152[/C][C]0.549699691203877[/C][/ROW]
[ROW][C]77[/C][C]5235.2[/C][C]5263.94741484672[/C][C]-3.91279930194803[/C][C]-0.378234767859808[/C][C]-2.53766635925883[/C][/ROW]
[ROW][C]78[/C][C]5239[/C][C]5248.10514389686[/C][C]-4.30219943067159[/C][C]-0.38438035205841[/C][C]-0.7799856582037[/C][/ROW]
[ROW][C]79[/C][C]5270.4[/C][C]5259.38737121042[/C][C]-3.79353902540884[/C][C]-0.379056543132207[/C][C]1.01884651770422[/C][/ROW]
[ROW][C]80[/C][C]5255[/C][C]5255.46976849211[/C][C]-3.79758947519735[/C][C]-0.379089036295105[/C][C]-0.00811015606996152[/C][/ROW]
[ROW][C]81[/C][C]5264.4[/C][C]5259.24365170763[/C][C]-3.55029250384991[/C][C]-0.377398215092859[/C][C]0.494928013131486[/C][/ROW]
[ROW][C]82[/C][C]5281.8[/C][C]5270.99288464199[/C][C]-3.05035863548412[/C][C]-0.374295421415697[/C][C]1.0000521714362[/C][/ROW]
[ROW][C]83[/C][C]5255.6[/C][C]5261.02845047934[/C][C]-3.2763874483[/C][C]-0.375611243086266[/C][C]-0.451923536875996[/C][/ROW]
[ROW][C]84[/C][C]5241.4[/C][C]5248.52224279405[/C][C]-3.57825059197913[/C][C]-0.377285881088922[/C][C]-0.603270380542677[/C][/ROW]
[ROW][C]85[/C][C]5212.2[/C][C]5225.18961419973[/C][C]-4.19439158528924[/C][C]1.28287583973141[/C][C]-1.3335545906429[/C][/ROW]
[ROW][C]86[/C][C]5225.2[/C][C]5223.53032147326[/C][C]-4.10956231689144[/C][C]-0.0983669427981572[/C][C]0.160635424321502[/C][/ROW]
[ROW][C]87[/C][C]5217[/C][C]5218.07717725583[/C][C]-4.15395895430895[/C][C]-0.102713900317264[/C][C]-0.0874244276685519[/C][/ROW]
[ROW][C]88[/C][C]5240[/C][C]5229.04235921793[/C][C]-3.65688753955288[/C][C]-0.0803898828601771[/C][C]0.987890210532655[/C][/ROW]
[ROW][C]89[/C][C]5227.6[/C][C]5226.71091558904[/C][C]-3.61339563738011[/C][C]-0.079455263012317[/C][C]0.0866412200994135[/C][/ROW]
[ROW][C]90[/C][C]5231.8[/C][C]5228.17055771777[/C][C]-3.44704332088791[/C][C]-0.0775972285116061[/C][C]0.33158201824326[/C][/ROW]
[ROW][C]91[/C][C]5233[/C][C]5229.54997736189[/C][C]-3.28879675769317[/C][C]-0.0765532144275303[/C][C]0.315433815751205[/C][/ROW]
[ROW][C]92[/C][C]5171.2[/C][C]5194.49248805619[/C][C]-4.33049709444869[/C][C]-0.0812843547285804[/C][C]-2.07611650460001[/C][/ROW]
[ROW][C]93[/C][C]5173.4[/C][C]5180.52397885111[/C][C]-4.64658278673077[/C][C]-0.0824183464201137[/C][C]-0.629830845186514[/C][/ROW]
[ROW][C]94[/C][C]5088.4[/C][C]5125.38007834281[/C][C]-6.30300480688554[/C][C]-0.0875806580200943[/C][C]-3.29985239266699[/C][/ROW]
[ROW][C]95[/C][C]5098.4[/C][C]5107.18018468361[/C][C]-6.69332649550157[/C][C]-0.0886963226628638[/C][C]-0.777413624950201[/C][/ROW]
[ROW][C]96[/C][C]5128.4[/C][C]5116.66686959087[/C][C]-6.16237861466323[/C][C]-0.0872655009341045[/C][C]1.0572836791368[/C][/ROW]
[ROW][C]97[/C][C]5079[/C][C]5092.96886071487[/C][C]-6.72189500942282[/C][C]-1.29637643927191[/C][C]-1.17873694276591[/C][/ROW]
[ROW][C]98[/C][C]5083.8[/C][C]5084.74509763107[/C][C]-6.77184406273103[/C][C]0.108266828291822[/C][C]-0.0955212178650831[/C][/ROW]
[ROW][C]99[/C][C]5091.4[/C][C]5085.67730001949[/C][C]-6.51755144876422[/C][C]0.130098205288217[/C][C]0.501552635573553[/C][/ROW]
[ROW][C]100[/C][C]5081.6[/C][C]5080.49406598754[/C][C]-6.47364011665566[/C][C]0.131784407805461[/C][C]0.0871797197604084[/C][/ROW]
[ROW][C]101[/C][C]5116.4[/C][C]5098.42444555726[/C][C]-5.6714589006935[/C][C]0.145848265668566[/C][C]1.59498401882174[/C][/ROW]
[ROW][C]102[/C][C]5155[/C][C]5128.63166628544[/C][C]-4.49259107161004[/C][C]0.155724947208174[/C][C]2.34469978239041[/C][/ROW]
[ROW][C]103[/C][C]5102.8[/C][C]5111.71918983018[/C][C]-4.90062668047049[/C][C]0.153948511762305[/C][C]-0.811573240047816[/C][/ROW]
[ROW][C]104[/C][C]5121.6[/C][C]5115.27092304144[/C][C]-4.62293333418612[/C][C]0.154662749599545[/C][C]0.552287236824493[/C][/ROW]
[ROW][C]105[/C][C]5131.6[/C][C]5122.66587643147[/C][C]-4.22807218240573[/C][C]0.15536210561327[/C][C]0.785240779064264[/C][/ROW]
[ROW][C]106[/C][C]5109.4[/C][C]5113.12539507832[/C][C]-4.40263199305884[/C][C]0.155117824504952[/C][C]-0.347103802782109[/C][/ROW]
[ROW][C]107[/C][C]5102.2[/C][C]5104.86381708241[/C][C]-4.52944376293919[/C][C]0.15496363641859[/C][C]-0.252134472303295[/C][/ROW]
[ROW][C]108[/C][C]5117.2[/C][C]5109.99101561407[/C][C]-4.21208218571557[/C][C]0.155317581450124[/C][C]0.630937815625883[/C][/ROW]
[ROW][C]109[/C][C]5083.8[/C][C]5094.7537318667[/C][C]-4.56828159005398[/C][C]-2.98199814651071[/C][C]-0.73873764110092[/C][/ROW]
[ROW][C]110[/C][C]5140.8[/C][C]5119.62315453489[/C][C]-3.59313344877167[/C][C]0.439988711410417[/C][C]1.87769580808582[/C][/ROW]
[ROW][C]111[/C][C]5133.6[/C][C]5125.93766364098[/C][C]-3.26643132307532[/C][C]0.465024630217498[/C][C]0.645276662671968[/C][/ROW]
[ROW][C]112[/C][C]5088[/C][C]5102.37541382925[/C][C]-3.93450245333555[/C][C]0.442519880127454[/C][C]-1.32603142799529[/C][/ROW]
[ROW][C]113[/C][C]5121.6[/C][C]5111.56404386397[/C][C]-3.5028312759721[/C][C]0.44893221210392[/C][C]0.857621220827507[/C][/ROW]
[ROW][C]114[/C][C]5087.2[/C][C]5095.74844160278[/C][C]-3.90774093149263[/C][C]0.446252498417767[/C][C]-0.804578912377338[/C][/ROW]
[ROW][C]115[/C][C]5077.8[/C][C]5083.46945711318[/C][C]-4.18300967523122[/C][C]0.44542250399405[/C][C]-0.546971540629106[/C][/ROW]
[ROW][C]116[/C][C]5136.8[/C][C]5112.26472481919[/C][C]-3.09860370633124[/C][C]0.446980986673262[/C][C]2.15467657824967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302661&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
15445.25445.2000
25403.65417.69000588922-2.01727636011362-2.00692412481831-1.30292005455826
35425.65422.63636472309-1.72024797163078-1.718890003904820.434429061086157
45424.45423.87220930566-1.63542763401175-1.641085023623370.195216727863689
554465436.58320798005-1.30414420271748-1.359732616503660.96155748834909
654495443.78510562331-1.12441830242363-1.218910090775390.572435391812797
75453.45449.40652768074-0.984713177924671-1.1172575895860.454314953058851
854075425.67205612004-1.46093322048589-1.4415416012347-1.53146982757831
954665448.63027585286-0.93803982500581-1.106327568636891.64240989121815
105499.65477.66116745471-0.27914609068664-0.7070356777990162.01359626081904
115473.45475.52921200571-0.320983838568396-0.73107048287873-0.124354789401001
125497.25488.0735525269-0.0229193779167396-0.5684099030332410.862550012711987
135499.45489.93501267971-0.141977053333947.959604246560880.160974476376068
145504.45499.364644938850.270583440264524-0.4070512101218930.530831643106082
155486.65492.311618889130.0474159112494698-0.540940467226101-0.469598114943843
165540.85520.3503504860.750597520861854-0.2227806887892281.84925095757742
175502.85510.798798841380.511658456431514-0.30786258633034-0.685250013906202
1855195515.866862279980.615232797558652-0.2767396692470990.303477278419863
195497.25505.650047937060.367387996295227-0.343170411669312-0.721351684128991
205451.25474.95377128084-0.35558994431815-0.521852912173298-2.06738078050563
2154525462.00228676173-0.654812825497219-0.591249243273066-0.83765352785095
225426.45441.73433137438-1.13060821636995-0.695729762163739-1.30327108342774
235461.45452.87958247789-0.826700570297595-0.6322459095801270.815069186867978
245470.85463.1277740188-0.547205915684815-0.576560265710820.734762581421824
255440.25449.52207029371-0.4500300643782790.531631246666232-0.977675684796928
265418.85430.76317641077-1.13910391721839-0.434286961232774-1.08480048546843
275433.85432.29306530545-1.05647303301494-0.4046102337469280.172518257082832
285416.25422.83630436313-1.29386322866839-0.459667785606666-0.552471463408349
295406.45413.12372428416-1.52402629672584-0.497615261202891-0.55564147349728
305423.25418.53689009047-1.33555528709874-0.4728546762778170.458087627214349
315418.25418.04541061192-1.31250932733825-0.4702253896520920.0557238299809753
3254265422.32031249527-1.15853904691093-0.4541764791930280.368705953868757
335441.65433.15430368527-0.824555649414672-0.4215245699961330.790988569128313
3454175423.76937771009-1.06551244372226-0.443904892577078-0.564341112806844
355405.45413.01974517119-1.34091920279496-0.468357539260519-0.638124884239306
365418.65415.92453847625-1.21899421355729-0.45797781820380.279641322118082
375411.65410.71675859507-1.270685094207883.8203002431131-0.284209634571096
385398.25402.93308984864-1.50405250025397-0.446764201718231-0.397204023745211
395460.25435.70893112175-0.40261260134108-0.1833383404063032.22142408459879
405462.85451.242394085520.085947692286287-0.1156364112693921.04457026585283
415465.45459.492343198930.332133548012581-0.09346173842058460.536226339849777
425431.65443.63385209829-0.154516017155651-0.126181914932274-1.06362453332585
435431.65436.71320144312-0.358341226187323-0.137627863691971-0.444407151678705
445454.85447.05513522104-0.0346135097429262-0.1213349176602540.702619062676369
455419.85431.4132119183-0.509144567648178-0.1435641537585-1.02455532774192
465417.85423.43832865718-0.737278253124468-0.153697936215244-0.489967048993752
475449.85438.40224842347-0.255157201869922-0.1332102808331941.03019482465349
485435.45436.64090615473-0.301619187079886-0.13510693627599-0.0988014428132841
4954145424.21305621865-0.575383499653223-1.38640364234442-0.842754230528027
505433.65429.47054115622-0.3719946951868030.1955300560203660.361502389518849
515406.65415.96225483121-0.802497633800980.119932252032786-0.852496815408907
525373.65391.12319338467-1.570173330523790.0481085829619314-1.5727020565278
535393.25391.62794705147-1.504512250856420.0517638466175770.13593412602717
5453705378.48912346346-1.871889746317940.0376699543925818-0.762226470356493
555346.65359.28232402079-2.419682573475020.0210830863822799-1.13553369217666
565390.45376.1968113501-1.807574818105960.03716456225004331.26629271940232
575362.45367.45089607978-2.027728461808690.0318662529993498-0.454359894174743
5853625363.42967514141-2.091126927799330.030429406707232-0.130527006444723
5953725367.47298945674-1.895600737945370.03465818114392810.401611989167362
605359.25361.87713746284-2.013790147651930.0322037322591682-0.242221361924953
615351.65355.74270320928-2.12664864634109-1.15849868143616-0.282332092901822
625357.85356.0227425032-2.044287878900520.1288140801053670.150687174575831
635326.85338.17441013527-2.566021174341960.0566383073727775-1.02674929153457
645364.25352.07764308513-2.030270824444490.09363498118319611.07666530909195
655354.25352.3898772001-1.954479008999840.0964991034985720.153267161405934
665337.65342.97068335651-2.195641467226480.0907686179736853-0.488390749226638
675328.25333.4627720384-2.431907739709780.0866645450606621-0.478357691294307
685302.65314.56534241556-2.964325122515220.0790309932570598-1.07703619071424
695303.45306.81992632684-3.11907374578760.0770530853595456-0.312712483609957
705346.45328.31315463069-2.321636114416160.08652541138764981.60968075486103
715308.45315.78280186714-2.652730479591660.0827944878012157-0.667623481582373
7253225318.20466742011-2.487990847906150.08457267531415770.331846546018019
735345.25331.81502447331-2.007091304870221.748884010346971.09325101134806
745293.25308.37324444727-2.73093669903427-0.336487991527837-1.35143201573283
755295.45299.91043567826-2.92044907410384-0.358172362599543-0.372709019958955
765311.25305.40158352042-2.64471256224501-0.3431763822331520.549699691203877
775235.25263.94741484672-3.91279930194803-0.378234767859808-2.53766635925883
7852395248.10514389686-4.30219943067159-0.38438035205841-0.7799856582037
795270.45259.38737121042-3.79353902540884-0.3790565431322071.01884651770422
8052555255.46976849211-3.79758947519735-0.379089036295105-0.00811015606996152
815264.45259.24365170763-3.55029250384991-0.3773982150928590.494928013131486
825281.85270.99288464199-3.05035863548412-0.3742954214156971.0000521714362
835255.65261.02845047934-3.2763874483-0.375611243086266-0.451923536875996
845241.45248.52224279405-3.57825059197913-0.377285881088922-0.603270380542677
855212.25225.18961419973-4.194391585289241.28287583973141-1.3335545906429
865225.25223.53032147326-4.10956231689144-0.09836694279815720.160635424321502
8752175218.07717725583-4.15395895430895-0.102713900317264-0.0874244276685519
8852405229.04235921793-3.65688753955288-0.08038988286017710.987890210532655
895227.65226.71091558904-3.61339563738011-0.0794552630123170.0866412200994135
905231.85228.17055771777-3.44704332088791-0.07759722851160610.33158201824326
9152335229.54997736189-3.28879675769317-0.07655321442753030.315433815751205
925171.25194.49248805619-4.33049709444869-0.0812843547285804-2.07611650460001
935173.45180.52397885111-4.64658278673077-0.0824183464201137-0.629830845186514
945088.45125.38007834281-6.30300480688554-0.0875806580200943-3.29985239266699
955098.45107.18018468361-6.69332649550157-0.0886963226628638-0.777413624950201
965128.45116.66686959087-6.16237861466323-0.08726550093410451.0572836791368
9750795092.96886071487-6.72189500942282-1.29637643927191-1.17873694276591
985083.85084.74509763107-6.771844062731030.108266828291822-0.0955212178650831
995091.45085.67730001949-6.517551448764220.1300982052882170.501552635573553
1005081.65080.49406598754-6.473640116655660.1317844078054610.0871797197604084
1015116.45098.42444555726-5.67145890069350.1458482656685661.59498401882174
10251555128.63166628544-4.492591071610040.1557249472081742.34469978239041
1035102.85111.71918983018-4.900626680470490.153948511762305-0.811573240047816
1045121.65115.27092304144-4.622933334186120.1546627495995450.552287236824493
1055131.65122.66587643147-4.228072182405730.155362105613270.785240779064264
1065109.45113.12539507832-4.402631993058840.155117824504952-0.347103802782109
1075102.25104.86381708241-4.529443762939190.15496363641859-0.252134472303295
1085117.25109.99101561407-4.212082185715570.1553175814501240.630937815625883
1095083.85094.7537318667-4.56828159005398-2.98199814651071-0.73873764110092
1105140.85119.62315453489-3.593133448771670.4399887114104171.87769580808582
1115133.65125.93766364098-3.266431323075320.4650246302174980.645276662671968
11250885102.37541382925-3.934502453335550.442519880127454-1.32603142799529
1135121.65111.56404386397-3.50283127597210.448932212103920.857621220827507
1145087.25095.74844160278-3.907740931492630.446252498417767-0.804578912377338
1155077.85083.46945711318-4.183009675231220.44542250399405-0.546971540629106
1165136.85112.26472481919-3.098603706331240.4469809866732622.15467657824967







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15112.154731734345110.98467502071.17005671363702
25104.564283824725107.86592670203-3.3016428773131
35101.83980613685104.74717838336-2.90737224655868
45108.67018677565101.628430064697.04175671090608
55092.98299080175098.50968174602-5.52669094432138
65090.296592173575095.39093342735-5.09434125377433
75091.669565769925092.27218510868-0.602619338754304
85093.881913538965089.153436790014.72847674894826
95090.133637217975086.034688471344.09894874663025
105087.264735632885082.915940152674.34879548021271
115078.535209895475079.797191834-1.26198193852408
125073.985057714245076.67844351533-2.69338580108845

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5112.15473173434 & 5110.9846750207 & 1.17005671363702 \tabularnewline
2 & 5104.56428382472 & 5107.86592670203 & -3.3016428773131 \tabularnewline
3 & 5101.8398061368 & 5104.74717838336 & -2.90737224655868 \tabularnewline
4 & 5108.6701867756 & 5101.62843006469 & 7.04175671090608 \tabularnewline
5 & 5092.9829908017 & 5098.50968174602 & -5.52669094432138 \tabularnewline
6 & 5090.29659217357 & 5095.39093342735 & -5.09434125377433 \tabularnewline
7 & 5091.66956576992 & 5092.27218510868 & -0.602619338754304 \tabularnewline
8 & 5093.88191353896 & 5089.15343679001 & 4.72847674894826 \tabularnewline
9 & 5090.13363721797 & 5086.03468847134 & 4.09894874663025 \tabularnewline
10 & 5087.26473563288 & 5082.91594015267 & 4.34879548021271 \tabularnewline
11 & 5078.53520989547 & 5079.797191834 & -1.26198193852408 \tabularnewline
12 & 5073.98505771424 & 5076.67844351533 & -2.69338580108845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302661&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]5112.15473173434[/C][C]5110.9846750207[/C][C]1.17005671363702[/C][/ROW]
[ROW][C]2[/C][C]5104.56428382472[/C][C]5107.86592670203[/C][C]-3.3016428773131[/C][/ROW]
[ROW][C]3[/C][C]5101.8398061368[/C][C]5104.74717838336[/C][C]-2.90737224655868[/C][/ROW]
[ROW][C]4[/C][C]5108.6701867756[/C][C]5101.62843006469[/C][C]7.04175671090608[/C][/ROW]
[ROW][C]5[/C][C]5092.9829908017[/C][C]5098.50968174602[/C][C]-5.52669094432138[/C][/ROW]
[ROW][C]6[/C][C]5090.29659217357[/C][C]5095.39093342735[/C][C]-5.09434125377433[/C][/ROW]
[ROW][C]7[/C][C]5091.66956576992[/C][C]5092.27218510868[/C][C]-0.602619338754304[/C][/ROW]
[ROW][C]8[/C][C]5093.88191353896[/C][C]5089.15343679001[/C][C]4.72847674894826[/C][/ROW]
[ROW][C]9[/C][C]5090.13363721797[/C][C]5086.03468847134[/C][C]4.09894874663025[/C][/ROW]
[ROW][C]10[/C][C]5087.26473563288[/C][C]5082.91594015267[/C][C]4.34879548021271[/C][/ROW]
[ROW][C]11[/C][C]5078.53520989547[/C][C]5079.797191834[/C][C]-1.26198193852408[/C][/ROW]
[ROW][C]12[/C][C]5073.98505771424[/C][C]5076.67844351533[/C][C]-2.69338580108845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302661&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
15112.154731734345110.98467502071.17005671363702
25104.564283824725107.86592670203-3.3016428773131
35101.83980613685104.74717838336-2.90737224655868
45108.67018677565101.628430064697.04175671090608
55092.98299080175098.50968174602-5.52669094432138
65090.296592173575095.39093342735-5.09434125377433
75091.669565769925092.27218510868-0.602619338754304
85093.881913538965089.153436790014.72847674894826
95090.133637217975086.034688471344.09894874663025
105087.264735632885082.915940152674.34879548021271
115078.535209895475079.797191834-1.26198193852408
125073.985057714245076.67844351533-2.69338580108845



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')