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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationThu, 22 Dec 2016 18:41:27 +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/t14824287153893oapuzv0n0xz.htm/, Retrieved Mon, 29 Apr 2024 04:32:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302596, Retrieved Mon, 29 Apr 2024 04:32:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Structural time s...] [2016-12-22 17:41:27] [d4ebbcc95b180bc93fc42d05f31a3dde] [Current]
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Dataseries X:
5572.3
5565.55
5576.85
5577.3
5598.85
5752.55
5782.2
5763
5694.6
5686.85
5691.6
5674.15
5635.55
5652.6
5675.7
5692.25
5747.05
5854.15
5894.8
5839.4
5778.15
5797.75
5790.7
5786.3
5758.6
5764.75
5804.75
5801.35
5829.75
5913.7
5962
5920.25
5879.1
5902.3
5889.95
5873.9
5856.1
5870.8
5900.1
5900.6
5944.3
6066.2
6098.75
6058.4
5998
6022.4
6018.7
5989.95
5972.55
5985.35
6004.45
6004.1
6071.05
6143.55
6191.25
6167.5
6081.35
6124.25
6118.3
6097.8
6074.55
6083.9
6084.65
6099.8
6124.45
6235.65
6278.05
6254.4
6177.3
6205.95
6217.2
6190.8
6189.55
6179.5
6195.35
6213
6243.45
6361.75
6395.2
6356.6
6276.5
6306.25
6318.4
6284.9
6249.5
6256
6272.9
6273.65
6313.95
6396.85
6426.35
6382.6
6319
6329.5
6321.8
6312.35
6260
6283.6
6295.15
6309.15
6315.75
6427.95
6446.55
6385.65
6351.45
6359.1
6350.05
6335.6
6333.55
6348.55
6369.1
6372.75
6413.95
6528.6
6558.4
6501.95
6430.5




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302596&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302596&T=0

As an alternative you can also use a QR Code:  

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

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







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
15572.35572.3000
25565.555566.74448411525-5.65423354330478-1.19448411524547-0.283552732468196
35576.855572.957505543853.090892571478473.892494456150430.427941436310622
45577.35577.585547621814.28281310795655-0.2855476218072690.0551230452832051
55598.855595.7398813637614.80894613036173.110118636245190.478664141064104
65752.555727.33005409951103.40460349060225.21994590048824.054060575698
75782.25797.4283651895878.0851460396642-15.2283651895797-1.15713967235811
857635781.843859676016.86559292318837-18.8438596760143-3.25463999646315
95694.65706.81572253158-55.3906393532818-12.2157225315755-2.84508514966757
105686.855675.99960724985-36.711084085594210.85039275015290.853638261311994
115691.65683.41825519128-3.167476731813638.181744808716161.53291313548044
125674.155677.71371222964-5.09597711100001-3.56371222963829-0.0881307498432941
135635.555642.1638762226-28.1973927116656-6.61387622260283-1.05838340798167
145652.65645.1823014174-4.440263960130727.417698582602261.10193967648718
155675.75662.54128211211.474547911197113.1587178879990.726051785008695
165692.255689.0916600019322.53371753645583.158339998069170.512258596445967
175747.055766.2602086331462.6474832571426-19.21020863313671.82854440337346
185854.155831.5993855435664.611811684765322.55061445643990.0896989288262441
195894.85891.6713619961961.2948900854873.12863800380928-0.151667823113679
205839.45858.01942008216-8.14024102620836-18.6194200821579-3.17308648376945
215778.155801.74064156665-43.3472860914712-23.5906415666463-1.60890063210728
225797.755789.00907857013-20.95704616029998.740921429872971.02325564289546
235790.75780.04787832127-12.186006369891410.6521216787250.400829607597672
245786.35778.41002078766-4.479796328181667.88997921233870.352242840600584
255758.65771.909134071-5.95626927044819-13.3091340709971-0.0676585804259621
265764.755760.28483373442-10.10206503486654.4651662655804-0.189719448561434
275804.755784.373019386614.615179819954720.37698061340381.12784051756036
285801.355812.2244785725824.1797349844792-10.87447857257620.439642747699125
295829.755852.554323498635.8912865389477-22.80432349859510.535393237397038
305913.75894.4886829584840.257524788118419.21131704152430.199243671124289
3159625933.6399442355639.458766129169728.3600557644354-0.0365122649578506
325920.255933.6102491068110.9174527573752-13.3602491068137-1.30450448592699
335879.15915.68643418929-9.93564441800693-36.5864341892845-0.952929719523747
345902.35897.79823847143-15.68531867377694.50176152857231-0.262770148606886
355889.955881.71352150152-15.97395782042938.23647849847907-0.0131904220535858
365873.95863.84774220965-17.340232140233610.0522577903532-0.0624708536040089
375856.15861.99328395163-6.1491625709692-5.893283951631240.512342278195063
385870.85870.960751207734.77087955487917-0.1607512077278910.49894490107538
395900.15881.458726124988.885367936180418.64127387501780.187875966086818
405900.65911.7265697210924.2388106219106-11.12656972108730.703650179933587
415944.35965.4035646311245.4323371829198-21.10356463111850.969426445738213
426066.26042.8796540342668.464737942775923.32034596574471.05142045989749
436098.756071.160408075139.615698126615627.5895919248952-1.3181868618805
446058.46072.0944029439911.8279058875208-13.6944029439902-1.2700691168778
4559986041.60699434434-18.5848549355088-43.6069943443412-1.38981748976827
466022.46017.22735392661-22.74961142886165.17264607338596-0.190328824242338
476018.76005.91791915678-14.530843214547512.78208084322170.375604824192353
485989.955984.52437701127-19.45970049809725.42562298872879-0.2253790800864
495972.555976.86307453113-10.980822133043-4.313074531129880.387875989685924
505985.355980.86807748793-0.2194967611884424.481922512069560.491582313313261
516004.455988.802951422865.6174524423900815.64704857713720.266618499881007
526004.16020.22527159624.0822107801754-16.1252715960020.84520619818899
536071.056094.1881636254259.8389491236794-23.13816362542031.63551458638766
546143.556121.0786958544536.233838621915722.4713041455467-1.07802577664668
556191.256153.4843609734633.494213497601337.7656390265369-0.12515610491091
566167.56172.8550344615123.3846554048305-5.35503446150715-0.462024942982046
576081.356137.02341529918-19.0206096067299-55.6734152991785-1.93790855657361
586124.256119.65434523894-17.83789495857744.595654761061670.0540493124729241
596118.36102.52586208823-17.330004648765515.77413791176910.0232125935216533
606097.86092.0636775266-12.41317414719755.736322473395180.224814139470516
616074.556080.03546957989-12.1374500176745-5.485469579885270.0126074310407811
626083.96076.90623014615-5.690558659191266.993769853852170.294496427648438
636084.656076.28827349133-2.067782081571028.361726508674170.165509065306765
646099.86120.7879976143631.1824453622889-20.98799761435931.52110069957679
656124.456143.7979752752125.3397102833438-19.347975275208-0.267211488098053
666235.656206.2938622221951.900434127045229.35613777781021.21336959455014
676278.056242.1432231471540.436288720663335.9067768528483-0.523702633937661
686254.46249.8703033982317.07631560913724.52969660177012-1.06748925829678
696177.36239.12519868537-2.79878597035357-61.8251986853729-0.908295532416477
706205.956207.70238133769-23.2484143763256-1.7523813376949-0.934561200969447
716217.26198.73693234196-13.045635105740618.46306765804030.466334781772391
726190.86184.30123755763-14.03872771008136.49876244237162-0.0454032792131953
736189.556189.79116442315-0.0833042995187423-0.2411644231458180.637935385832431
746179.56176.00877737122-9.865766269141443.49122262878418-0.446883630567242
756195.356192.253018347888.752350987900263.096981652124190.850663734556073
7662136227.7252483118727.8024539945992-14.725248311870.871211172830762
776243.456272.8656326415340.1751827911506-29.415632641530.565785991298826
786361.756327.400290531650.423240941593734.34970946839570.468248805891212
796395.26356.7491840626435.392675016149638.4508159373558-0.686641148725439
806356.66352.45649099397.09554715472864.14350900609937-1.29301242829322
816276.56334.83821958326-10.5286665682362-58.3382195832623-0.805427340890319
826306.256313.72146845509-18.0798738964668-7.47146845508976-0.345109969258774
836318.46298.39353908411-16.11724429287520.00646091589470.0897091710227974
846284.96281.84706143184-16.42342344189323.05293856816244-0.0139970466575053
856249.56247.16953470449-29.44618447674172.33046529550915-0.5952061823402
8662566250.20701084516-6.286919396178235.792989154844461.05800683507959
876272.96271.8798522000713.62579304813531.020147799931270.909865802224817
886273.656293.9221589036719.6193438710165-20.27215890367270.274050382304599
896313.956343.5196777720440.982655622515-29.56967777203580.976820331008873
906396.856364.032782742426.392995831843232.8172172575999-0.666699922678851
916426.356379.3178470293118.479736161799347.0321529706877-0.361517961962233
926382.66376.629631160133.404937842714985.97036883986731-0.688799045485832
9363196375.45177636070.141306274053867-56.4517763607046-0.149146838620569
946329.56344.8557392155-21.7496922488967-15.3557392154979-1.00051681514605
956321.86303.05034724937-36.034572308685118.7496527506323-0.652962414206784
966312.356294.91359544106-16.159787502518817.43640455893640.908519769122728
9762606268.6264800518-23.375001428618-8.62648005179748-0.329740570646352
986283.66276.76626697228-0.9354598575517776.833733027722181.0251623066047
996295.156294.1979329668212.13176284090280.9520670331830640.597098038266722
1006309.156333.4068445258131.3943130062282-24.25684452580840.880664231415156
1016315.756345.9426890540917.9707994557634-30.1926890540933-0.613735860018762
1026427.956387.4231325717634.70846508858440.52686742823790.764910222235321
1036446.556401.3046342985719.886416368522845.2453657014303-0.677177649935168
1046385.656386.46817575877-4.81539197943503-0.818175758768894-1.12864942215936
1056351.456394.398236204484.25073678125305-42.94823620447730.414314991012859
1066359.16374.24970345374-13.1060109396217-15.1497034537442-0.793305754810963
1076350.056340.89161200598-27.51480642843559.15838799402177-0.658638641660453
1086335.66312.9325708752-27.830936375821522.6674291248031-0.014450270671156
1096333.556337.995825431889.8097225036725-4.445825431881471.7201081798669
1106348.556348.3941476205210.22835985727210.1558523794835560.0191262110396667
1116369.16371.9655391116219.7122206119677-2.865539111620840.433368731592919
1126372.756393.1203262192820.737505709552-20.37032621928340.0468714671072726
1136413.956445.6625577347443.3530166018303-31.71255773473671.03394620758353
1146528.66484.7360958491140.309334286464343.863904150887-0.139101857974582
1156558.46508.2843410948428.392023143833250.1156589051608-0.544489796484064
1166501.956512.5053977837211.213193533224-10.5553977837162-0.784908405360404
1176430.56475.7845957573-22.8484932028469-45.2845957572968-1.55657925592384

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5572.3 & 5572.3 & 0 & 0 & 0 \tabularnewline
2 & 5565.55 & 5566.74448411525 & -5.65423354330478 & -1.19448411524547 & -0.283552732468196 \tabularnewline
3 & 5576.85 & 5572.95750554385 & 3.09089257147847 & 3.89249445615043 & 0.427941436310622 \tabularnewline
4 & 5577.3 & 5577.58554762181 & 4.28281310795655 & -0.285547621807269 & 0.0551230452832051 \tabularnewline
5 & 5598.85 & 5595.73988136376 & 14.8089461303617 & 3.11011863624519 & 0.478664141064104 \tabularnewline
6 & 5752.55 & 5727.33005409951 & 103.404603490602 & 25.2199459004882 & 4.054060575698 \tabularnewline
7 & 5782.2 & 5797.42836518958 & 78.0851460396642 & -15.2283651895797 & -1.15713967235811 \tabularnewline
8 & 5763 & 5781.84385967601 & 6.86559292318837 & -18.8438596760143 & -3.25463999646315 \tabularnewline
9 & 5694.6 & 5706.81572253158 & -55.3906393532818 & -12.2157225315755 & -2.84508514966757 \tabularnewline
10 & 5686.85 & 5675.99960724985 & -36.7110840855942 & 10.8503927501529 & 0.853638261311994 \tabularnewline
11 & 5691.6 & 5683.41825519128 & -3.16747673181363 & 8.18174480871616 & 1.53291313548044 \tabularnewline
12 & 5674.15 & 5677.71371222964 & -5.09597711100001 & -3.56371222963829 & -0.0881307498432941 \tabularnewline
13 & 5635.55 & 5642.1638762226 & -28.1973927116656 & -6.61387622260283 & -1.05838340798167 \tabularnewline
14 & 5652.6 & 5645.1823014174 & -4.44026396013072 & 7.41769858260226 & 1.10193967648718 \tabularnewline
15 & 5675.7 & 5662.541282112 & 11.4745479111971 & 13.158717887999 & 0.726051785008695 \tabularnewline
16 & 5692.25 & 5689.09166000193 & 22.5337175364558 & 3.15833999806917 & 0.512258596445967 \tabularnewline
17 & 5747.05 & 5766.26020863314 & 62.6474832571426 & -19.2102086331367 & 1.82854440337346 \tabularnewline
18 & 5854.15 & 5831.59938554356 & 64.6118116847653 & 22.5506144564399 & 0.0896989288262441 \tabularnewline
19 & 5894.8 & 5891.67136199619 & 61.294890085487 & 3.12863800380928 & -0.151667823113679 \tabularnewline
20 & 5839.4 & 5858.01942008216 & -8.14024102620836 & -18.6194200821579 & -3.17308648376945 \tabularnewline
21 & 5778.15 & 5801.74064156665 & -43.3472860914712 & -23.5906415666463 & -1.60890063210728 \tabularnewline
22 & 5797.75 & 5789.00907857013 & -20.9570461602999 & 8.74092142987297 & 1.02325564289546 \tabularnewline
23 & 5790.7 & 5780.04787832127 & -12.1860063698914 & 10.652121678725 & 0.400829607597672 \tabularnewline
24 & 5786.3 & 5778.41002078766 & -4.47979632818166 & 7.8899792123387 & 0.352242840600584 \tabularnewline
25 & 5758.6 & 5771.909134071 & -5.95626927044819 & -13.3091340709971 & -0.0676585804259621 \tabularnewline
26 & 5764.75 & 5760.28483373442 & -10.1020650348665 & 4.4651662655804 & -0.189719448561434 \tabularnewline
27 & 5804.75 & 5784.3730193866 & 14.6151798199547 & 20.3769806134038 & 1.12784051756036 \tabularnewline
28 & 5801.35 & 5812.22447857258 & 24.1797349844792 & -10.8744785725762 & 0.439642747699125 \tabularnewline
29 & 5829.75 & 5852.5543234986 & 35.8912865389477 & -22.8043234985951 & 0.535393237397038 \tabularnewline
30 & 5913.7 & 5894.48868295848 & 40.2575247881184 & 19.2113170415243 & 0.199243671124289 \tabularnewline
31 & 5962 & 5933.63994423556 & 39.4587661291697 & 28.3600557644354 & -0.0365122649578506 \tabularnewline
32 & 5920.25 & 5933.61024910681 & 10.9174527573752 & -13.3602491068137 & -1.30450448592699 \tabularnewline
33 & 5879.1 & 5915.68643418929 & -9.93564441800693 & -36.5864341892845 & -0.952929719523747 \tabularnewline
34 & 5902.3 & 5897.79823847143 & -15.6853186737769 & 4.50176152857231 & -0.262770148606886 \tabularnewline
35 & 5889.95 & 5881.71352150152 & -15.9739578204293 & 8.23647849847907 & -0.0131904220535858 \tabularnewline
36 & 5873.9 & 5863.84774220965 & -17.3402321402336 & 10.0522577903532 & -0.0624708536040089 \tabularnewline
37 & 5856.1 & 5861.99328395163 & -6.1491625709692 & -5.89328395163124 & 0.512342278195063 \tabularnewline
38 & 5870.8 & 5870.96075120773 & 4.77087955487917 & -0.160751207727891 & 0.49894490107538 \tabularnewline
39 & 5900.1 & 5881.45872612498 & 8.8853679361804 & 18.6412738750178 & 0.187875966086818 \tabularnewline
40 & 5900.6 & 5911.72656972109 & 24.2388106219106 & -11.1265697210873 & 0.703650179933587 \tabularnewline
41 & 5944.3 & 5965.40356463112 & 45.4323371829198 & -21.1035646311185 & 0.969426445738213 \tabularnewline
42 & 6066.2 & 6042.87965403426 & 68.4647379427759 & 23.3203459657447 & 1.05142045989749 \tabularnewline
43 & 6098.75 & 6071.1604080751 & 39.6156981266156 & 27.5895919248952 & -1.3181868618805 \tabularnewline
44 & 6058.4 & 6072.09440294399 & 11.8279058875208 & -13.6944029439902 & -1.2700691168778 \tabularnewline
45 & 5998 & 6041.60699434434 & -18.5848549355088 & -43.6069943443412 & -1.38981748976827 \tabularnewline
46 & 6022.4 & 6017.22735392661 & -22.7496114288616 & 5.17264607338596 & -0.190328824242338 \tabularnewline
47 & 6018.7 & 6005.91791915678 & -14.5308432145475 & 12.7820808432217 & 0.375604824192353 \tabularnewline
48 & 5989.95 & 5984.52437701127 & -19.4597004980972 & 5.42562298872879 & -0.2253790800864 \tabularnewline
49 & 5972.55 & 5976.86307453113 & -10.980822133043 & -4.31307453112988 & 0.387875989685924 \tabularnewline
50 & 5985.35 & 5980.86807748793 & -0.219496761188442 & 4.48192251206956 & 0.491582313313261 \tabularnewline
51 & 6004.45 & 5988.80295142286 & 5.61745244239008 & 15.6470485771372 & 0.266618499881007 \tabularnewline
52 & 6004.1 & 6020.225271596 & 24.0822107801754 & -16.125271596002 & 0.84520619818899 \tabularnewline
53 & 6071.05 & 6094.18816362542 & 59.8389491236794 & -23.1381636254203 & 1.63551458638766 \tabularnewline
54 & 6143.55 & 6121.07869585445 & 36.2338386219157 & 22.4713041455467 & -1.07802577664668 \tabularnewline
55 & 6191.25 & 6153.48436097346 & 33.4942134976013 & 37.7656390265369 & -0.12515610491091 \tabularnewline
56 & 6167.5 & 6172.85503446151 & 23.3846554048305 & -5.35503446150715 & -0.462024942982046 \tabularnewline
57 & 6081.35 & 6137.02341529918 & -19.0206096067299 & -55.6734152991785 & -1.93790855657361 \tabularnewline
58 & 6124.25 & 6119.65434523894 & -17.8378949585774 & 4.59565476106167 & 0.0540493124729241 \tabularnewline
59 & 6118.3 & 6102.52586208823 & -17.3300046487655 & 15.7741379117691 & 0.0232125935216533 \tabularnewline
60 & 6097.8 & 6092.0636775266 & -12.4131741471975 & 5.73632247339518 & 0.224814139470516 \tabularnewline
61 & 6074.55 & 6080.03546957989 & -12.1374500176745 & -5.48546957988527 & 0.0126074310407811 \tabularnewline
62 & 6083.9 & 6076.90623014615 & -5.69055865919126 & 6.99376985385217 & 0.294496427648438 \tabularnewline
63 & 6084.65 & 6076.28827349133 & -2.06778208157102 & 8.36172650867417 & 0.165509065306765 \tabularnewline
64 & 6099.8 & 6120.78799761436 & 31.1824453622889 & -20.9879976143593 & 1.52110069957679 \tabularnewline
65 & 6124.45 & 6143.79797527521 & 25.3397102833438 & -19.347975275208 & -0.267211488098053 \tabularnewline
66 & 6235.65 & 6206.29386222219 & 51.9004341270452 & 29.3561377778102 & 1.21336959455014 \tabularnewline
67 & 6278.05 & 6242.14322314715 & 40.4362887206633 & 35.9067768528483 & -0.523702633937661 \tabularnewline
68 & 6254.4 & 6249.87030339823 & 17.0763156091372 & 4.52969660177012 & -1.06748925829678 \tabularnewline
69 & 6177.3 & 6239.12519868537 & -2.79878597035357 & -61.8251986853729 & -0.908295532416477 \tabularnewline
70 & 6205.95 & 6207.70238133769 & -23.2484143763256 & -1.7523813376949 & -0.934561200969447 \tabularnewline
71 & 6217.2 & 6198.73693234196 & -13.0456351057406 & 18.4630676580403 & 0.466334781772391 \tabularnewline
72 & 6190.8 & 6184.30123755763 & -14.0387277100813 & 6.49876244237162 & -0.0454032792131953 \tabularnewline
73 & 6189.55 & 6189.79116442315 & -0.0833042995187423 & -0.241164423145818 & 0.637935385832431 \tabularnewline
74 & 6179.5 & 6176.00877737122 & -9.86576626914144 & 3.49122262878418 & -0.446883630567242 \tabularnewline
75 & 6195.35 & 6192.25301834788 & 8.75235098790026 & 3.09698165212419 & 0.850663734556073 \tabularnewline
76 & 6213 & 6227.72524831187 & 27.8024539945992 & -14.72524831187 & 0.871211172830762 \tabularnewline
77 & 6243.45 & 6272.86563264153 & 40.1751827911506 & -29.41563264153 & 0.565785991298826 \tabularnewline
78 & 6361.75 & 6327.4002905316 & 50.4232409415937 & 34.3497094683957 & 0.468248805891212 \tabularnewline
79 & 6395.2 & 6356.74918406264 & 35.3926750161496 & 38.4508159373558 & -0.686641148725439 \tabularnewline
80 & 6356.6 & 6352.4564909939 & 7.0955471547286 & 4.14350900609937 & -1.29301242829322 \tabularnewline
81 & 6276.5 & 6334.83821958326 & -10.5286665682362 & -58.3382195832623 & -0.805427340890319 \tabularnewline
82 & 6306.25 & 6313.72146845509 & -18.0798738964668 & -7.47146845508976 & -0.345109969258774 \tabularnewline
83 & 6318.4 & 6298.39353908411 & -16.117244292875 & 20.0064609158947 & 0.0897091710227974 \tabularnewline
84 & 6284.9 & 6281.84706143184 & -16.4234234418932 & 3.05293856816244 & -0.0139970466575053 \tabularnewline
85 & 6249.5 & 6247.16953470449 & -29.4461844767417 & 2.33046529550915 & -0.5952061823402 \tabularnewline
86 & 6256 & 6250.20701084516 & -6.28691939617823 & 5.79298915484446 & 1.05800683507959 \tabularnewline
87 & 6272.9 & 6271.87985220007 & 13.6257930481353 & 1.02014779993127 & 0.909865802224817 \tabularnewline
88 & 6273.65 & 6293.92215890367 & 19.6193438710165 & -20.2721589036727 & 0.274050382304599 \tabularnewline
89 & 6313.95 & 6343.51967777204 & 40.982655622515 & -29.5696777720358 & 0.976820331008873 \tabularnewline
90 & 6396.85 & 6364.0327827424 & 26.3929958318432 & 32.8172172575999 & -0.666699922678851 \tabularnewline
91 & 6426.35 & 6379.31784702931 & 18.4797361617993 & 47.0321529706877 & -0.361517961962233 \tabularnewline
92 & 6382.6 & 6376.62963116013 & 3.40493784271498 & 5.97036883986731 & -0.688799045485832 \tabularnewline
93 & 6319 & 6375.4517763607 & 0.141306274053867 & -56.4517763607046 & -0.149146838620569 \tabularnewline
94 & 6329.5 & 6344.8557392155 & -21.7496922488967 & -15.3557392154979 & -1.00051681514605 \tabularnewline
95 & 6321.8 & 6303.05034724937 & -36.0345723086851 & 18.7496527506323 & -0.652962414206784 \tabularnewline
96 & 6312.35 & 6294.91359544106 & -16.1597875025188 & 17.4364045589364 & 0.908519769122728 \tabularnewline
97 & 6260 & 6268.6264800518 & -23.375001428618 & -8.62648005179748 & -0.329740570646352 \tabularnewline
98 & 6283.6 & 6276.76626697228 & -0.935459857551777 & 6.83373302772218 & 1.0251623066047 \tabularnewline
99 & 6295.15 & 6294.19793296682 & 12.1317628409028 & 0.952067033183064 & 0.597098038266722 \tabularnewline
100 & 6309.15 & 6333.40684452581 & 31.3943130062282 & -24.2568445258084 & 0.880664231415156 \tabularnewline
101 & 6315.75 & 6345.94268905409 & 17.9707994557634 & -30.1926890540933 & -0.613735860018762 \tabularnewline
102 & 6427.95 & 6387.42313257176 & 34.708465088584 & 40.5268674282379 & 0.764910222235321 \tabularnewline
103 & 6446.55 & 6401.30463429857 & 19.8864163685228 & 45.2453657014303 & -0.677177649935168 \tabularnewline
104 & 6385.65 & 6386.46817575877 & -4.81539197943503 & -0.818175758768894 & -1.12864942215936 \tabularnewline
105 & 6351.45 & 6394.39823620448 & 4.25073678125305 & -42.9482362044773 & 0.414314991012859 \tabularnewline
106 & 6359.1 & 6374.24970345374 & -13.1060109396217 & -15.1497034537442 & -0.793305754810963 \tabularnewline
107 & 6350.05 & 6340.89161200598 & -27.5148064284355 & 9.15838799402177 & -0.658638641660453 \tabularnewline
108 & 6335.6 & 6312.9325708752 & -27.8309363758215 & 22.6674291248031 & -0.014450270671156 \tabularnewline
109 & 6333.55 & 6337.99582543188 & 9.8097225036725 & -4.44582543188147 & 1.7201081798669 \tabularnewline
110 & 6348.55 & 6348.39414762052 & 10.2283598572721 & 0.155852379483556 & 0.0191262110396667 \tabularnewline
111 & 6369.1 & 6371.96553911162 & 19.7122206119677 & -2.86553911162084 & 0.433368731592919 \tabularnewline
112 & 6372.75 & 6393.12032621928 & 20.737505709552 & -20.3703262192834 & 0.0468714671072726 \tabularnewline
113 & 6413.95 & 6445.66255773474 & 43.3530166018303 & -31.7125577347367 & 1.03394620758353 \tabularnewline
114 & 6528.6 & 6484.73609584911 & 40.3093342864643 & 43.863904150887 & -0.139101857974582 \tabularnewline
115 & 6558.4 & 6508.28434109484 & 28.3920231438332 & 50.1156589051608 & -0.544489796484064 \tabularnewline
116 & 6501.95 & 6512.50539778372 & 11.213193533224 & -10.5553977837162 & -0.784908405360404 \tabularnewline
117 & 6430.5 & 6475.7845957573 & -22.8484932028469 & -45.2845957572968 & -1.55657925592384 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302596&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]5572.3[/C][C]5572.3[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5565.55[/C][C]5566.74448411525[/C][C]-5.65423354330478[/C][C]-1.19448411524547[/C][C]-0.283552732468196[/C][/ROW]
[ROW][C]3[/C][C]5576.85[/C][C]5572.95750554385[/C][C]3.09089257147847[/C][C]3.89249445615043[/C][C]0.427941436310622[/C][/ROW]
[ROW][C]4[/C][C]5577.3[/C][C]5577.58554762181[/C][C]4.28281310795655[/C][C]-0.285547621807269[/C][C]0.0551230452832051[/C][/ROW]
[ROW][C]5[/C][C]5598.85[/C][C]5595.73988136376[/C][C]14.8089461303617[/C][C]3.11011863624519[/C][C]0.478664141064104[/C][/ROW]
[ROW][C]6[/C][C]5752.55[/C][C]5727.33005409951[/C][C]103.404603490602[/C][C]25.2199459004882[/C][C]4.054060575698[/C][/ROW]
[ROW][C]7[/C][C]5782.2[/C][C]5797.42836518958[/C][C]78.0851460396642[/C][C]-15.2283651895797[/C][C]-1.15713967235811[/C][/ROW]
[ROW][C]8[/C][C]5763[/C][C]5781.84385967601[/C][C]6.86559292318837[/C][C]-18.8438596760143[/C][C]-3.25463999646315[/C][/ROW]
[ROW][C]9[/C][C]5694.6[/C][C]5706.81572253158[/C][C]-55.3906393532818[/C][C]-12.2157225315755[/C][C]-2.84508514966757[/C][/ROW]
[ROW][C]10[/C][C]5686.85[/C][C]5675.99960724985[/C][C]-36.7110840855942[/C][C]10.8503927501529[/C][C]0.853638261311994[/C][/ROW]
[ROW][C]11[/C][C]5691.6[/C][C]5683.41825519128[/C][C]-3.16747673181363[/C][C]8.18174480871616[/C][C]1.53291313548044[/C][/ROW]
[ROW][C]12[/C][C]5674.15[/C][C]5677.71371222964[/C][C]-5.09597711100001[/C][C]-3.56371222963829[/C][C]-0.0881307498432941[/C][/ROW]
[ROW][C]13[/C][C]5635.55[/C][C]5642.1638762226[/C][C]-28.1973927116656[/C][C]-6.61387622260283[/C][C]-1.05838340798167[/C][/ROW]
[ROW][C]14[/C][C]5652.6[/C][C]5645.1823014174[/C][C]-4.44026396013072[/C][C]7.41769858260226[/C][C]1.10193967648718[/C][/ROW]
[ROW][C]15[/C][C]5675.7[/C][C]5662.541282112[/C][C]11.4745479111971[/C][C]13.158717887999[/C][C]0.726051785008695[/C][/ROW]
[ROW][C]16[/C][C]5692.25[/C][C]5689.09166000193[/C][C]22.5337175364558[/C][C]3.15833999806917[/C][C]0.512258596445967[/C][/ROW]
[ROW][C]17[/C][C]5747.05[/C][C]5766.26020863314[/C][C]62.6474832571426[/C][C]-19.2102086331367[/C][C]1.82854440337346[/C][/ROW]
[ROW][C]18[/C][C]5854.15[/C][C]5831.59938554356[/C][C]64.6118116847653[/C][C]22.5506144564399[/C][C]0.0896989288262441[/C][/ROW]
[ROW][C]19[/C][C]5894.8[/C][C]5891.67136199619[/C][C]61.294890085487[/C][C]3.12863800380928[/C][C]-0.151667823113679[/C][/ROW]
[ROW][C]20[/C][C]5839.4[/C][C]5858.01942008216[/C][C]-8.14024102620836[/C][C]-18.6194200821579[/C][C]-3.17308648376945[/C][/ROW]
[ROW][C]21[/C][C]5778.15[/C][C]5801.74064156665[/C][C]-43.3472860914712[/C][C]-23.5906415666463[/C][C]-1.60890063210728[/C][/ROW]
[ROW][C]22[/C][C]5797.75[/C][C]5789.00907857013[/C][C]-20.9570461602999[/C][C]8.74092142987297[/C][C]1.02325564289546[/C][/ROW]
[ROW][C]23[/C][C]5790.7[/C][C]5780.04787832127[/C][C]-12.1860063698914[/C][C]10.652121678725[/C][C]0.400829607597672[/C][/ROW]
[ROW][C]24[/C][C]5786.3[/C][C]5778.41002078766[/C][C]-4.47979632818166[/C][C]7.8899792123387[/C][C]0.352242840600584[/C][/ROW]
[ROW][C]25[/C][C]5758.6[/C][C]5771.909134071[/C][C]-5.95626927044819[/C][C]-13.3091340709971[/C][C]-0.0676585804259621[/C][/ROW]
[ROW][C]26[/C][C]5764.75[/C][C]5760.28483373442[/C][C]-10.1020650348665[/C][C]4.4651662655804[/C][C]-0.189719448561434[/C][/ROW]
[ROW][C]27[/C][C]5804.75[/C][C]5784.3730193866[/C][C]14.6151798199547[/C][C]20.3769806134038[/C][C]1.12784051756036[/C][/ROW]
[ROW][C]28[/C][C]5801.35[/C][C]5812.22447857258[/C][C]24.1797349844792[/C][C]-10.8744785725762[/C][C]0.439642747699125[/C][/ROW]
[ROW][C]29[/C][C]5829.75[/C][C]5852.5543234986[/C][C]35.8912865389477[/C][C]-22.8043234985951[/C][C]0.535393237397038[/C][/ROW]
[ROW][C]30[/C][C]5913.7[/C][C]5894.48868295848[/C][C]40.2575247881184[/C][C]19.2113170415243[/C][C]0.199243671124289[/C][/ROW]
[ROW][C]31[/C][C]5962[/C][C]5933.63994423556[/C][C]39.4587661291697[/C][C]28.3600557644354[/C][C]-0.0365122649578506[/C][/ROW]
[ROW][C]32[/C][C]5920.25[/C][C]5933.61024910681[/C][C]10.9174527573752[/C][C]-13.3602491068137[/C][C]-1.30450448592699[/C][/ROW]
[ROW][C]33[/C][C]5879.1[/C][C]5915.68643418929[/C][C]-9.93564441800693[/C][C]-36.5864341892845[/C][C]-0.952929719523747[/C][/ROW]
[ROW][C]34[/C][C]5902.3[/C][C]5897.79823847143[/C][C]-15.6853186737769[/C][C]4.50176152857231[/C][C]-0.262770148606886[/C][/ROW]
[ROW][C]35[/C][C]5889.95[/C][C]5881.71352150152[/C][C]-15.9739578204293[/C][C]8.23647849847907[/C][C]-0.0131904220535858[/C][/ROW]
[ROW][C]36[/C][C]5873.9[/C][C]5863.84774220965[/C][C]-17.3402321402336[/C][C]10.0522577903532[/C][C]-0.0624708536040089[/C][/ROW]
[ROW][C]37[/C][C]5856.1[/C][C]5861.99328395163[/C][C]-6.1491625709692[/C][C]-5.89328395163124[/C][C]0.512342278195063[/C][/ROW]
[ROW][C]38[/C][C]5870.8[/C][C]5870.96075120773[/C][C]4.77087955487917[/C][C]-0.160751207727891[/C][C]0.49894490107538[/C][/ROW]
[ROW][C]39[/C][C]5900.1[/C][C]5881.45872612498[/C][C]8.8853679361804[/C][C]18.6412738750178[/C][C]0.187875966086818[/C][/ROW]
[ROW][C]40[/C][C]5900.6[/C][C]5911.72656972109[/C][C]24.2388106219106[/C][C]-11.1265697210873[/C][C]0.703650179933587[/C][/ROW]
[ROW][C]41[/C][C]5944.3[/C][C]5965.40356463112[/C][C]45.4323371829198[/C][C]-21.1035646311185[/C][C]0.969426445738213[/C][/ROW]
[ROW][C]42[/C][C]6066.2[/C][C]6042.87965403426[/C][C]68.4647379427759[/C][C]23.3203459657447[/C][C]1.05142045989749[/C][/ROW]
[ROW][C]43[/C][C]6098.75[/C][C]6071.1604080751[/C][C]39.6156981266156[/C][C]27.5895919248952[/C][C]-1.3181868618805[/C][/ROW]
[ROW][C]44[/C][C]6058.4[/C][C]6072.09440294399[/C][C]11.8279058875208[/C][C]-13.6944029439902[/C][C]-1.2700691168778[/C][/ROW]
[ROW][C]45[/C][C]5998[/C][C]6041.60699434434[/C][C]-18.5848549355088[/C][C]-43.6069943443412[/C][C]-1.38981748976827[/C][/ROW]
[ROW][C]46[/C][C]6022.4[/C][C]6017.22735392661[/C][C]-22.7496114288616[/C][C]5.17264607338596[/C][C]-0.190328824242338[/C][/ROW]
[ROW][C]47[/C][C]6018.7[/C][C]6005.91791915678[/C][C]-14.5308432145475[/C][C]12.7820808432217[/C][C]0.375604824192353[/C][/ROW]
[ROW][C]48[/C][C]5989.95[/C][C]5984.52437701127[/C][C]-19.4597004980972[/C][C]5.42562298872879[/C][C]-0.2253790800864[/C][/ROW]
[ROW][C]49[/C][C]5972.55[/C][C]5976.86307453113[/C][C]-10.980822133043[/C][C]-4.31307453112988[/C][C]0.387875989685924[/C][/ROW]
[ROW][C]50[/C][C]5985.35[/C][C]5980.86807748793[/C][C]-0.219496761188442[/C][C]4.48192251206956[/C][C]0.491582313313261[/C][/ROW]
[ROW][C]51[/C][C]6004.45[/C][C]5988.80295142286[/C][C]5.61745244239008[/C][C]15.6470485771372[/C][C]0.266618499881007[/C][/ROW]
[ROW][C]52[/C][C]6004.1[/C][C]6020.225271596[/C][C]24.0822107801754[/C][C]-16.125271596002[/C][C]0.84520619818899[/C][/ROW]
[ROW][C]53[/C][C]6071.05[/C][C]6094.18816362542[/C][C]59.8389491236794[/C][C]-23.1381636254203[/C][C]1.63551458638766[/C][/ROW]
[ROW][C]54[/C][C]6143.55[/C][C]6121.07869585445[/C][C]36.2338386219157[/C][C]22.4713041455467[/C][C]-1.07802577664668[/C][/ROW]
[ROW][C]55[/C][C]6191.25[/C][C]6153.48436097346[/C][C]33.4942134976013[/C][C]37.7656390265369[/C][C]-0.12515610491091[/C][/ROW]
[ROW][C]56[/C][C]6167.5[/C][C]6172.85503446151[/C][C]23.3846554048305[/C][C]-5.35503446150715[/C][C]-0.462024942982046[/C][/ROW]
[ROW][C]57[/C][C]6081.35[/C][C]6137.02341529918[/C][C]-19.0206096067299[/C][C]-55.6734152991785[/C][C]-1.93790855657361[/C][/ROW]
[ROW][C]58[/C][C]6124.25[/C][C]6119.65434523894[/C][C]-17.8378949585774[/C][C]4.59565476106167[/C][C]0.0540493124729241[/C][/ROW]
[ROW][C]59[/C][C]6118.3[/C][C]6102.52586208823[/C][C]-17.3300046487655[/C][C]15.7741379117691[/C][C]0.0232125935216533[/C][/ROW]
[ROW][C]60[/C][C]6097.8[/C][C]6092.0636775266[/C][C]-12.4131741471975[/C][C]5.73632247339518[/C][C]0.224814139470516[/C][/ROW]
[ROW][C]61[/C][C]6074.55[/C][C]6080.03546957989[/C][C]-12.1374500176745[/C][C]-5.48546957988527[/C][C]0.0126074310407811[/C][/ROW]
[ROW][C]62[/C][C]6083.9[/C][C]6076.90623014615[/C][C]-5.69055865919126[/C][C]6.99376985385217[/C][C]0.294496427648438[/C][/ROW]
[ROW][C]63[/C][C]6084.65[/C][C]6076.28827349133[/C][C]-2.06778208157102[/C][C]8.36172650867417[/C][C]0.165509065306765[/C][/ROW]
[ROW][C]64[/C][C]6099.8[/C][C]6120.78799761436[/C][C]31.1824453622889[/C][C]-20.9879976143593[/C][C]1.52110069957679[/C][/ROW]
[ROW][C]65[/C][C]6124.45[/C][C]6143.79797527521[/C][C]25.3397102833438[/C][C]-19.347975275208[/C][C]-0.267211488098053[/C][/ROW]
[ROW][C]66[/C][C]6235.65[/C][C]6206.29386222219[/C][C]51.9004341270452[/C][C]29.3561377778102[/C][C]1.21336959455014[/C][/ROW]
[ROW][C]67[/C][C]6278.05[/C][C]6242.14322314715[/C][C]40.4362887206633[/C][C]35.9067768528483[/C][C]-0.523702633937661[/C][/ROW]
[ROW][C]68[/C][C]6254.4[/C][C]6249.87030339823[/C][C]17.0763156091372[/C][C]4.52969660177012[/C][C]-1.06748925829678[/C][/ROW]
[ROW][C]69[/C][C]6177.3[/C][C]6239.12519868537[/C][C]-2.79878597035357[/C][C]-61.8251986853729[/C][C]-0.908295532416477[/C][/ROW]
[ROW][C]70[/C][C]6205.95[/C][C]6207.70238133769[/C][C]-23.2484143763256[/C][C]-1.7523813376949[/C][C]-0.934561200969447[/C][/ROW]
[ROW][C]71[/C][C]6217.2[/C][C]6198.73693234196[/C][C]-13.0456351057406[/C][C]18.4630676580403[/C][C]0.466334781772391[/C][/ROW]
[ROW][C]72[/C][C]6190.8[/C][C]6184.30123755763[/C][C]-14.0387277100813[/C][C]6.49876244237162[/C][C]-0.0454032792131953[/C][/ROW]
[ROW][C]73[/C][C]6189.55[/C][C]6189.79116442315[/C][C]-0.0833042995187423[/C][C]-0.241164423145818[/C][C]0.637935385832431[/C][/ROW]
[ROW][C]74[/C][C]6179.5[/C][C]6176.00877737122[/C][C]-9.86576626914144[/C][C]3.49122262878418[/C][C]-0.446883630567242[/C][/ROW]
[ROW][C]75[/C][C]6195.35[/C][C]6192.25301834788[/C][C]8.75235098790026[/C][C]3.09698165212419[/C][C]0.850663734556073[/C][/ROW]
[ROW][C]76[/C][C]6213[/C][C]6227.72524831187[/C][C]27.8024539945992[/C][C]-14.72524831187[/C][C]0.871211172830762[/C][/ROW]
[ROW][C]77[/C][C]6243.45[/C][C]6272.86563264153[/C][C]40.1751827911506[/C][C]-29.41563264153[/C][C]0.565785991298826[/C][/ROW]
[ROW][C]78[/C][C]6361.75[/C][C]6327.4002905316[/C][C]50.4232409415937[/C][C]34.3497094683957[/C][C]0.468248805891212[/C][/ROW]
[ROW][C]79[/C][C]6395.2[/C][C]6356.74918406264[/C][C]35.3926750161496[/C][C]38.4508159373558[/C][C]-0.686641148725439[/C][/ROW]
[ROW][C]80[/C][C]6356.6[/C][C]6352.4564909939[/C][C]7.0955471547286[/C][C]4.14350900609937[/C][C]-1.29301242829322[/C][/ROW]
[ROW][C]81[/C][C]6276.5[/C][C]6334.83821958326[/C][C]-10.5286665682362[/C][C]-58.3382195832623[/C][C]-0.805427340890319[/C][/ROW]
[ROW][C]82[/C][C]6306.25[/C][C]6313.72146845509[/C][C]-18.0798738964668[/C][C]-7.47146845508976[/C][C]-0.345109969258774[/C][/ROW]
[ROW][C]83[/C][C]6318.4[/C][C]6298.39353908411[/C][C]-16.117244292875[/C][C]20.0064609158947[/C][C]0.0897091710227974[/C][/ROW]
[ROW][C]84[/C][C]6284.9[/C][C]6281.84706143184[/C][C]-16.4234234418932[/C][C]3.05293856816244[/C][C]-0.0139970466575053[/C][/ROW]
[ROW][C]85[/C][C]6249.5[/C][C]6247.16953470449[/C][C]-29.4461844767417[/C][C]2.33046529550915[/C][C]-0.5952061823402[/C][/ROW]
[ROW][C]86[/C][C]6256[/C][C]6250.20701084516[/C][C]-6.28691939617823[/C][C]5.79298915484446[/C][C]1.05800683507959[/C][/ROW]
[ROW][C]87[/C][C]6272.9[/C][C]6271.87985220007[/C][C]13.6257930481353[/C][C]1.02014779993127[/C][C]0.909865802224817[/C][/ROW]
[ROW][C]88[/C][C]6273.65[/C][C]6293.92215890367[/C][C]19.6193438710165[/C][C]-20.2721589036727[/C][C]0.274050382304599[/C][/ROW]
[ROW][C]89[/C][C]6313.95[/C][C]6343.51967777204[/C][C]40.982655622515[/C][C]-29.5696777720358[/C][C]0.976820331008873[/C][/ROW]
[ROW][C]90[/C][C]6396.85[/C][C]6364.0327827424[/C][C]26.3929958318432[/C][C]32.8172172575999[/C][C]-0.666699922678851[/C][/ROW]
[ROW][C]91[/C][C]6426.35[/C][C]6379.31784702931[/C][C]18.4797361617993[/C][C]47.0321529706877[/C][C]-0.361517961962233[/C][/ROW]
[ROW][C]92[/C][C]6382.6[/C][C]6376.62963116013[/C][C]3.40493784271498[/C][C]5.97036883986731[/C][C]-0.688799045485832[/C][/ROW]
[ROW][C]93[/C][C]6319[/C][C]6375.4517763607[/C][C]0.141306274053867[/C][C]-56.4517763607046[/C][C]-0.149146838620569[/C][/ROW]
[ROW][C]94[/C][C]6329.5[/C][C]6344.8557392155[/C][C]-21.7496922488967[/C][C]-15.3557392154979[/C][C]-1.00051681514605[/C][/ROW]
[ROW][C]95[/C][C]6321.8[/C][C]6303.05034724937[/C][C]-36.0345723086851[/C][C]18.7496527506323[/C][C]-0.652962414206784[/C][/ROW]
[ROW][C]96[/C][C]6312.35[/C][C]6294.91359544106[/C][C]-16.1597875025188[/C][C]17.4364045589364[/C][C]0.908519769122728[/C][/ROW]
[ROW][C]97[/C][C]6260[/C][C]6268.6264800518[/C][C]-23.375001428618[/C][C]-8.62648005179748[/C][C]-0.329740570646352[/C][/ROW]
[ROW][C]98[/C][C]6283.6[/C][C]6276.76626697228[/C][C]-0.935459857551777[/C][C]6.83373302772218[/C][C]1.0251623066047[/C][/ROW]
[ROW][C]99[/C][C]6295.15[/C][C]6294.19793296682[/C][C]12.1317628409028[/C][C]0.952067033183064[/C][C]0.597098038266722[/C][/ROW]
[ROW][C]100[/C][C]6309.15[/C][C]6333.40684452581[/C][C]31.3943130062282[/C][C]-24.2568445258084[/C][C]0.880664231415156[/C][/ROW]
[ROW][C]101[/C][C]6315.75[/C][C]6345.94268905409[/C][C]17.9707994557634[/C][C]-30.1926890540933[/C][C]-0.613735860018762[/C][/ROW]
[ROW][C]102[/C][C]6427.95[/C][C]6387.42313257176[/C][C]34.708465088584[/C][C]40.5268674282379[/C][C]0.764910222235321[/C][/ROW]
[ROW][C]103[/C][C]6446.55[/C][C]6401.30463429857[/C][C]19.8864163685228[/C][C]45.2453657014303[/C][C]-0.677177649935168[/C][/ROW]
[ROW][C]104[/C][C]6385.65[/C][C]6386.46817575877[/C][C]-4.81539197943503[/C][C]-0.818175758768894[/C][C]-1.12864942215936[/C][/ROW]
[ROW][C]105[/C][C]6351.45[/C][C]6394.39823620448[/C][C]4.25073678125305[/C][C]-42.9482362044773[/C][C]0.414314991012859[/C][/ROW]
[ROW][C]106[/C][C]6359.1[/C][C]6374.24970345374[/C][C]-13.1060109396217[/C][C]-15.1497034537442[/C][C]-0.793305754810963[/C][/ROW]
[ROW][C]107[/C][C]6350.05[/C][C]6340.89161200598[/C][C]-27.5148064284355[/C][C]9.15838799402177[/C][C]-0.658638641660453[/C][/ROW]
[ROW][C]108[/C][C]6335.6[/C][C]6312.9325708752[/C][C]-27.8309363758215[/C][C]22.6674291248031[/C][C]-0.014450270671156[/C][/ROW]
[ROW][C]109[/C][C]6333.55[/C][C]6337.99582543188[/C][C]9.8097225036725[/C][C]-4.44582543188147[/C][C]1.7201081798669[/C][/ROW]
[ROW][C]110[/C][C]6348.55[/C][C]6348.39414762052[/C][C]10.2283598572721[/C][C]0.155852379483556[/C][C]0.0191262110396667[/C][/ROW]
[ROW][C]111[/C][C]6369.1[/C][C]6371.96553911162[/C][C]19.7122206119677[/C][C]-2.86553911162084[/C][C]0.433368731592919[/C][/ROW]
[ROW][C]112[/C][C]6372.75[/C][C]6393.12032621928[/C][C]20.737505709552[/C][C]-20.3703262192834[/C][C]0.0468714671072726[/C][/ROW]
[ROW][C]113[/C][C]6413.95[/C][C]6445.66255773474[/C][C]43.3530166018303[/C][C]-31.7125577347367[/C][C]1.03394620758353[/C][/ROW]
[ROW][C]114[/C][C]6528.6[/C][C]6484.73609584911[/C][C]40.3093342864643[/C][C]43.863904150887[/C][C]-0.139101857974582[/C][/ROW]
[ROW][C]115[/C][C]6558.4[/C][C]6508.28434109484[/C][C]28.3920231438332[/C][C]50.1156589051608[/C][C]-0.544489796484064[/C][/ROW]
[ROW][C]116[/C][C]6501.95[/C][C]6512.50539778372[/C][C]11.213193533224[/C][C]-10.5553977837162[/C][C]-0.784908405360404[/C][/ROW]
[ROW][C]117[/C][C]6430.5[/C][C]6475.7845957573[/C][C]-22.8484932028469[/C][C]-45.2845957572968[/C][C]-1.55657925592384[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302596&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
15572.35572.3000
25565.555566.74448411525-5.65423354330478-1.19448411524547-0.283552732468196
35576.855572.957505543853.090892571478473.892494456150430.427941436310622
45577.35577.585547621814.28281310795655-0.2855476218072690.0551230452832051
55598.855595.7398813637614.80894613036173.110118636245190.478664141064104
65752.555727.33005409951103.40460349060225.21994590048824.054060575698
75782.25797.4283651895878.0851460396642-15.2283651895797-1.15713967235811
857635781.843859676016.86559292318837-18.8438596760143-3.25463999646315
95694.65706.81572253158-55.3906393532818-12.2157225315755-2.84508514966757
105686.855675.99960724985-36.711084085594210.85039275015290.853638261311994
115691.65683.41825519128-3.167476731813638.181744808716161.53291313548044
125674.155677.71371222964-5.09597711100001-3.56371222963829-0.0881307498432941
135635.555642.1638762226-28.1973927116656-6.61387622260283-1.05838340798167
145652.65645.1823014174-4.440263960130727.417698582602261.10193967648718
155675.75662.54128211211.474547911197113.1587178879990.726051785008695
165692.255689.0916600019322.53371753645583.158339998069170.512258596445967
175747.055766.2602086331462.6474832571426-19.21020863313671.82854440337346
185854.155831.5993855435664.611811684765322.55061445643990.0896989288262441
195894.85891.6713619961961.2948900854873.12863800380928-0.151667823113679
205839.45858.01942008216-8.14024102620836-18.6194200821579-3.17308648376945
215778.155801.74064156665-43.3472860914712-23.5906415666463-1.60890063210728
225797.755789.00907857013-20.95704616029998.740921429872971.02325564289546
235790.75780.04787832127-12.186006369891410.6521216787250.400829607597672
245786.35778.41002078766-4.479796328181667.88997921233870.352242840600584
255758.65771.909134071-5.95626927044819-13.3091340709971-0.0676585804259621
265764.755760.28483373442-10.10206503486654.4651662655804-0.189719448561434
275804.755784.373019386614.615179819954720.37698061340381.12784051756036
285801.355812.2244785725824.1797349844792-10.87447857257620.439642747699125
295829.755852.554323498635.8912865389477-22.80432349859510.535393237397038
305913.75894.4886829584840.257524788118419.21131704152430.199243671124289
3159625933.6399442355639.458766129169728.3600557644354-0.0365122649578506
325920.255933.6102491068110.9174527573752-13.3602491068137-1.30450448592699
335879.15915.68643418929-9.93564441800693-36.5864341892845-0.952929719523747
345902.35897.79823847143-15.68531867377694.50176152857231-0.262770148606886
355889.955881.71352150152-15.97395782042938.23647849847907-0.0131904220535858
365873.95863.84774220965-17.340232140233610.0522577903532-0.0624708536040089
375856.15861.99328395163-6.1491625709692-5.893283951631240.512342278195063
385870.85870.960751207734.77087955487917-0.1607512077278910.49894490107538
395900.15881.458726124988.885367936180418.64127387501780.187875966086818
405900.65911.7265697210924.2388106219106-11.12656972108730.703650179933587
415944.35965.4035646311245.4323371829198-21.10356463111850.969426445738213
426066.26042.8796540342668.464737942775923.32034596574471.05142045989749
436098.756071.160408075139.615698126615627.5895919248952-1.3181868618805
446058.46072.0944029439911.8279058875208-13.6944029439902-1.2700691168778
4559986041.60699434434-18.5848549355088-43.6069943443412-1.38981748976827
466022.46017.22735392661-22.74961142886165.17264607338596-0.190328824242338
476018.76005.91791915678-14.530843214547512.78208084322170.375604824192353
485989.955984.52437701127-19.45970049809725.42562298872879-0.2253790800864
495972.555976.86307453113-10.980822133043-4.313074531129880.387875989685924
505985.355980.86807748793-0.2194967611884424.481922512069560.491582313313261
516004.455988.802951422865.6174524423900815.64704857713720.266618499881007
526004.16020.22527159624.0822107801754-16.1252715960020.84520619818899
536071.056094.1881636254259.8389491236794-23.13816362542031.63551458638766
546143.556121.0786958544536.233838621915722.4713041455467-1.07802577664668
556191.256153.4843609734633.494213497601337.7656390265369-0.12515610491091
566167.56172.8550344615123.3846554048305-5.35503446150715-0.462024942982046
576081.356137.02341529918-19.0206096067299-55.6734152991785-1.93790855657361
586124.256119.65434523894-17.83789495857744.595654761061670.0540493124729241
596118.36102.52586208823-17.330004648765515.77413791176910.0232125935216533
606097.86092.0636775266-12.41317414719755.736322473395180.224814139470516
616074.556080.03546957989-12.1374500176745-5.485469579885270.0126074310407811
626083.96076.90623014615-5.690558659191266.993769853852170.294496427648438
636084.656076.28827349133-2.067782081571028.361726508674170.165509065306765
646099.86120.7879976143631.1824453622889-20.98799761435931.52110069957679
656124.456143.7979752752125.3397102833438-19.347975275208-0.267211488098053
666235.656206.2938622221951.900434127045229.35613777781021.21336959455014
676278.056242.1432231471540.436288720663335.9067768528483-0.523702633937661
686254.46249.8703033982317.07631560913724.52969660177012-1.06748925829678
696177.36239.12519868537-2.79878597035357-61.8251986853729-0.908295532416477
706205.956207.70238133769-23.2484143763256-1.7523813376949-0.934561200969447
716217.26198.73693234196-13.045635105740618.46306765804030.466334781772391
726190.86184.30123755763-14.03872771008136.49876244237162-0.0454032792131953
736189.556189.79116442315-0.0833042995187423-0.2411644231458180.637935385832431
746179.56176.00877737122-9.865766269141443.49122262878418-0.446883630567242
756195.356192.253018347888.752350987900263.096981652124190.850663734556073
7662136227.7252483118727.8024539945992-14.725248311870.871211172830762
776243.456272.8656326415340.1751827911506-29.415632641530.565785991298826
786361.756327.400290531650.423240941593734.34970946839570.468248805891212
796395.26356.7491840626435.392675016149638.4508159373558-0.686641148725439
806356.66352.45649099397.09554715472864.14350900609937-1.29301242829322
816276.56334.83821958326-10.5286665682362-58.3382195832623-0.805427340890319
826306.256313.72146845509-18.0798738964668-7.47146845508976-0.345109969258774
836318.46298.39353908411-16.11724429287520.00646091589470.0897091710227974
846284.96281.84706143184-16.42342344189323.05293856816244-0.0139970466575053
856249.56247.16953470449-29.44618447674172.33046529550915-0.5952061823402
8662566250.20701084516-6.286919396178235.792989154844461.05800683507959
876272.96271.8798522000713.62579304813531.020147799931270.909865802224817
886273.656293.9221589036719.6193438710165-20.27215890367270.274050382304599
896313.956343.5196777720440.982655622515-29.56967777203580.976820331008873
906396.856364.032782742426.392995831843232.8172172575999-0.666699922678851
916426.356379.3178470293118.479736161799347.0321529706877-0.361517961962233
926382.66376.629631160133.404937842714985.97036883986731-0.688799045485832
9363196375.45177636070.141306274053867-56.4517763607046-0.149146838620569
946329.56344.8557392155-21.7496922488967-15.3557392154979-1.00051681514605
956321.86303.05034724937-36.034572308685118.7496527506323-0.652962414206784
966312.356294.91359544106-16.159787502518817.43640455893640.908519769122728
9762606268.6264800518-23.375001428618-8.62648005179748-0.329740570646352
986283.66276.76626697228-0.9354598575517776.833733027722181.0251623066047
996295.156294.1979329668212.13176284090280.9520670331830640.597098038266722
1006309.156333.4068445258131.3943130062282-24.25684452580840.880664231415156
1016315.756345.9426890540917.9707994557634-30.1926890540933-0.613735860018762
1026427.956387.4231325717634.70846508858440.52686742823790.764910222235321
1036446.556401.3046342985719.886416368522845.2453657014303-0.677177649935168
1046385.656386.46817575877-4.81539197943503-0.818175758768894-1.12864942215936
1056351.456394.398236204484.25073678125305-42.94823620447730.414314991012859
1066359.16374.24970345374-13.1060109396217-15.1497034537442-0.793305754810963
1076350.056340.89161200598-27.51480642843559.15838799402177-0.658638641660453
1086335.66312.9325708752-27.830936375821522.6674291248031-0.014450270671156
1096333.556337.995825431889.8097225036725-4.445825431881471.7201081798669
1106348.556348.3941476205210.22835985727210.1558523794835560.0191262110396667
1116369.16371.9655391116219.7122206119677-2.865539111620840.433368731592919
1126372.756393.1203262192820.737505709552-20.37032621928340.0468714671072726
1136413.956445.6625577347443.3530166018303-31.71255773473671.03394620758353
1146528.66484.7360958491140.309334286464343.863904150887-0.139101857974582
1156558.46508.2843410948428.392023143833250.1156589051608-0.544489796484064
1166501.956512.5053977837211.213193533224-10.5553977837162-0.784908405360404
1176430.56475.7845957573-22.8484932028469-45.2845957572968-1.55657925592384







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
16453.070578336386443.844906478479.22567185791116
26444.194207501976449.717369184-5.52316168203053
36424.615928827236455.58983188953-30.9739030623057
46403.47664028736461.46229459507-57.9856543077643
56411.489040274596467.3347573006-55.8457170260061
66428.416668520176473.20722000613-44.7905514859639
76432.562845776976479.07968271166-46.5168369346899
86466.416770957246484.9521454172-18.5353744599541
96578.662496357596490.8246081227387.8378882348566
106609.752809052556496.69707082826113.055738224288
116560.093877948396502.5695335337957.5243444145944
126500.969552466396508.44199623933-7.47244377293543

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 6453.07057833638 & 6443.84490647847 & 9.22567185791116 \tabularnewline
2 & 6444.19420750197 & 6449.717369184 & -5.52316168203053 \tabularnewline
3 & 6424.61592882723 & 6455.58983188953 & -30.9739030623057 \tabularnewline
4 & 6403.4766402873 & 6461.46229459507 & -57.9856543077643 \tabularnewline
5 & 6411.48904027459 & 6467.3347573006 & -55.8457170260061 \tabularnewline
6 & 6428.41666852017 & 6473.20722000613 & -44.7905514859639 \tabularnewline
7 & 6432.56284577697 & 6479.07968271166 & -46.5168369346899 \tabularnewline
8 & 6466.41677095724 & 6484.9521454172 & -18.5353744599541 \tabularnewline
9 & 6578.66249635759 & 6490.82460812273 & 87.8378882348566 \tabularnewline
10 & 6609.75280905255 & 6496.69707082826 & 113.055738224288 \tabularnewline
11 & 6560.09387794839 & 6502.56953353379 & 57.5243444145944 \tabularnewline
12 & 6500.96955246639 & 6508.44199623933 & -7.47244377293543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302596&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]6453.07057833638[/C][C]6443.84490647847[/C][C]9.22567185791116[/C][/ROW]
[ROW][C]2[/C][C]6444.19420750197[/C][C]6449.717369184[/C][C]-5.52316168203053[/C][/ROW]
[ROW][C]3[/C][C]6424.61592882723[/C][C]6455.58983188953[/C][C]-30.9739030623057[/C][/ROW]
[ROW][C]4[/C][C]6403.4766402873[/C][C]6461.46229459507[/C][C]-57.9856543077643[/C][/ROW]
[ROW][C]5[/C][C]6411.48904027459[/C][C]6467.3347573006[/C][C]-55.8457170260061[/C][/ROW]
[ROW][C]6[/C][C]6428.41666852017[/C][C]6473.20722000613[/C][C]-44.7905514859639[/C][/ROW]
[ROW][C]7[/C][C]6432.56284577697[/C][C]6479.07968271166[/C][C]-46.5168369346899[/C][/ROW]
[ROW][C]8[/C][C]6466.41677095724[/C][C]6484.9521454172[/C][C]-18.5353744599541[/C][/ROW]
[ROW][C]9[/C][C]6578.66249635759[/C][C]6490.82460812273[/C][C]87.8378882348566[/C][/ROW]
[ROW][C]10[/C][C]6609.75280905255[/C][C]6496.69707082826[/C][C]113.055738224288[/C][/ROW]
[ROW][C]11[/C][C]6560.09387794839[/C][C]6502.56953353379[/C][C]57.5243444145944[/C][/ROW]
[ROW][C]12[/C][C]6500.96955246639[/C][C]6508.44199623933[/C][C]-7.47244377293543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302596&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302596&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
16453.070578336386443.844906478479.22567185791116
26444.194207501976449.717369184-5.52316168203053
36424.615928827236455.58983188953-30.9739030623057
46403.47664028736461.46229459507-57.9856543077643
56411.489040274596467.3347573006-55.8457170260061
66428.416668520176473.20722000613-44.7905514859639
76432.562845776976479.07968271166-46.5168369346899
86466.416770957246484.9521454172-18.5353744599541
96578.662496357596490.8246081227387.8378882348566
106609.752809052556496.69707082826113.055738224288
116560.093877948396502.5695335337957.5243444145944
126500.969552466396508.44199623933-7.47244377293543



Parameters (Session):
par1 = 1 ;
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')