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 computationTue, 13 Dec 2016 21:20:56 +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/13/t1481660520236ewtccx48ifmi.htm/, Retrieved Sat, 04 May 2024 23:32:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299221, Retrieved Sat, 04 May 2024 23:32:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact42
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...] [2016-12-13 20:20:56] [130d73899007e5ff8a4f636b9bcfb397] [Current]
Feedback Forum

Post a new message
Dataseries X:
5622
5601
5358
5182
5133
5086
5101
5107
5096
5051
4942
4914
4881
4756
4749
4712
4676
4580
4529
4453
4400
4523
4462
4441
4551
4736
4772
4761
4704
4717
4819
4631
4583
4525
4496
4474
4419
4400
4352
4260
4206
4126
4119
4069
4035
4004
3983
3912
3882
3832
3793
3762
3744
3711
3722
3702
3845
3788
3768
3867
3999
3968
3920




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299221&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299221&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
156225622000
256015602.08045787121-1.43268900305661-1.08045787121212-0.178061976336427
353585359.9164963398-24.4222361677654-1.91649633979935-3.44528411319586
451825183.72343974435-44.1403526646926-1.72343974435142-2.12951796681838
551335134.49552455174-44.9303679174063-1.49552455174315-0.0703237072074213
650865087.58695017117-45.2725642212442-1.586950171174-0.0270507840424586
751015102.43061253762-34.1566855588032-1.430612537624650.815964666716247
851075108.48751557896-26.4056925761103-1.487515578961460.543113542402741
950965097.51679289576-23.3523934426172-1.516792895755730.207779692024014
1050515052.57979465794-27.6922636085177-1.57979465794386-0.289947140965068
1149424943.69260330634-44.1851314490527-1.69260330634323-1.08920179092639
1249144915.46756643215-40.922367377742-1.467566432152870.21391043274606
1348814867.23760256742-42.354379278439813.7623974325794-0.114313047255831
1447564758.45817812891-55.6095622192809-2.4581781289115-0.750539326830333
1547494751.74144693621-45.532518113908-2.741446936208030.653884329842729
1647124714.95239134175-43.7288568844128-2.952391341746180.116897975330076
1746764678.64149602375-42.1979912582137-2.641496023754260.0991910635999745
1845804583.08370319514-53.2132722120339-3.08370319513563-0.713564425055119
1945294531.66188104465-52.8433809294935-2.661881044648690.0239579527915933
2044534455.86889551069-57.582585377082-2.86889551069198-0.306931923299988
2144004402.74012931985-56.6627598970774-2.740129319845330.0595686162664063
2245234524.99873711788-19.7084289061637-1.998737117875622.39310632608532
2344624465.35253328497-27.9576483060251-3.35253328496638-0.534197049911758
2444414443.62905227719-26.6700045211202-2.62905227718770.0833814820025298
2545514503.16925476259-9.119007486084247.83074523741241.24895619479427
2647364736.0567815180939.7173843387745-0.05678151809357782.93020042639005
2747724773.1466893833239.1746169345564-1.1466893833168-0.0351278224853771
2847614762.3801898788628.857441158848-1.38018987886183-0.667457308439108
2947044704.8292461092811.0104342899926-0.829246109283187-1.15508400093509
3047174717.9920426252511.4549460662702-0.9920426252522420.0287749697035794
3148194819.1070798073429.9709035269768-0.1070798073396141.19875150330401
3246314633.01116246132-14.6487249583743-2.0111624613223-2.8889587724248
3345834584.35565541947-21.6713721682825-1.35565541947009-0.454712226475734
3445254524.9552095469-29.46271871378860.0447904530969846-0.50450007204064
3544964497.0825316818-29.1343555113528-1.082531681803820.0212625271150049
3644744474.88150765854-27.7026937483744-0.8815076585357320.0927019236586494
3744194414.99024127718-34.29033467899264.00975872281858-0.454069395821305
3844004399.44620449557-30.48453973626870.5537955044313640.233679466986833
3943524352.50313767079-33.8827887610136-0.503137670789782-0.22003151352351
4042604260.58936178449-45.8672891837854-0.58936178449197-0.775447287612354
4142064205.97350544249-47.67370490826260.0264945575118788-0.11692703102146
4241264127.566042728-54.0191723894147-1.56604272799907-0.410796807929136
4341194116.85394062964-45.07808516996032.146059370360360.578886352835856
4440694070.38867088709-45.3644755896221-1.38867088709422-0.0185432755334741
4540354035.4489641105-43.2122465490459-0.4489641104959910.13935808316302
4640044003.29962374277-40.92826705721110.7003762572282220.147892462713961
4739833983.44853787461-36.5766837617768-0.4485378746092150.281781520942969
4839123912.43309569452-43.6857201663714-0.433095694518737-0.460318207309647
4938823879.47156006416-41.48593344602392.528439935837160.149194838891701
5038323831.62747942235-42.78137611651510.372520577650326-0.0805522414347824
5137933793.14318161147-41.8945182161337-0.1431816114726540.0574404760253326
5237623762.64969633559-39.5406917383727-0.6496963355854140.152317425781446
5337443743.60825264497-35.309154519140.3917473550255390.273921051849326
5437113713.07667794578-34.3230089285938-2.076677945781430.0638446760604688
5537223719.6142703515-25.88918572434732.385729648498310.546059743622331
5637023703.61291431347-23.8483183664095-1.612914313472420.132144993235718
5738453844.2038663804510.09212751083120.7961336195510082.19768891317269
5837883788.75011997462-3.43664902432784-0.750119974620152-0.876023528271495
5937683768.30982170256-6.94633885544876-0.309821702555457-0.227267532907584
6038673866.6837554439414.78793055042960.3162445560643121.40732535513697
6139993987.1839284756136.499691803466311.81607152439141.45802095793743
6239683969.0760259406225.3478325466368-1.07602594061901-0.699052637512238
6339203922.0762128025510.4218180344923-2.07621280254923-0.966948709481625

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5622 & 5622 & 0 & 0 & 0 \tabularnewline
2 & 5601 & 5602.08045787121 & -1.43268900305661 & -1.08045787121212 & -0.178061976336427 \tabularnewline
3 & 5358 & 5359.9164963398 & -24.4222361677654 & -1.91649633979935 & -3.44528411319586 \tabularnewline
4 & 5182 & 5183.72343974435 & -44.1403526646926 & -1.72343974435142 & -2.12951796681838 \tabularnewline
5 & 5133 & 5134.49552455174 & -44.9303679174063 & -1.49552455174315 & -0.0703237072074213 \tabularnewline
6 & 5086 & 5087.58695017117 & -45.2725642212442 & -1.586950171174 & -0.0270507840424586 \tabularnewline
7 & 5101 & 5102.43061253762 & -34.1566855588032 & -1.43061253762465 & 0.815964666716247 \tabularnewline
8 & 5107 & 5108.48751557896 & -26.4056925761103 & -1.48751557896146 & 0.543113542402741 \tabularnewline
9 & 5096 & 5097.51679289576 & -23.3523934426172 & -1.51679289575573 & 0.207779692024014 \tabularnewline
10 & 5051 & 5052.57979465794 & -27.6922636085177 & -1.57979465794386 & -0.289947140965068 \tabularnewline
11 & 4942 & 4943.69260330634 & -44.1851314490527 & -1.69260330634323 & -1.08920179092639 \tabularnewline
12 & 4914 & 4915.46756643215 & -40.922367377742 & -1.46756643215287 & 0.21391043274606 \tabularnewline
13 & 4881 & 4867.23760256742 & -42.3543792784398 & 13.7623974325794 & -0.114313047255831 \tabularnewline
14 & 4756 & 4758.45817812891 & -55.6095622192809 & -2.4581781289115 & -0.750539326830333 \tabularnewline
15 & 4749 & 4751.74144693621 & -45.532518113908 & -2.74144693620803 & 0.653884329842729 \tabularnewline
16 & 4712 & 4714.95239134175 & -43.7288568844128 & -2.95239134174618 & 0.116897975330076 \tabularnewline
17 & 4676 & 4678.64149602375 & -42.1979912582137 & -2.64149602375426 & 0.0991910635999745 \tabularnewline
18 & 4580 & 4583.08370319514 & -53.2132722120339 & -3.08370319513563 & -0.713564425055119 \tabularnewline
19 & 4529 & 4531.66188104465 & -52.8433809294935 & -2.66188104464869 & 0.0239579527915933 \tabularnewline
20 & 4453 & 4455.86889551069 & -57.582585377082 & -2.86889551069198 & -0.306931923299988 \tabularnewline
21 & 4400 & 4402.74012931985 & -56.6627598970774 & -2.74012931984533 & 0.0595686162664063 \tabularnewline
22 & 4523 & 4524.99873711788 & -19.7084289061637 & -1.99873711787562 & 2.39310632608532 \tabularnewline
23 & 4462 & 4465.35253328497 & -27.9576483060251 & -3.35253328496638 & -0.534197049911758 \tabularnewline
24 & 4441 & 4443.62905227719 & -26.6700045211202 & -2.6290522771877 & 0.0833814820025298 \tabularnewline
25 & 4551 & 4503.16925476259 & -9.1190074860842 & 47.8307452374124 & 1.24895619479427 \tabularnewline
26 & 4736 & 4736.05678151809 & 39.7173843387745 & -0.0567815180935778 & 2.93020042639005 \tabularnewline
27 & 4772 & 4773.14668938332 & 39.1746169345564 & -1.1466893833168 & -0.0351278224853771 \tabularnewline
28 & 4761 & 4762.38018987886 & 28.857441158848 & -1.38018987886183 & -0.667457308439108 \tabularnewline
29 & 4704 & 4704.82924610928 & 11.0104342899926 & -0.829246109283187 & -1.15508400093509 \tabularnewline
30 & 4717 & 4717.99204262525 & 11.4549460662702 & -0.992042625252242 & 0.0287749697035794 \tabularnewline
31 & 4819 & 4819.10707980734 & 29.9709035269768 & -0.107079807339614 & 1.19875150330401 \tabularnewline
32 & 4631 & 4633.01116246132 & -14.6487249583743 & -2.0111624613223 & -2.8889587724248 \tabularnewline
33 & 4583 & 4584.35565541947 & -21.6713721682825 & -1.35565541947009 & -0.454712226475734 \tabularnewline
34 & 4525 & 4524.9552095469 & -29.4627187137886 & 0.0447904530969846 & -0.50450007204064 \tabularnewline
35 & 4496 & 4497.0825316818 & -29.1343555113528 & -1.08253168180382 & 0.0212625271150049 \tabularnewline
36 & 4474 & 4474.88150765854 & -27.7026937483744 & -0.881507658535732 & 0.0927019236586494 \tabularnewline
37 & 4419 & 4414.99024127718 & -34.2903346789926 & 4.00975872281858 & -0.454069395821305 \tabularnewline
38 & 4400 & 4399.44620449557 & -30.4845397362687 & 0.553795504431364 & 0.233679466986833 \tabularnewline
39 & 4352 & 4352.50313767079 & -33.8827887610136 & -0.503137670789782 & -0.22003151352351 \tabularnewline
40 & 4260 & 4260.58936178449 & -45.8672891837854 & -0.58936178449197 & -0.775447287612354 \tabularnewline
41 & 4206 & 4205.97350544249 & -47.6737049082626 & 0.0264945575118788 & -0.11692703102146 \tabularnewline
42 & 4126 & 4127.566042728 & -54.0191723894147 & -1.56604272799907 & -0.410796807929136 \tabularnewline
43 & 4119 & 4116.85394062964 & -45.0780851699603 & 2.14605937036036 & 0.578886352835856 \tabularnewline
44 & 4069 & 4070.38867088709 & -45.3644755896221 & -1.38867088709422 & -0.0185432755334741 \tabularnewline
45 & 4035 & 4035.4489641105 & -43.2122465490459 & -0.448964110495991 & 0.13935808316302 \tabularnewline
46 & 4004 & 4003.29962374277 & -40.9282670572111 & 0.700376257228222 & 0.147892462713961 \tabularnewline
47 & 3983 & 3983.44853787461 & -36.5766837617768 & -0.448537874609215 & 0.281781520942969 \tabularnewline
48 & 3912 & 3912.43309569452 & -43.6857201663714 & -0.433095694518737 & -0.460318207309647 \tabularnewline
49 & 3882 & 3879.47156006416 & -41.4859334460239 & 2.52843993583716 & 0.149194838891701 \tabularnewline
50 & 3832 & 3831.62747942235 & -42.7813761165151 & 0.372520577650326 & -0.0805522414347824 \tabularnewline
51 & 3793 & 3793.14318161147 & -41.8945182161337 & -0.143181611472654 & 0.0574404760253326 \tabularnewline
52 & 3762 & 3762.64969633559 & -39.5406917383727 & -0.649696335585414 & 0.152317425781446 \tabularnewline
53 & 3744 & 3743.60825264497 & -35.30915451914 & 0.391747355025539 & 0.273921051849326 \tabularnewline
54 & 3711 & 3713.07667794578 & -34.3230089285938 & -2.07667794578143 & 0.0638446760604688 \tabularnewline
55 & 3722 & 3719.6142703515 & -25.8891857243473 & 2.38572964849831 & 0.546059743622331 \tabularnewline
56 & 3702 & 3703.61291431347 & -23.8483183664095 & -1.61291431347242 & 0.132144993235718 \tabularnewline
57 & 3845 & 3844.20386638045 & 10.0921275108312 & 0.796133619551008 & 2.19768891317269 \tabularnewline
58 & 3788 & 3788.75011997462 & -3.43664902432784 & -0.750119974620152 & -0.876023528271495 \tabularnewline
59 & 3768 & 3768.30982170256 & -6.94633885544876 & -0.309821702555457 & -0.227267532907584 \tabularnewline
60 & 3867 & 3866.68375544394 & 14.7879305504296 & 0.316244556064312 & 1.40732535513697 \tabularnewline
61 & 3999 & 3987.18392847561 & 36.4996918034663 & 11.8160715243914 & 1.45802095793743 \tabularnewline
62 & 3968 & 3969.07602594062 & 25.3478325466368 & -1.07602594061901 & -0.699052637512238 \tabularnewline
63 & 3920 & 3922.07621280255 & 10.4218180344923 & -2.07621280254923 & -0.966948709481625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299221&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]5622[/C][C]5622[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5601[/C][C]5602.08045787121[/C][C]-1.43268900305661[/C][C]-1.08045787121212[/C][C]-0.178061976336427[/C][/ROW]
[ROW][C]3[/C][C]5358[/C][C]5359.9164963398[/C][C]-24.4222361677654[/C][C]-1.91649633979935[/C][C]-3.44528411319586[/C][/ROW]
[ROW][C]4[/C][C]5182[/C][C]5183.72343974435[/C][C]-44.1403526646926[/C][C]-1.72343974435142[/C][C]-2.12951796681838[/C][/ROW]
[ROW][C]5[/C][C]5133[/C][C]5134.49552455174[/C][C]-44.9303679174063[/C][C]-1.49552455174315[/C][C]-0.0703237072074213[/C][/ROW]
[ROW][C]6[/C][C]5086[/C][C]5087.58695017117[/C][C]-45.2725642212442[/C][C]-1.586950171174[/C][C]-0.0270507840424586[/C][/ROW]
[ROW][C]7[/C][C]5101[/C][C]5102.43061253762[/C][C]-34.1566855588032[/C][C]-1.43061253762465[/C][C]0.815964666716247[/C][/ROW]
[ROW][C]8[/C][C]5107[/C][C]5108.48751557896[/C][C]-26.4056925761103[/C][C]-1.48751557896146[/C][C]0.543113542402741[/C][/ROW]
[ROW][C]9[/C][C]5096[/C][C]5097.51679289576[/C][C]-23.3523934426172[/C][C]-1.51679289575573[/C][C]0.207779692024014[/C][/ROW]
[ROW][C]10[/C][C]5051[/C][C]5052.57979465794[/C][C]-27.6922636085177[/C][C]-1.57979465794386[/C][C]-0.289947140965068[/C][/ROW]
[ROW][C]11[/C][C]4942[/C][C]4943.69260330634[/C][C]-44.1851314490527[/C][C]-1.69260330634323[/C][C]-1.08920179092639[/C][/ROW]
[ROW][C]12[/C][C]4914[/C][C]4915.46756643215[/C][C]-40.922367377742[/C][C]-1.46756643215287[/C][C]0.21391043274606[/C][/ROW]
[ROW][C]13[/C][C]4881[/C][C]4867.23760256742[/C][C]-42.3543792784398[/C][C]13.7623974325794[/C][C]-0.114313047255831[/C][/ROW]
[ROW][C]14[/C][C]4756[/C][C]4758.45817812891[/C][C]-55.6095622192809[/C][C]-2.4581781289115[/C][C]-0.750539326830333[/C][/ROW]
[ROW][C]15[/C][C]4749[/C][C]4751.74144693621[/C][C]-45.532518113908[/C][C]-2.74144693620803[/C][C]0.653884329842729[/C][/ROW]
[ROW][C]16[/C][C]4712[/C][C]4714.95239134175[/C][C]-43.7288568844128[/C][C]-2.95239134174618[/C][C]0.116897975330076[/C][/ROW]
[ROW][C]17[/C][C]4676[/C][C]4678.64149602375[/C][C]-42.1979912582137[/C][C]-2.64149602375426[/C][C]0.0991910635999745[/C][/ROW]
[ROW][C]18[/C][C]4580[/C][C]4583.08370319514[/C][C]-53.2132722120339[/C][C]-3.08370319513563[/C][C]-0.713564425055119[/C][/ROW]
[ROW][C]19[/C][C]4529[/C][C]4531.66188104465[/C][C]-52.8433809294935[/C][C]-2.66188104464869[/C][C]0.0239579527915933[/C][/ROW]
[ROW][C]20[/C][C]4453[/C][C]4455.86889551069[/C][C]-57.582585377082[/C][C]-2.86889551069198[/C][C]-0.306931923299988[/C][/ROW]
[ROW][C]21[/C][C]4400[/C][C]4402.74012931985[/C][C]-56.6627598970774[/C][C]-2.74012931984533[/C][C]0.0595686162664063[/C][/ROW]
[ROW][C]22[/C][C]4523[/C][C]4524.99873711788[/C][C]-19.7084289061637[/C][C]-1.99873711787562[/C][C]2.39310632608532[/C][/ROW]
[ROW][C]23[/C][C]4462[/C][C]4465.35253328497[/C][C]-27.9576483060251[/C][C]-3.35253328496638[/C][C]-0.534197049911758[/C][/ROW]
[ROW][C]24[/C][C]4441[/C][C]4443.62905227719[/C][C]-26.6700045211202[/C][C]-2.6290522771877[/C][C]0.0833814820025298[/C][/ROW]
[ROW][C]25[/C][C]4551[/C][C]4503.16925476259[/C][C]-9.1190074860842[/C][C]47.8307452374124[/C][C]1.24895619479427[/C][/ROW]
[ROW][C]26[/C][C]4736[/C][C]4736.05678151809[/C][C]39.7173843387745[/C][C]-0.0567815180935778[/C][C]2.93020042639005[/C][/ROW]
[ROW][C]27[/C][C]4772[/C][C]4773.14668938332[/C][C]39.1746169345564[/C][C]-1.1466893833168[/C][C]-0.0351278224853771[/C][/ROW]
[ROW][C]28[/C][C]4761[/C][C]4762.38018987886[/C][C]28.857441158848[/C][C]-1.38018987886183[/C][C]-0.667457308439108[/C][/ROW]
[ROW][C]29[/C][C]4704[/C][C]4704.82924610928[/C][C]11.0104342899926[/C][C]-0.829246109283187[/C][C]-1.15508400093509[/C][/ROW]
[ROW][C]30[/C][C]4717[/C][C]4717.99204262525[/C][C]11.4549460662702[/C][C]-0.992042625252242[/C][C]0.0287749697035794[/C][/ROW]
[ROW][C]31[/C][C]4819[/C][C]4819.10707980734[/C][C]29.9709035269768[/C][C]-0.107079807339614[/C][C]1.19875150330401[/C][/ROW]
[ROW][C]32[/C][C]4631[/C][C]4633.01116246132[/C][C]-14.6487249583743[/C][C]-2.0111624613223[/C][C]-2.8889587724248[/C][/ROW]
[ROW][C]33[/C][C]4583[/C][C]4584.35565541947[/C][C]-21.6713721682825[/C][C]-1.35565541947009[/C][C]-0.454712226475734[/C][/ROW]
[ROW][C]34[/C][C]4525[/C][C]4524.9552095469[/C][C]-29.4627187137886[/C][C]0.0447904530969846[/C][C]-0.50450007204064[/C][/ROW]
[ROW][C]35[/C][C]4496[/C][C]4497.0825316818[/C][C]-29.1343555113528[/C][C]-1.08253168180382[/C][C]0.0212625271150049[/C][/ROW]
[ROW][C]36[/C][C]4474[/C][C]4474.88150765854[/C][C]-27.7026937483744[/C][C]-0.881507658535732[/C][C]0.0927019236586494[/C][/ROW]
[ROW][C]37[/C][C]4419[/C][C]4414.99024127718[/C][C]-34.2903346789926[/C][C]4.00975872281858[/C][C]-0.454069395821305[/C][/ROW]
[ROW][C]38[/C][C]4400[/C][C]4399.44620449557[/C][C]-30.4845397362687[/C][C]0.553795504431364[/C][C]0.233679466986833[/C][/ROW]
[ROW][C]39[/C][C]4352[/C][C]4352.50313767079[/C][C]-33.8827887610136[/C][C]-0.503137670789782[/C][C]-0.22003151352351[/C][/ROW]
[ROW][C]40[/C][C]4260[/C][C]4260.58936178449[/C][C]-45.8672891837854[/C][C]-0.58936178449197[/C][C]-0.775447287612354[/C][/ROW]
[ROW][C]41[/C][C]4206[/C][C]4205.97350544249[/C][C]-47.6737049082626[/C][C]0.0264945575118788[/C][C]-0.11692703102146[/C][/ROW]
[ROW][C]42[/C][C]4126[/C][C]4127.566042728[/C][C]-54.0191723894147[/C][C]-1.56604272799907[/C][C]-0.410796807929136[/C][/ROW]
[ROW][C]43[/C][C]4119[/C][C]4116.85394062964[/C][C]-45.0780851699603[/C][C]2.14605937036036[/C][C]0.578886352835856[/C][/ROW]
[ROW][C]44[/C][C]4069[/C][C]4070.38867088709[/C][C]-45.3644755896221[/C][C]-1.38867088709422[/C][C]-0.0185432755334741[/C][/ROW]
[ROW][C]45[/C][C]4035[/C][C]4035.4489641105[/C][C]-43.2122465490459[/C][C]-0.448964110495991[/C][C]0.13935808316302[/C][/ROW]
[ROW][C]46[/C][C]4004[/C][C]4003.29962374277[/C][C]-40.9282670572111[/C][C]0.700376257228222[/C][C]0.147892462713961[/C][/ROW]
[ROW][C]47[/C][C]3983[/C][C]3983.44853787461[/C][C]-36.5766837617768[/C][C]-0.448537874609215[/C][C]0.281781520942969[/C][/ROW]
[ROW][C]48[/C][C]3912[/C][C]3912.43309569452[/C][C]-43.6857201663714[/C][C]-0.433095694518737[/C][C]-0.460318207309647[/C][/ROW]
[ROW][C]49[/C][C]3882[/C][C]3879.47156006416[/C][C]-41.4859334460239[/C][C]2.52843993583716[/C][C]0.149194838891701[/C][/ROW]
[ROW][C]50[/C][C]3832[/C][C]3831.62747942235[/C][C]-42.7813761165151[/C][C]0.372520577650326[/C][C]-0.0805522414347824[/C][/ROW]
[ROW][C]51[/C][C]3793[/C][C]3793.14318161147[/C][C]-41.8945182161337[/C][C]-0.143181611472654[/C][C]0.0574404760253326[/C][/ROW]
[ROW][C]52[/C][C]3762[/C][C]3762.64969633559[/C][C]-39.5406917383727[/C][C]-0.649696335585414[/C][C]0.152317425781446[/C][/ROW]
[ROW][C]53[/C][C]3744[/C][C]3743.60825264497[/C][C]-35.30915451914[/C][C]0.391747355025539[/C][C]0.273921051849326[/C][/ROW]
[ROW][C]54[/C][C]3711[/C][C]3713.07667794578[/C][C]-34.3230089285938[/C][C]-2.07667794578143[/C][C]0.0638446760604688[/C][/ROW]
[ROW][C]55[/C][C]3722[/C][C]3719.6142703515[/C][C]-25.8891857243473[/C][C]2.38572964849831[/C][C]0.546059743622331[/C][/ROW]
[ROW][C]56[/C][C]3702[/C][C]3703.61291431347[/C][C]-23.8483183664095[/C][C]-1.61291431347242[/C][C]0.132144993235718[/C][/ROW]
[ROW][C]57[/C][C]3845[/C][C]3844.20386638045[/C][C]10.0921275108312[/C][C]0.796133619551008[/C][C]2.19768891317269[/C][/ROW]
[ROW][C]58[/C][C]3788[/C][C]3788.75011997462[/C][C]-3.43664902432784[/C][C]-0.750119974620152[/C][C]-0.876023528271495[/C][/ROW]
[ROW][C]59[/C][C]3768[/C][C]3768.30982170256[/C][C]-6.94633885544876[/C][C]-0.309821702555457[/C][C]-0.227267532907584[/C][/ROW]
[ROW][C]60[/C][C]3867[/C][C]3866.68375544394[/C][C]14.7879305504296[/C][C]0.316244556064312[/C][C]1.40732535513697[/C][/ROW]
[ROW][C]61[/C][C]3999[/C][C]3987.18392847561[/C][C]36.4996918034663[/C][C]11.8160715243914[/C][C]1.45802095793743[/C][/ROW]
[ROW][C]62[/C][C]3968[/C][C]3969.07602594062[/C][C]25.3478325466368[/C][C]-1.07602594061901[/C][C]-0.699052637512238[/C][/ROW]
[ROW][C]63[/C][C]3920[/C][C]3922.07621280255[/C][C]10.4218180344923[/C][C]-2.07621280254923[/C][C]-0.966948709481625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299221&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
156225622000
256015602.08045787121-1.43268900305661-1.08045787121212-0.178061976336427
353585359.9164963398-24.4222361677654-1.91649633979935-3.44528411319586
451825183.72343974435-44.1403526646926-1.72343974435142-2.12951796681838
551335134.49552455174-44.9303679174063-1.49552455174315-0.0703237072074213
650865087.58695017117-45.2725642212442-1.586950171174-0.0270507840424586
751015102.43061253762-34.1566855588032-1.430612537624650.815964666716247
851075108.48751557896-26.4056925761103-1.487515578961460.543113542402741
950965097.51679289576-23.3523934426172-1.516792895755730.207779692024014
1050515052.57979465794-27.6922636085177-1.57979465794386-0.289947140965068
1149424943.69260330634-44.1851314490527-1.69260330634323-1.08920179092639
1249144915.46756643215-40.922367377742-1.467566432152870.21391043274606
1348814867.23760256742-42.354379278439813.7623974325794-0.114313047255831
1447564758.45817812891-55.6095622192809-2.4581781289115-0.750539326830333
1547494751.74144693621-45.532518113908-2.741446936208030.653884329842729
1647124714.95239134175-43.7288568844128-2.952391341746180.116897975330076
1746764678.64149602375-42.1979912582137-2.641496023754260.0991910635999745
1845804583.08370319514-53.2132722120339-3.08370319513563-0.713564425055119
1945294531.66188104465-52.8433809294935-2.661881044648690.0239579527915933
2044534455.86889551069-57.582585377082-2.86889551069198-0.306931923299988
2144004402.74012931985-56.6627598970774-2.740129319845330.0595686162664063
2245234524.99873711788-19.7084289061637-1.998737117875622.39310632608532
2344624465.35253328497-27.9576483060251-3.35253328496638-0.534197049911758
2444414443.62905227719-26.6700045211202-2.62905227718770.0833814820025298
2545514503.16925476259-9.119007486084247.83074523741241.24895619479427
2647364736.0567815180939.7173843387745-0.05678151809357782.93020042639005
2747724773.1466893833239.1746169345564-1.1466893833168-0.0351278224853771
2847614762.3801898788628.857441158848-1.38018987886183-0.667457308439108
2947044704.8292461092811.0104342899926-0.829246109283187-1.15508400093509
3047174717.9920426252511.4549460662702-0.9920426252522420.0287749697035794
3148194819.1070798073429.9709035269768-0.1070798073396141.19875150330401
3246314633.01116246132-14.6487249583743-2.0111624613223-2.8889587724248
3345834584.35565541947-21.6713721682825-1.35565541947009-0.454712226475734
3445254524.9552095469-29.46271871378860.0447904530969846-0.50450007204064
3544964497.0825316818-29.1343555113528-1.082531681803820.0212625271150049
3644744474.88150765854-27.7026937483744-0.8815076585357320.0927019236586494
3744194414.99024127718-34.29033467899264.00975872281858-0.454069395821305
3844004399.44620449557-30.48453973626870.5537955044313640.233679466986833
3943524352.50313767079-33.8827887610136-0.503137670789782-0.22003151352351
4042604260.58936178449-45.8672891837854-0.58936178449197-0.775447287612354
4142064205.97350544249-47.67370490826260.0264945575118788-0.11692703102146
4241264127.566042728-54.0191723894147-1.56604272799907-0.410796807929136
4341194116.85394062964-45.07808516996032.146059370360360.578886352835856
4440694070.38867088709-45.3644755896221-1.38867088709422-0.0185432755334741
4540354035.4489641105-43.2122465490459-0.4489641104959910.13935808316302
4640044003.29962374277-40.92826705721110.7003762572282220.147892462713961
4739833983.44853787461-36.5766837617768-0.4485378746092150.281781520942969
4839123912.43309569452-43.6857201663714-0.433095694518737-0.460318207309647
4938823879.47156006416-41.48593344602392.528439935837160.149194838891701
5038323831.62747942235-42.78137611651510.372520577650326-0.0805522414347824
5137933793.14318161147-41.8945182161337-0.1431816114726540.0574404760253326
5237623762.64969633559-39.5406917383727-0.6496963355854140.152317425781446
5337443743.60825264497-35.309154519140.3917473550255390.273921051849326
5437113713.07667794578-34.3230089285938-2.076677945781430.0638446760604688
5537223719.6142703515-25.88918572434732.385729648498310.546059743622331
5637023703.61291431347-23.8483183664095-1.612914313472420.132144993235718
5738453844.2038663804510.09212751083120.7961336195510082.19768891317269
5837883788.75011997462-3.43664902432784-0.750119974620152-0.876023528271495
5937683768.30982170256-6.94633885544876-0.309821702555457-0.227267532907584
6038673866.6837554439414.78793055042960.3162445560643121.40732535513697
6139993987.1839284756136.499691803466311.81607152439141.45802095793743
6239683969.0760259406225.3478325466368-1.07602594061901-0.699052637512238
6339203922.0762128025510.4218180344923-2.07621280254923-0.966948709481625







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
13855.950886293453862.66231147878-6.71142518533734
23818.335230829843840.27224693146-21.9370161016234
33775.220434568753817.88218238414-42.6617478153924
43794.406616117443795.49211783682-1.08550171938457
53732.355298671883773.1020532895-40.7467546176206
63739.646476816233750.71198874218-11.0655119259492
73727.39078183023728.32192419486-0.931142364666766
83685.309321340493705.93185964754-20.6225383070515
93680.541046373323683.54179510022-3.00074872690069
103710.498067966313661.151730552949.3463374134054
113703.230091382213638.7616660055864.4684253766246
123651.319225432163616.3716014582634.9476239738964

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 3855.95088629345 & 3862.66231147878 & -6.71142518533734 \tabularnewline
2 & 3818.33523082984 & 3840.27224693146 & -21.9370161016234 \tabularnewline
3 & 3775.22043456875 & 3817.88218238414 & -42.6617478153924 \tabularnewline
4 & 3794.40661611744 & 3795.49211783682 & -1.08550171938457 \tabularnewline
5 & 3732.35529867188 & 3773.1020532895 & -40.7467546176206 \tabularnewline
6 & 3739.64647681623 & 3750.71198874218 & -11.0655119259492 \tabularnewline
7 & 3727.3907818302 & 3728.32192419486 & -0.931142364666766 \tabularnewline
8 & 3685.30932134049 & 3705.93185964754 & -20.6225383070515 \tabularnewline
9 & 3680.54104637332 & 3683.54179510022 & -3.00074872690069 \tabularnewline
10 & 3710.49806796631 & 3661.1517305529 & 49.3463374134054 \tabularnewline
11 & 3703.23009138221 & 3638.76166600558 & 64.4684253766246 \tabularnewline
12 & 3651.31922543216 & 3616.37160145826 & 34.9476239738964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299221&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]3855.95088629345[/C][C]3862.66231147878[/C][C]-6.71142518533734[/C][/ROW]
[ROW][C]2[/C][C]3818.33523082984[/C][C]3840.27224693146[/C][C]-21.9370161016234[/C][/ROW]
[ROW][C]3[/C][C]3775.22043456875[/C][C]3817.88218238414[/C][C]-42.6617478153924[/C][/ROW]
[ROW][C]4[/C][C]3794.40661611744[/C][C]3795.49211783682[/C][C]-1.08550171938457[/C][/ROW]
[ROW][C]5[/C][C]3732.35529867188[/C][C]3773.1020532895[/C][C]-40.7467546176206[/C][/ROW]
[ROW][C]6[/C][C]3739.64647681623[/C][C]3750.71198874218[/C][C]-11.0655119259492[/C][/ROW]
[ROW][C]7[/C][C]3727.3907818302[/C][C]3728.32192419486[/C][C]-0.931142364666766[/C][/ROW]
[ROW][C]8[/C][C]3685.30932134049[/C][C]3705.93185964754[/C][C]-20.6225383070515[/C][/ROW]
[ROW][C]9[/C][C]3680.54104637332[/C][C]3683.54179510022[/C][C]-3.00074872690069[/C][/ROW]
[ROW][C]10[/C][C]3710.49806796631[/C][C]3661.1517305529[/C][C]49.3463374134054[/C][/ROW]
[ROW][C]11[/C][C]3703.23009138221[/C][C]3638.76166600558[/C][C]64.4684253766246[/C][/ROW]
[ROW][C]12[/C][C]3651.31922543216[/C][C]3616.37160145826[/C][C]34.9476239738964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299221&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
13855.950886293453862.66231147878-6.71142518533734
23818.335230829843840.27224693146-21.9370161016234
33775.220434568753817.88218238414-42.6617478153924
43794.406616117443795.49211783682-1.08550171938457
53732.355298671883773.1020532895-40.7467546176206
63739.646476816233750.71198874218-11.0655119259492
73727.39078183023728.32192419486-0.931142364666766
83685.309321340493705.93185964754-20.6225383070515
93680.541046373323683.54179510022-3.00074872690069
103710.498067966313661.151730552949.3463374134054
113703.230091382213638.7616660055864.4684253766246
123651.319225432163616.3716014582634.9476239738964



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')