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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, 15 Dec 2016 20:01:50 +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/15/t148182892063ff8fa5ji6jsu5.htm/, Retrieved Fri, 03 May 2024 10:59:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299966, Retrieved Fri, 03 May 2024 10:59:09 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
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...] [2016-12-15 19:01:50] [153c3207812fd13fe5ceee3276565119] [Current]
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Dataseries X:
200
2100
1250
2250
5850
4900
4700
3650
4950
10250
3850
3050
9150
8650
7350
7050
8150
9200
7050
11800
10950
13200
5250
14500
8000
8350
8750
7750
7300
9750
7100
9500
7050
7300
5900
8350
8050
4200
7300
6900
5300
9600
7900
4150
4900
8100
7200
6700
7350
4650
7100




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=299966&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=299966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299966&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
1200200000
22100965.28158822611480.9188118335624141.8610742075080.776808290979275
312501110.9701682699486.223732597098355.20741390769650.0659187382801694
422501572.83315030644109.891281343032156.7833647157690.401806170000432
558503228.37718627908188.880938743754381.7834255295681.70931189657582
649003933.76706624866211.355922822379195.815231278210.583645197010141
747004283.55185238561216.689826013948206.0808838570640.158625365281126
836504110.71677335948202.9992744287138.505786353821-0.450463835921579
949504463.83320750336207.915535074525253.3466972048740.174664647737058
10102506637.72152634319268.803207072685546.1194624217372.29700970806168
1138505737.72944316643234.223701711713-57.5963089888293-1.36963324541208
1230504796.02522496978200.761421565159100.724419067426-1.38099076709912
1391506438.8127029495448.0152985568317-122.5778081526032.38018496711971
1486507392.1377551872681.4184646283872113.4245796389740.908505962644757
1573507452.3416544339780.6701153950351-73.8896219761047-0.0224770687036986
1670507357.9360437798875.6432989688809-55.8527786580969-0.196133071558823
1781507604.282636190779.7332780966923290.5551259670050.196889432270787
1892008210.5017525256790.7137385404269186.9247109755170.61657053764138
1970507838.3861682916681.995568962012-75.1574517597385-0.546587803161793
20118009268.32237991282105.582676395337441.3268274474391.59963724827876
21109509990.69512112513115.812905879335-0.8827699383523960.734125365985881
221320011041.4997133169130.715312675588699.3753415199931.11494993451509
2352509151.8754730524499.6145179327473-743.427281521675-2.41233125191628
241450011069.6840580792123.558304214426575.0069980246592.17624426478419
25800010614.1876323963148.157188053666-1605.87333910497-0.807764350381969
2683509795.42557732275128.083869133749-93.5361338558763-1.06526882478879
2787509449.04081750869116.899417970637-34.4465237095987-0.527109325415067
2877508913.14622535329103.891592619396-210.225281121516-0.749902122252929
2973008301.2973836559991.907305442050670.5163115797992-0.83888784553265
3097508737.7517410640396.9348509737423489.0905924785670.408219983088076
3171008348.8940854207390.5235461392288-505.586550975428-0.579009902840966
3295008671.5905651464793.3775343806396471.5866850709450.277674569484135
3370508241.1321182146887.2521494443014-383.909492813968-0.627789735538817
3473007620.9072713121279.2811342390258771.163353582918-0.848982030428465
3559007407.6330965935876.144820802226-1055.33639746848-0.351437251681709
3683507528.7769143885476.48447830143751.2338397133420.0542354963549573
3780507997.5032029877767.4637979525955-597.2332244451730.515614627535562
3842006709.9295751479849.3962262767498-543.921991827927-1.5535141090794
3973006860.4364929861551.1928120946091295.3171882308860.114974114159167
4069006952.1789795948151.8324515157249-111.5415430420320.0471257892978286
4153006433.937161705444.1812487196157-282.827853851453-0.672975161045951
4296007332.2181977479854.1778024117326978.0900079285351.01727184751791
4379007802.7205448776558.5791833398921-535.3837199462810.498324462114823
4441506443.421141536444.6239810555563-130.864453295054-1.70197006310343
4549005970.5949066428639.7790075385576-279.64703035744-0.622182381453319
4681006416.494531021743.42725935993391061.816699817460.488857567380724
4772007101.4918612587248.7291345415574-885.3247327995980.773085186157459
4867006797.0065300949247.0475615287677448.155462755201-0.427271712339795
4973507039.2327116574444.3980623913499-3.252379365006660.248914397114701
5046506448.790636425338.4708743068803-861.903992245853-0.742901316026392
5171006563.6078518354539.5513306588395426.1995924674940.0880989285353244

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 200 & 200 & 0 & 0 & 0 \tabularnewline
2 & 2100 & 965.281588226114 & 80.9188118335624 & 141.861074207508 & 0.776808290979275 \tabularnewline
3 & 1250 & 1110.97016826994 & 86.2237325970983 & 55.2074139076965 & 0.0659187382801694 \tabularnewline
4 & 2250 & 1572.83315030644 & 109.891281343032 & 156.783364715769 & 0.401806170000432 \tabularnewline
5 & 5850 & 3228.37718627908 & 188.880938743754 & 381.783425529568 & 1.70931189657582 \tabularnewline
6 & 4900 & 3933.76706624866 & 211.355922822379 & 195.81523127821 & 0.583645197010141 \tabularnewline
7 & 4700 & 4283.55185238561 & 216.689826013948 & 206.080883857064 & 0.158625365281126 \tabularnewline
8 & 3650 & 4110.71677335948 & 202.9992744287 & 138.505786353821 & -0.450463835921579 \tabularnewline
9 & 4950 & 4463.83320750336 & 207.915535074525 & 253.346697204874 & 0.174664647737058 \tabularnewline
10 & 10250 & 6637.72152634319 & 268.803207072685 & 546.119462421737 & 2.29700970806168 \tabularnewline
11 & 3850 & 5737.72944316643 & 234.223701711713 & -57.5963089888293 & -1.36963324541208 \tabularnewline
12 & 3050 & 4796.02522496978 & 200.761421565159 & 100.724419067426 & -1.38099076709912 \tabularnewline
13 & 9150 & 6438.81270294954 & 48.0152985568317 & -122.577808152603 & 2.38018496711971 \tabularnewline
14 & 8650 & 7392.13775518726 & 81.4184646283872 & 113.424579638974 & 0.908505962644757 \tabularnewline
15 & 7350 & 7452.34165443397 & 80.6701153950351 & -73.8896219761047 & -0.0224770687036986 \tabularnewline
16 & 7050 & 7357.93604377988 & 75.6432989688809 & -55.8527786580969 & -0.196133071558823 \tabularnewline
17 & 8150 & 7604.2826361907 & 79.7332780966923 & 290.555125967005 & 0.196889432270787 \tabularnewline
18 & 9200 & 8210.50175252567 & 90.7137385404269 & 186.924710975517 & 0.61657053764138 \tabularnewline
19 & 7050 & 7838.38616829166 & 81.995568962012 & -75.1574517597385 & -0.546587803161793 \tabularnewline
20 & 11800 & 9268.32237991282 & 105.582676395337 & 441.326827447439 & 1.59963724827876 \tabularnewline
21 & 10950 & 9990.69512112513 & 115.812905879335 & -0.882769938352396 & 0.734125365985881 \tabularnewline
22 & 13200 & 11041.4997133169 & 130.715312675588 & 699.375341519993 & 1.11494993451509 \tabularnewline
23 & 5250 & 9151.87547305244 & 99.6145179327473 & -743.427281521675 & -2.41233125191628 \tabularnewline
24 & 14500 & 11069.6840580792 & 123.558304214426 & 575.006998024659 & 2.17624426478419 \tabularnewline
25 & 8000 & 10614.1876323963 & 148.157188053666 & -1605.87333910497 & -0.807764350381969 \tabularnewline
26 & 8350 & 9795.42557732275 & 128.083869133749 & -93.5361338558763 & -1.06526882478879 \tabularnewline
27 & 8750 & 9449.04081750869 & 116.899417970637 & -34.4465237095987 & -0.527109325415067 \tabularnewline
28 & 7750 & 8913.14622535329 & 103.891592619396 & -210.225281121516 & -0.749902122252929 \tabularnewline
29 & 7300 & 8301.29738365599 & 91.9073054420506 & 70.5163115797992 & -0.83888784553265 \tabularnewline
30 & 9750 & 8737.75174106403 & 96.9348509737423 & 489.090592478567 & 0.408219983088076 \tabularnewline
31 & 7100 & 8348.89408542073 & 90.5235461392288 & -505.586550975428 & -0.579009902840966 \tabularnewline
32 & 9500 & 8671.59056514647 & 93.3775343806396 & 471.586685070945 & 0.277674569484135 \tabularnewline
33 & 7050 & 8241.13211821468 & 87.2521494443014 & -383.909492813968 & -0.627789735538817 \tabularnewline
34 & 7300 & 7620.90727131212 & 79.2811342390258 & 771.163353582918 & -0.848982030428465 \tabularnewline
35 & 5900 & 7407.63309659358 & 76.144820802226 & -1055.33639746848 & -0.351437251681709 \tabularnewline
36 & 8350 & 7528.77691438854 & 76.48447830143 & 751.233839713342 & 0.0542354963549573 \tabularnewline
37 & 8050 & 7997.50320298777 & 67.4637979525955 & -597.233224445173 & 0.515614627535562 \tabularnewline
38 & 4200 & 6709.92957514798 & 49.3962262767498 & -543.921991827927 & -1.5535141090794 \tabularnewline
39 & 7300 & 6860.43649298615 & 51.1928120946091 & 295.317188230886 & 0.114974114159167 \tabularnewline
40 & 6900 & 6952.17897959481 & 51.8324515157249 & -111.541543042032 & 0.0471257892978286 \tabularnewline
41 & 5300 & 6433.9371617054 & 44.1812487196157 & -282.827853851453 & -0.672975161045951 \tabularnewline
42 & 9600 & 7332.21819774798 & 54.1778024117326 & 978.090007928535 & 1.01727184751791 \tabularnewline
43 & 7900 & 7802.72054487765 & 58.5791833398921 & -535.383719946281 & 0.498324462114823 \tabularnewline
44 & 4150 & 6443.4211415364 & 44.6239810555563 & -130.864453295054 & -1.70197006310343 \tabularnewline
45 & 4900 & 5970.59490664286 & 39.7790075385576 & -279.64703035744 & -0.622182381453319 \tabularnewline
46 & 8100 & 6416.4945310217 & 43.4272593599339 & 1061.81669981746 & 0.488857567380724 \tabularnewline
47 & 7200 & 7101.49186125872 & 48.7291345415574 & -885.324732799598 & 0.773085186157459 \tabularnewline
48 & 6700 & 6797.00653009492 & 47.0475615287677 & 448.155462755201 & -0.427271712339795 \tabularnewline
49 & 7350 & 7039.23271165744 & 44.3980623913499 & -3.25237936500666 & 0.248914397114701 \tabularnewline
50 & 4650 & 6448.7906364253 & 38.4708743068803 & -861.903992245853 & -0.742901316026392 \tabularnewline
51 & 7100 & 6563.60785183545 & 39.5513306588395 & 426.199592467494 & 0.0880989285353244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299966&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]200[/C][C]200[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2100[/C][C]965.281588226114[/C][C]80.9188118335624[/C][C]141.861074207508[/C][C]0.776808290979275[/C][/ROW]
[ROW][C]3[/C][C]1250[/C][C]1110.97016826994[/C][C]86.2237325970983[/C][C]55.2074139076965[/C][C]0.0659187382801694[/C][/ROW]
[ROW][C]4[/C][C]2250[/C][C]1572.83315030644[/C][C]109.891281343032[/C][C]156.783364715769[/C][C]0.401806170000432[/C][/ROW]
[ROW][C]5[/C][C]5850[/C][C]3228.37718627908[/C][C]188.880938743754[/C][C]381.783425529568[/C][C]1.70931189657582[/C][/ROW]
[ROW][C]6[/C][C]4900[/C][C]3933.76706624866[/C][C]211.355922822379[/C][C]195.81523127821[/C][C]0.583645197010141[/C][/ROW]
[ROW][C]7[/C][C]4700[/C][C]4283.55185238561[/C][C]216.689826013948[/C][C]206.080883857064[/C][C]0.158625365281126[/C][/ROW]
[ROW][C]8[/C][C]3650[/C][C]4110.71677335948[/C][C]202.9992744287[/C][C]138.505786353821[/C][C]-0.450463835921579[/C][/ROW]
[ROW][C]9[/C][C]4950[/C][C]4463.83320750336[/C][C]207.915535074525[/C][C]253.346697204874[/C][C]0.174664647737058[/C][/ROW]
[ROW][C]10[/C][C]10250[/C][C]6637.72152634319[/C][C]268.803207072685[/C][C]546.119462421737[/C][C]2.29700970806168[/C][/ROW]
[ROW][C]11[/C][C]3850[/C][C]5737.72944316643[/C][C]234.223701711713[/C][C]-57.5963089888293[/C][C]-1.36963324541208[/C][/ROW]
[ROW][C]12[/C][C]3050[/C][C]4796.02522496978[/C][C]200.761421565159[/C][C]100.724419067426[/C][C]-1.38099076709912[/C][/ROW]
[ROW][C]13[/C][C]9150[/C][C]6438.81270294954[/C][C]48.0152985568317[/C][C]-122.577808152603[/C][C]2.38018496711971[/C][/ROW]
[ROW][C]14[/C][C]8650[/C][C]7392.13775518726[/C][C]81.4184646283872[/C][C]113.424579638974[/C][C]0.908505962644757[/C][/ROW]
[ROW][C]15[/C][C]7350[/C][C]7452.34165443397[/C][C]80.6701153950351[/C][C]-73.8896219761047[/C][C]-0.0224770687036986[/C][/ROW]
[ROW][C]16[/C][C]7050[/C][C]7357.93604377988[/C][C]75.6432989688809[/C][C]-55.8527786580969[/C][C]-0.196133071558823[/C][/ROW]
[ROW][C]17[/C][C]8150[/C][C]7604.2826361907[/C][C]79.7332780966923[/C][C]290.555125967005[/C][C]0.196889432270787[/C][/ROW]
[ROW][C]18[/C][C]9200[/C][C]8210.50175252567[/C][C]90.7137385404269[/C][C]186.924710975517[/C][C]0.61657053764138[/C][/ROW]
[ROW][C]19[/C][C]7050[/C][C]7838.38616829166[/C][C]81.995568962012[/C][C]-75.1574517597385[/C][C]-0.546587803161793[/C][/ROW]
[ROW][C]20[/C][C]11800[/C][C]9268.32237991282[/C][C]105.582676395337[/C][C]441.326827447439[/C][C]1.59963724827876[/C][/ROW]
[ROW][C]21[/C][C]10950[/C][C]9990.69512112513[/C][C]115.812905879335[/C][C]-0.882769938352396[/C][C]0.734125365985881[/C][/ROW]
[ROW][C]22[/C][C]13200[/C][C]11041.4997133169[/C][C]130.715312675588[/C][C]699.375341519993[/C][C]1.11494993451509[/C][/ROW]
[ROW][C]23[/C][C]5250[/C][C]9151.87547305244[/C][C]99.6145179327473[/C][C]-743.427281521675[/C][C]-2.41233125191628[/C][/ROW]
[ROW][C]24[/C][C]14500[/C][C]11069.6840580792[/C][C]123.558304214426[/C][C]575.006998024659[/C][C]2.17624426478419[/C][/ROW]
[ROW][C]25[/C][C]8000[/C][C]10614.1876323963[/C][C]148.157188053666[/C][C]-1605.87333910497[/C][C]-0.807764350381969[/C][/ROW]
[ROW][C]26[/C][C]8350[/C][C]9795.42557732275[/C][C]128.083869133749[/C][C]-93.5361338558763[/C][C]-1.06526882478879[/C][/ROW]
[ROW][C]27[/C][C]8750[/C][C]9449.04081750869[/C][C]116.899417970637[/C][C]-34.4465237095987[/C][C]-0.527109325415067[/C][/ROW]
[ROW][C]28[/C][C]7750[/C][C]8913.14622535329[/C][C]103.891592619396[/C][C]-210.225281121516[/C][C]-0.749902122252929[/C][/ROW]
[ROW][C]29[/C][C]7300[/C][C]8301.29738365599[/C][C]91.9073054420506[/C][C]70.5163115797992[/C][C]-0.83888784553265[/C][/ROW]
[ROW][C]30[/C][C]9750[/C][C]8737.75174106403[/C][C]96.9348509737423[/C][C]489.090592478567[/C][C]0.408219983088076[/C][/ROW]
[ROW][C]31[/C][C]7100[/C][C]8348.89408542073[/C][C]90.5235461392288[/C][C]-505.586550975428[/C][C]-0.579009902840966[/C][/ROW]
[ROW][C]32[/C][C]9500[/C][C]8671.59056514647[/C][C]93.3775343806396[/C][C]471.586685070945[/C][C]0.277674569484135[/C][/ROW]
[ROW][C]33[/C][C]7050[/C][C]8241.13211821468[/C][C]87.2521494443014[/C][C]-383.909492813968[/C][C]-0.627789735538817[/C][/ROW]
[ROW][C]34[/C][C]7300[/C][C]7620.90727131212[/C][C]79.2811342390258[/C][C]771.163353582918[/C][C]-0.848982030428465[/C][/ROW]
[ROW][C]35[/C][C]5900[/C][C]7407.63309659358[/C][C]76.144820802226[/C][C]-1055.33639746848[/C][C]-0.351437251681709[/C][/ROW]
[ROW][C]36[/C][C]8350[/C][C]7528.77691438854[/C][C]76.48447830143[/C][C]751.233839713342[/C][C]0.0542354963549573[/C][/ROW]
[ROW][C]37[/C][C]8050[/C][C]7997.50320298777[/C][C]67.4637979525955[/C][C]-597.233224445173[/C][C]0.515614627535562[/C][/ROW]
[ROW][C]38[/C][C]4200[/C][C]6709.92957514798[/C][C]49.3962262767498[/C][C]-543.921991827927[/C][C]-1.5535141090794[/C][/ROW]
[ROW][C]39[/C][C]7300[/C][C]6860.43649298615[/C][C]51.1928120946091[/C][C]295.317188230886[/C][C]0.114974114159167[/C][/ROW]
[ROW][C]40[/C][C]6900[/C][C]6952.17897959481[/C][C]51.8324515157249[/C][C]-111.541543042032[/C][C]0.0471257892978286[/C][/ROW]
[ROW][C]41[/C][C]5300[/C][C]6433.9371617054[/C][C]44.1812487196157[/C][C]-282.827853851453[/C][C]-0.672975161045951[/C][/ROW]
[ROW][C]42[/C][C]9600[/C][C]7332.21819774798[/C][C]54.1778024117326[/C][C]978.090007928535[/C][C]1.01727184751791[/C][/ROW]
[ROW][C]43[/C][C]7900[/C][C]7802.72054487765[/C][C]58.5791833398921[/C][C]-535.383719946281[/C][C]0.498324462114823[/C][/ROW]
[ROW][C]44[/C][C]4150[/C][C]6443.4211415364[/C][C]44.6239810555563[/C][C]-130.864453295054[/C][C]-1.70197006310343[/C][/ROW]
[ROW][C]45[/C][C]4900[/C][C]5970.59490664286[/C][C]39.7790075385576[/C][C]-279.64703035744[/C][C]-0.622182381453319[/C][/ROW]
[ROW][C]46[/C][C]8100[/C][C]6416.4945310217[/C][C]43.4272593599339[/C][C]1061.81669981746[/C][C]0.488857567380724[/C][/ROW]
[ROW][C]47[/C][C]7200[/C][C]7101.49186125872[/C][C]48.7291345415574[/C][C]-885.324732799598[/C][C]0.773085186157459[/C][/ROW]
[ROW][C]48[/C][C]6700[/C][C]6797.00653009492[/C][C]47.0475615287677[/C][C]448.155462755201[/C][C]-0.427271712339795[/C][/ROW]
[ROW][C]49[/C][C]7350[/C][C]7039.23271165744[/C][C]44.3980623913499[/C][C]-3.25237936500666[/C][C]0.248914397114701[/C][/ROW]
[ROW][C]50[/C][C]4650[/C][C]6448.7906364253[/C][C]38.4708743068803[/C][C]-861.903992245853[/C][C]-0.742901316026392[/C][/ROW]
[ROW][C]51[/C][C]7100[/C][C]6563.60785183545[/C][C]39.5513306588395[/C][C]426.199592467494[/C][C]0.0880989285353244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299966&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
1200200000
22100965.28158822611480.9188118335624141.8610742075080.776808290979275
312501110.9701682699486.223732597098355.20741390769650.0659187382801694
422501572.83315030644109.891281343032156.7833647157690.401806170000432
558503228.37718627908188.880938743754381.7834255295681.70931189657582
649003933.76706624866211.355922822379195.815231278210.583645197010141
747004283.55185238561216.689826013948206.0808838570640.158625365281126
836504110.71677335948202.9992744287138.505786353821-0.450463835921579
949504463.83320750336207.915535074525253.3466972048740.174664647737058
10102506637.72152634319268.803207072685546.1194624217372.29700970806168
1138505737.72944316643234.223701711713-57.5963089888293-1.36963324541208
1230504796.02522496978200.761421565159100.724419067426-1.38099076709912
1391506438.8127029495448.0152985568317-122.5778081526032.38018496711971
1486507392.1377551872681.4184646283872113.4245796389740.908505962644757
1573507452.3416544339780.6701153950351-73.8896219761047-0.0224770687036986
1670507357.9360437798875.6432989688809-55.8527786580969-0.196133071558823
1781507604.282636190779.7332780966923290.5551259670050.196889432270787
1892008210.5017525256790.7137385404269186.9247109755170.61657053764138
1970507838.3861682916681.995568962012-75.1574517597385-0.546587803161793
20118009268.32237991282105.582676395337441.3268274474391.59963724827876
21109509990.69512112513115.812905879335-0.8827699383523960.734125365985881
221320011041.4997133169130.715312675588699.3753415199931.11494993451509
2352509151.8754730524499.6145179327473-743.427281521675-2.41233125191628
241450011069.6840580792123.558304214426575.0069980246592.17624426478419
25800010614.1876323963148.157188053666-1605.87333910497-0.807764350381969
2683509795.42557732275128.083869133749-93.5361338558763-1.06526882478879
2787509449.04081750869116.899417970637-34.4465237095987-0.527109325415067
2877508913.14622535329103.891592619396-210.225281121516-0.749902122252929
2973008301.2973836559991.907305442050670.5163115797992-0.83888784553265
3097508737.7517410640396.9348509737423489.0905924785670.408219983088076
3171008348.8940854207390.5235461392288-505.586550975428-0.579009902840966
3295008671.5905651464793.3775343806396471.5866850709450.277674569484135
3370508241.1321182146887.2521494443014-383.909492813968-0.627789735538817
3473007620.9072713121279.2811342390258771.163353582918-0.848982030428465
3559007407.6330965935876.144820802226-1055.33639746848-0.351437251681709
3683507528.7769143885476.48447830143751.2338397133420.0542354963549573
3780507997.5032029877767.4637979525955-597.2332244451730.515614627535562
3842006709.9295751479849.3962262767498-543.921991827927-1.5535141090794
3973006860.4364929861551.1928120946091295.3171882308860.114974114159167
4069006952.1789795948151.8324515157249-111.5415430420320.0471257892978286
4153006433.937161705444.1812487196157-282.827853851453-0.672975161045951
4296007332.2181977479854.1778024117326978.0900079285351.01727184751791
4379007802.7205448776558.5791833398921-535.3837199462810.498324462114823
4441506443.421141536444.6239810555563-130.864453295054-1.70197006310343
4549005970.5949066428639.7790075385576-279.64703035744-0.622182381453319
4681006416.494531021743.42725935993391061.816699817460.488857567380724
4772007101.4918612587248.7291345415574-885.3247327995980.773085186157459
4867006797.0065300949247.0475615287677448.155462755201-0.427271712339795
4973507039.2327116574444.3980623913499-3.252379365006660.248914397114701
5046506448.790636425338.4708743068803-861.903992245853-0.742901316026392
5171006563.6078518354539.5513306588395426.1995924674940.0880989285353244







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
16275.070041231866596.22075069392-321.150709462058
25197.491375265896571.18398539798-1373.69261013209
38699.117606394256546.147220102032152.97038629221
47064.038130338796521.11045480609542.9276755327
55674.140090844046496.07368951015-821.933598666105
65876.277490087216471.0369242142-594.759434126997
77914.987480509056446.000158918261468.98732159079
86033.986883904686420.96339362232-386.976509717637
96674.58960755976395.92662832638278.662979233322
107030.842980220646370.88986303043659.953117190207
114342.078985821066345.85309773449-2003.77411191343
126719.601826617636320.81633243855398.785494179083
135974.628857680546295.7795671426-321.150709462058
144897.050191714576270.74280184666-1373.69261013209
158398.676422842936245.706036550722152.97038629221
166763.596946787476220.66927125477542.9276755327
175373.698907292736195.63250595883-821.933598666104
185575.836306535896170.59574066289-594.759434126997

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 6275.07004123186 & 6596.22075069392 & -321.150709462058 \tabularnewline
2 & 5197.49137526589 & 6571.18398539798 & -1373.69261013209 \tabularnewline
3 & 8699.11760639425 & 6546.14722010203 & 2152.97038629221 \tabularnewline
4 & 7064.03813033879 & 6521.11045480609 & 542.9276755327 \tabularnewline
5 & 5674.14009084404 & 6496.07368951015 & -821.933598666105 \tabularnewline
6 & 5876.27749008721 & 6471.0369242142 & -594.759434126997 \tabularnewline
7 & 7914.98748050905 & 6446.00015891826 & 1468.98732159079 \tabularnewline
8 & 6033.98688390468 & 6420.96339362232 & -386.976509717637 \tabularnewline
9 & 6674.5896075597 & 6395.92662832638 & 278.662979233322 \tabularnewline
10 & 7030.84298022064 & 6370.88986303043 & 659.953117190207 \tabularnewline
11 & 4342.07898582106 & 6345.85309773449 & -2003.77411191343 \tabularnewline
12 & 6719.60182661763 & 6320.81633243855 & 398.785494179083 \tabularnewline
13 & 5974.62885768054 & 6295.7795671426 & -321.150709462058 \tabularnewline
14 & 4897.05019171457 & 6270.74280184666 & -1373.69261013209 \tabularnewline
15 & 8398.67642284293 & 6245.70603655072 & 2152.97038629221 \tabularnewline
16 & 6763.59694678747 & 6220.66927125477 & 542.9276755327 \tabularnewline
17 & 5373.69890729273 & 6195.63250595883 & -821.933598666104 \tabularnewline
18 & 5575.83630653589 & 6170.59574066289 & -594.759434126997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299966&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]6275.07004123186[/C][C]6596.22075069392[/C][C]-321.150709462058[/C][/ROW]
[ROW][C]2[/C][C]5197.49137526589[/C][C]6571.18398539798[/C][C]-1373.69261013209[/C][/ROW]
[ROW][C]3[/C][C]8699.11760639425[/C][C]6546.14722010203[/C][C]2152.97038629221[/C][/ROW]
[ROW][C]4[/C][C]7064.03813033879[/C][C]6521.11045480609[/C][C]542.9276755327[/C][/ROW]
[ROW][C]5[/C][C]5674.14009084404[/C][C]6496.07368951015[/C][C]-821.933598666105[/C][/ROW]
[ROW][C]6[/C][C]5876.27749008721[/C][C]6471.0369242142[/C][C]-594.759434126997[/C][/ROW]
[ROW][C]7[/C][C]7914.98748050905[/C][C]6446.00015891826[/C][C]1468.98732159079[/C][/ROW]
[ROW][C]8[/C][C]6033.98688390468[/C][C]6420.96339362232[/C][C]-386.976509717637[/C][/ROW]
[ROW][C]9[/C][C]6674.5896075597[/C][C]6395.92662832638[/C][C]278.662979233322[/C][/ROW]
[ROW][C]10[/C][C]7030.84298022064[/C][C]6370.88986303043[/C][C]659.953117190207[/C][/ROW]
[ROW][C]11[/C][C]4342.07898582106[/C][C]6345.85309773449[/C][C]-2003.77411191343[/C][/ROW]
[ROW][C]12[/C][C]6719.60182661763[/C][C]6320.81633243855[/C][C]398.785494179083[/C][/ROW]
[ROW][C]13[/C][C]5974.62885768054[/C][C]6295.7795671426[/C][C]-321.150709462058[/C][/ROW]
[ROW][C]14[/C][C]4897.05019171457[/C][C]6270.74280184666[/C][C]-1373.69261013209[/C][/ROW]
[ROW][C]15[/C][C]8398.67642284293[/C][C]6245.70603655072[/C][C]2152.97038629221[/C][/ROW]
[ROW][C]16[/C][C]6763.59694678747[/C][C]6220.66927125477[/C][C]542.9276755327[/C][/ROW]
[ROW][C]17[/C][C]5373.69890729273[/C][C]6195.63250595883[/C][C]-821.933598666104[/C][/ROW]
[ROW][C]18[/C][C]5575.83630653589[/C][C]6170.59574066289[/C][C]-594.759434126997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299966&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299966&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
16275.070041231866596.22075069392-321.150709462058
25197.491375265896571.18398539798-1373.69261013209
38699.117606394256546.147220102032152.97038629221
47064.038130338796521.11045480609542.9276755327
55674.140090844046496.07368951015-821.933598666105
65876.277490087216471.0369242142-594.759434126997
77914.987480509056446.000158918261468.98732159079
86033.986883904686420.96339362232-386.976509717637
96674.58960755976395.92662832638278.662979233322
107030.842980220646370.88986303043659.953117190207
114342.078985821066345.85309773449-2003.77411191343
126719.601826617636320.81633243855398.785494179083
135974.628857680546295.7795671426-321.150709462058
144897.050191714576270.74280184666-1373.69261013209
158398.676422842936245.706036550722152.97038629221
166763.596946787476220.66927125477542.9276755327
175373.698907292736195.63250595883-821.933598666104
185575.836306535896170.59574066289-594.759434126997



Parameters (Session):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')