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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 21 Dec 2016 16:39:31 +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/21/t14823350806z6jv4jxmn0nk3u.htm/, Retrieved Fri, 01 Nov 2024 03:29:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302394, Retrieved Fri, 01 Nov 2024 03:29:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-21 15:39:31] [361c8dad91b3f1ef2e651cd04783c23b] [Current]
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Dataseries X:
5300
3800
3900
5400
6100
4200
4000
4600
7300
4400
4000
5300
9300
4300
3400
6000
6500
3400
2900
5000
5800
3000
2300
4000
5800
2900
2200
3900
5300
3000
2000
3700
6000
2800
1800
3900
5400
2400
1700
3500
5400
3900
2900
4600
5400
2900
2700
4500
6300
2800
1900
5100
6200
3500
3500
6000
6000
3400
2800
4900




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=302394&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=302394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302394&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
153005300000
238004110.63933182253-341.182104507436-282.071172387331-0.680378916117956
339003994.64427267692-290.669507687907-133.0558234319440.428326816137182
454004588.63115764696-151.150708761998542.6603065889332.42535540396693
561004950.59052186233-143.456093712423941.5772410529161.71956444149553
642004852.99493134869-139.636033192133-667.8693064538840.130647697913972
740004638.38499667779-147.356308114967-615.69650845802-0.207819591533801
846004407.3494398371-154.739827411048219.968608091703-0.245056224235321
973005089.9165764839-107.849979766381913.889073633282.57847474940788
1044005147.05144044611-97.263221775834-803.3657493268650.495327616223063
1140004943.99958945023-104.778934014065-908.734519606821-0.313841767179693
1253005103.4512593633-87.1485443498541106.8808698246210.794742238633787
1393006041.79453730157-28.17928183221162901.44148287933.13295866895902
1443005823.03568742823-39.0861065387168-1456.94386911672-0.580817358678747
1534005289.76364866299-67.9998918519453-1719.27804296462-1.50229604675062
1660005605.83920339813-46.1649242992738260.9408008147621.17262222487987
1765004760.87864354408-89.05977293620072018.5415047949-2.45234716228631
1834004535.34763192304-96.2444213115163-1087.5337895882-0.419411207515178
1929004505.25329549349-92.7766428655704-1628.425152337220.203334819542868
2050004377.97731140545-94.5545214513584634.135958243075-0.106242982396169
2158004053.76210733416-106.0856346524261827.14882502595-0.708906368854486
2230003974.81166890057-104.744998608551-984.3874184403710.0838572433641297
2323003872.895084992-104.606571852963-1573.894044698780.00874693193056243
2440003562.73844231804-114.548106547318509.957879802903-0.636335230488315
2558003627.42690903118-106.0014921160072109.078449679420.555529979889523
2629003681.51295727432-98.4537147788256-838.2908150649920.496600384972143
2722003658.13688781071-94.9440532094524-1484.78685755120.233044294377766
2839003557.20327975485-95.2216805658892344.924707665967-0.0186044342267392
2953003392.35602955354-98.42064382899991932.40409666895-0.21641651891538
3030003513.33186346507-88.4180325359664-591.4148538721370.682341946743878
3120003480.1889320864-85.9142974562408-1499.873966106380.171993189839651
3237003391.09769303645-86.0573296385848310.034399003587-0.00988985804722541
3360003657.29503640244-70.29076652630692217.105375808251.0970561476281
3428003582.01806312083-70.5127626774533-780.239244441287-0.0155350236453873
3518003453.68761502354-73.0748918130801-1633.05179159046-0.180198361241614
3639003526.49525061999-66.6379616309329321.4155098090470.454810245835971
3754003369.83904601005-70.5940180924612062.3158759987-0.280727601969208
3824003235.77612402572-73.3730881522017-813.096601358264-0.197984422372977
3917003242.26973280884-69.887563126159-1570.817882585780.249194925604817
4035003165.06471737959-70.2059471831941337.551653058291-0.0228364112332746
4154003182.95227219183-66.38363468854322185.541207720640.274978550018147
4239003780.99514511036-37.628017248226-118.6848355237262.07434550916496
4329004153.28164303497-19.9284272464395-1399.955706509571.27996816220039
4446004326.83768497839-11.5916558510457203.9163951957970.604251007799844
4554004083.28966752995-21.56672866332611399.74033582791-0.724498443873203
4629003708.31465521211-36.7377964017069-681.788840092594-1.10398339507008
4727003801.53439927118-31.1680134182426-1148.068453345770.406010273940477
4845003925.31025222618-24.5371581969143519.2010066556720.484122514965247
4963004260.62438160014-9.158052654499651910.488539563571.12446361123594
5028004048.68531278678-17.8136764913591-1176.04719149432-0.633705513528648
5119003666.60782078653-33.3445809601471-1636.11103111281-1.13844153679658
5251004003.84134014689-17.5607466818586963.3868233220461.15825969569464
5362004100.33651430181-12.70740319905862058.795541075120.356510887800448
5435004294.10260155745-3.92904969233386-868.0911745141060.645424630825045
5535004747.5053574681315.4993962913391-1411.399736365381.4296726931019
5660004991.4122092536825.1956584155627926.7276630815710.714064408107432
5760004709.5984739112.17118951357621400.43903295084-0.959839843785264
5834004601.508419459127.07233171255281-1158.40225577983-0.376002790961933
5928004453.539873890530.502491913665148-1597.96450331396-0.484761672827901
6049004163.12332671453-11.8189811474789841.163346597651-0.909639766263974

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 5300 & 5300 & 0 & 0 & 0 \tabularnewline
2 & 3800 & 4110.63933182253 & -341.182104507436 & -282.071172387331 & -0.680378916117956 \tabularnewline
3 & 3900 & 3994.64427267692 & -290.669507687907 & -133.055823431944 & 0.428326816137182 \tabularnewline
4 & 5400 & 4588.63115764696 & -151.150708761998 & 542.660306588933 & 2.42535540396693 \tabularnewline
5 & 6100 & 4950.59052186233 & -143.456093712423 & 941.577241052916 & 1.71956444149553 \tabularnewline
6 & 4200 & 4852.99493134869 & -139.636033192133 & -667.869306453884 & 0.130647697913972 \tabularnewline
7 & 4000 & 4638.38499667779 & -147.356308114967 & -615.69650845802 & -0.207819591533801 \tabularnewline
8 & 4600 & 4407.3494398371 & -154.739827411048 & 219.968608091703 & -0.245056224235321 \tabularnewline
9 & 7300 & 5089.9165764839 & -107.84997976638 & 1913.88907363328 & 2.57847474940788 \tabularnewline
10 & 4400 & 5147.05144044611 & -97.263221775834 & -803.365749326865 & 0.495327616223063 \tabularnewline
11 & 4000 & 4943.99958945023 & -104.778934014065 & -908.734519606821 & -0.313841767179693 \tabularnewline
12 & 5300 & 5103.4512593633 & -87.1485443498541 & 106.880869824621 & 0.794742238633787 \tabularnewline
13 & 9300 & 6041.79453730157 & -28.1792818322116 & 2901.4414828793 & 3.13295866895902 \tabularnewline
14 & 4300 & 5823.03568742823 & -39.0861065387168 & -1456.94386911672 & -0.580817358678747 \tabularnewline
15 & 3400 & 5289.76364866299 & -67.9998918519453 & -1719.27804296462 & -1.50229604675062 \tabularnewline
16 & 6000 & 5605.83920339813 & -46.1649242992738 & 260.940800814762 & 1.17262222487987 \tabularnewline
17 & 6500 & 4760.87864354408 & -89.0597729362007 & 2018.5415047949 & -2.45234716228631 \tabularnewline
18 & 3400 & 4535.34763192304 & -96.2444213115163 & -1087.5337895882 & -0.419411207515178 \tabularnewline
19 & 2900 & 4505.25329549349 & -92.7766428655704 & -1628.42515233722 & 0.203334819542868 \tabularnewline
20 & 5000 & 4377.97731140545 & -94.5545214513584 & 634.135958243075 & -0.106242982396169 \tabularnewline
21 & 5800 & 4053.76210733416 & -106.085634652426 & 1827.14882502595 & -0.708906368854486 \tabularnewline
22 & 3000 & 3974.81166890057 & -104.744998608551 & -984.387418440371 & 0.0838572433641297 \tabularnewline
23 & 2300 & 3872.895084992 & -104.606571852963 & -1573.89404469878 & 0.00874693193056243 \tabularnewline
24 & 4000 & 3562.73844231804 & -114.548106547318 & 509.957879802903 & -0.636335230488315 \tabularnewline
25 & 5800 & 3627.42690903118 & -106.001492116007 & 2109.07844967942 & 0.555529979889523 \tabularnewline
26 & 2900 & 3681.51295727432 & -98.4537147788256 & -838.290815064992 & 0.496600384972143 \tabularnewline
27 & 2200 & 3658.13688781071 & -94.9440532094524 & -1484.7868575512 & 0.233044294377766 \tabularnewline
28 & 3900 & 3557.20327975485 & -95.2216805658892 & 344.924707665967 & -0.0186044342267392 \tabularnewline
29 & 5300 & 3392.35602955354 & -98.4206438289999 & 1932.40409666895 & -0.21641651891538 \tabularnewline
30 & 3000 & 3513.33186346507 & -88.4180325359664 & -591.414853872137 & 0.682341946743878 \tabularnewline
31 & 2000 & 3480.1889320864 & -85.9142974562408 & -1499.87396610638 & 0.171993189839651 \tabularnewline
32 & 3700 & 3391.09769303645 & -86.0573296385848 & 310.034399003587 & -0.00988985804722541 \tabularnewline
33 & 6000 & 3657.29503640244 & -70.2907665263069 & 2217.10537580825 & 1.0970561476281 \tabularnewline
34 & 2800 & 3582.01806312083 & -70.5127626774533 & -780.239244441287 & -0.0155350236453873 \tabularnewline
35 & 1800 & 3453.68761502354 & -73.0748918130801 & -1633.05179159046 & -0.180198361241614 \tabularnewline
36 & 3900 & 3526.49525061999 & -66.6379616309329 & 321.415509809047 & 0.454810245835971 \tabularnewline
37 & 5400 & 3369.83904601005 & -70.594018092461 & 2062.3158759987 & -0.280727601969208 \tabularnewline
38 & 2400 & 3235.77612402572 & -73.3730881522017 & -813.096601358264 & -0.197984422372977 \tabularnewline
39 & 1700 & 3242.26973280884 & -69.887563126159 & -1570.81788258578 & 0.249194925604817 \tabularnewline
40 & 3500 & 3165.06471737959 & -70.2059471831941 & 337.551653058291 & -0.0228364112332746 \tabularnewline
41 & 5400 & 3182.95227219183 & -66.3836346885432 & 2185.54120772064 & 0.274978550018147 \tabularnewline
42 & 3900 & 3780.99514511036 & -37.628017248226 & -118.684835523726 & 2.07434550916496 \tabularnewline
43 & 2900 & 4153.28164303497 & -19.9284272464395 & -1399.95570650957 & 1.27996816220039 \tabularnewline
44 & 4600 & 4326.83768497839 & -11.5916558510457 & 203.916395195797 & 0.604251007799844 \tabularnewline
45 & 5400 & 4083.28966752995 & -21.5667286633261 & 1399.74033582791 & -0.724498443873203 \tabularnewline
46 & 2900 & 3708.31465521211 & -36.7377964017069 & -681.788840092594 & -1.10398339507008 \tabularnewline
47 & 2700 & 3801.53439927118 & -31.1680134182426 & -1148.06845334577 & 0.406010273940477 \tabularnewline
48 & 4500 & 3925.31025222618 & -24.5371581969143 & 519.201006655672 & 0.484122514965247 \tabularnewline
49 & 6300 & 4260.62438160014 & -9.15805265449965 & 1910.48853956357 & 1.12446361123594 \tabularnewline
50 & 2800 & 4048.68531278678 & -17.8136764913591 & -1176.04719149432 & -0.633705513528648 \tabularnewline
51 & 1900 & 3666.60782078653 & -33.3445809601471 & -1636.11103111281 & -1.13844153679658 \tabularnewline
52 & 5100 & 4003.84134014689 & -17.5607466818586 & 963.386823322046 & 1.15825969569464 \tabularnewline
53 & 6200 & 4100.33651430181 & -12.7074031990586 & 2058.79554107512 & 0.356510887800448 \tabularnewline
54 & 3500 & 4294.10260155745 & -3.92904969233386 & -868.091174514106 & 0.645424630825045 \tabularnewline
55 & 3500 & 4747.50535746813 & 15.4993962913391 & -1411.39973636538 & 1.4296726931019 \tabularnewline
56 & 6000 & 4991.41220925368 & 25.1956584155627 & 926.727663081571 & 0.714064408107432 \tabularnewline
57 & 6000 & 4709.59847391 & 12.1711895135762 & 1400.43903295084 & -0.959839843785264 \tabularnewline
58 & 3400 & 4601.50841945912 & 7.07233171255281 & -1158.40225577983 & -0.376002790961933 \tabularnewline
59 & 2800 & 4453.53987389053 & 0.502491913665148 & -1597.96450331396 & -0.484761672827901 \tabularnewline
60 & 4900 & 4163.12332671453 & -11.8189811474789 & 841.163346597651 & -0.909639766263974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302394&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]5300[/C][C]5300[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3800[/C][C]4110.63933182253[/C][C]-341.182104507436[/C][C]-282.071172387331[/C][C]-0.680378916117956[/C][/ROW]
[ROW][C]3[/C][C]3900[/C][C]3994.64427267692[/C][C]-290.669507687907[/C][C]-133.055823431944[/C][C]0.428326816137182[/C][/ROW]
[ROW][C]4[/C][C]5400[/C][C]4588.63115764696[/C][C]-151.150708761998[/C][C]542.660306588933[/C][C]2.42535540396693[/C][/ROW]
[ROW][C]5[/C][C]6100[/C][C]4950.59052186233[/C][C]-143.456093712423[/C][C]941.577241052916[/C][C]1.71956444149553[/C][/ROW]
[ROW][C]6[/C][C]4200[/C][C]4852.99493134869[/C][C]-139.636033192133[/C][C]-667.869306453884[/C][C]0.130647697913972[/C][/ROW]
[ROW][C]7[/C][C]4000[/C][C]4638.38499667779[/C][C]-147.356308114967[/C][C]-615.69650845802[/C][C]-0.207819591533801[/C][/ROW]
[ROW][C]8[/C][C]4600[/C][C]4407.3494398371[/C][C]-154.739827411048[/C][C]219.968608091703[/C][C]-0.245056224235321[/C][/ROW]
[ROW][C]9[/C][C]7300[/C][C]5089.9165764839[/C][C]-107.84997976638[/C][C]1913.88907363328[/C][C]2.57847474940788[/C][/ROW]
[ROW][C]10[/C][C]4400[/C][C]5147.05144044611[/C][C]-97.263221775834[/C][C]-803.365749326865[/C][C]0.495327616223063[/C][/ROW]
[ROW][C]11[/C][C]4000[/C][C]4943.99958945023[/C][C]-104.778934014065[/C][C]-908.734519606821[/C][C]-0.313841767179693[/C][/ROW]
[ROW][C]12[/C][C]5300[/C][C]5103.4512593633[/C][C]-87.1485443498541[/C][C]106.880869824621[/C][C]0.794742238633787[/C][/ROW]
[ROW][C]13[/C][C]9300[/C][C]6041.79453730157[/C][C]-28.1792818322116[/C][C]2901.4414828793[/C][C]3.13295866895902[/C][/ROW]
[ROW][C]14[/C][C]4300[/C][C]5823.03568742823[/C][C]-39.0861065387168[/C][C]-1456.94386911672[/C][C]-0.580817358678747[/C][/ROW]
[ROW][C]15[/C][C]3400[/C][C]5289.76364866299[/C][C]-67.9998918519453[/C][C]-1719.27804296462[/C][C]-1.50229604675062[/C][/ROW]
[ROW][C]16[/C][C]6000[/C][C]5605.83920339813[/C][C]-46.1649242992738[/C][C]260.940800814762[/C][C]1.17262222487987[/C][/ROW]
[ROW][C]17[/C][C]6500[/C][C]4760.87864354408[/C][C]-89.0597729362007[/C][C]2018.5415047949[/C][C]-2.45234716228631[/C][/ROW]
[ROW][C]18[/C][C]3400[/C][C]4535.34763192304[/C][C]-96.2444213115163[/C][C]-1087.5337895882[/C][C]-0.419411207515178[/C][/ROW]
[ROW][C]19[/C][C]2900[/C][C]4505.25329549349[/C][C]-92.7766428655704[/C][C]-1628.42515233722[/C][C]0.203334819542868[/C][/ROW]
[ROW][C]20[/C][C]5000[/C][C]4377.97731140545[/C][C]-94.5545214513584[/C][C]634.135958243075[/C][C]-0.106242982396169[/C][/ROW]
[ROW][C]21[/C][C]5800[/C][C]4053.76210733416[/C][C]-106.085634652426[/C][C]1827.14882502595[/C][C]-0.708906368854486[/C][/ROW]
[ROW][C]22[/C][C]3000[/C][C]3974.81166890057[/C][C]-104.744998608551[/C][C]-984.387418440371[/C][C]0.0838572433641297[/C][/ROW]
[ROW][C]23[/C][C]2300[/C][C]3872.895084992[/C][C]-104.606571852963[/C][C]-1573.89404469878[/C][C]0.00874693193056243[/C][/ROW]
[ROW][C]24[/C][C]4000[/C][C]3562.73844231804[/C][C]-114.548106547318[/C][C]509.957879802903[/C][C]-0.636335230488315[/C][/ROW]
[ROW][C]25[/C][C]5800[/C][C]3627.42690903118[/C][C]-106.001492116007[/C][C]2109.07844967942[/C][C]0.555529979889523[/C][/ROW]
[ROW][C]26[/C][C]2900[/C][C]3681.51295727432[/C][C]-98.4537147788256[/C][C]-838.290815064992[/C][C]0.496600384972143[/C][/ROW]
[ROW][C]27[/C][C]2200[/C][C]3658.13688781071[/C][C]-94.9440532094524[/C][C]-1484.7868575512[/C][C]0.233044294377766[/C][/ROW]
[ROW][C]28[/C][C]3900[/C][C]3557.20327975485[/C][C]-95.2216805658892[/C][C]344.924707665967[/C][C]-0.0186044342267392[/C][/ROW]
[ROW][C]29[/C][C]5300[/C][C]3392.35602955354[/C][C]-98.4206438289999[/C][C]1932.40409666895[/C][C]-0.21641651891538[/C][/ROW]
[ROW][C]30[/C][C]3000[/C][C]3513.33186346507[/C][C]-88.4180325359664[/C][C]-591.414853872137[/C][C]0.682341946743878[/C][/ROW]
[ROW][C]31[/C][C]2000[/C][C]3480.1889320864[/C][C]-85.9142974562408[/C][C]-1499.87396610638[/C][C]0.171993189839651[/C][/ROW]
[ROW][C]32[/C][C]3700[/C][C]3391.09769303645[/C][C]-86.0573296385848[/C][C]310.034399003587[/C][C]-0.00988985804722541[/C][/ROW]
[ROW][C]33[/C][C]6000[/C][C]3657.29503640244[/C][C]-70.2907665263069[/C][C]2217.10537580825[/C][C]1.0970561476281[/C][/ROW]
[ROW][C]34[/C][C]2800[/C][C]3582.01806312083[/C][C]-70.5127626774533[/C][C]-780.239244441287[/C][C]-0.0155350236453873[/C][/ROW]
[ROW][C]35[/C][C]1800[/C][C]3453.68761502354[/C][C]-73.0748918130801[/C][C]-1633.05179159046[/C][C]-0.180198361241614[/C][/ROW]
[ROW][C]36[/C][C]3900[/C][C]3526.49525061999[/C][C]-66.6379616309329[/C][C]321.415509809047[/C][C]0.454810245835971[/C][/ROW]
[ROW][C]37[/C][C]5400[/C][C]3369.83904601005[/C][C]-70.594018092461[/C][C]2062.3158759987[/C][C]-0.280727601969208[/C][/ROW]
[ROW][C]38[/C][C]2400[/C][C]3235.77612402572[/C][C]-73.3730881522017[/C][C]-813.096601358264[/C][C]-0.197984422372977[/C][/ROW]
[ROW][C]39[/C][C]1700[/C][C]3242.26973280884[/C][C]-69.887563126159[/C][C]-1570.81788258578[/C][C]0.249194925604817[/C][/ROW]
[ROW][C]40[/C][C]3500[/C][C]3165.06471737959[/C][C]-70.2059471831941[/C][C]337.551653058291[/C][C]-0.0228364112332746[/C][/ROW]
[ROW][C]41[/C][C]5400[/C][C]3182.95227219183[/C][C]-66.3836346885432[/C][C]2185.54120772064[/C][C]0.274978550018147[/C][/ROW]
[ROW][C]42[/C][C]3900[/C][C]3780.99514511036[/C][C]-37.628017248226[/C][C]-118.684835523726[/C][C]2.07434550916496[/C][/ROW]
[ROW][C]43[/C][C]2900[/C][C]4153.28164303497[/C][C]-19.9284272464395[/C][C]-1399.95570650957[/C][C]1.27996816220039[/C][/ROW]
[ROW][C]44[/C][C]4600[/C][C]4326.83768497839[/C][C]-11.5916558510457[/C][C]203.916395195797[/C][C]0.604251007799844[/C][/ROW]
[ROW][C]45[/C][C]5400[/C][C]4083.28966752995[/C][C]-21.5667286633261[/C][C]1399.74033582791[/C][C]-0.724498443873203[/C][/ROW]
[ROW][C]46[/C][C]2900[/C][C]3708.31465521211[/C][C]-36.7377964017069[/C][C]-681.788840092594[/C][C]-1.10398339507008[/C][/ROW]
[ROW][C]47[/C][C]2700[/C][C]3801.53439927118[/C][C]-31.1680134182426[/C][C]-1148.06845334577[/C][C]0.406010273940477[/C][/ROW]
[ROW][C]48[/C][C]4500[/C][C]3925.31025222618[/C][C]-24.5371581969143[/C][C]519.201006655672[/C][C]0.484122514965247[/C][/ROW]
[ROW][C]49[/C][C]6300[/C][C]4260.62438160014[/C][C]-9.15805265449965[/C][C]1910.48853956357[/C][C]1.12446361123594[/C][/ROW]
[ROW][C]50[/C][C]2800[/C][C]4048.68531278678[/C][C]-17.8136764913591[/C][C]-1176.04719149432[/C][C]-0.633705513528648[/C][/ROW]
[ROW][C]51[/C][C]1900[/C][C]3666.60782078653[/C][C]-33.3445809601471[/C][C]-1636.11103111281[/C][C]-1.13844153679658[/C][/ROW]
[ROW][C]52[/C][C]5100[/C][C]4003.84134014689[/C][C]-17.5607466818586[/C][C]963.386823322046[/C][C]1.15825969569464[/C][/ROW]
[ROW][C]53[/C][C]6200[/C][C]4100.33651430181[/C][C]-12.7074031990586[/C][C]2058.79554107512[/C][C]0.356510887800448[/C][/ROW]
[ROW][C]54[/C][C]3500[/C][C]4294.10260155745[/C][C]-3.92904969233386[/C][C]-868.091174514106[/C][C]0.645424630825045[/C][/ROW]
[ROW][C]55[/C][C]3500[/C][C]4747.50535746813[/C][C]15.4993962913391[/C][C]-1411.39973636538[/C][C]1.4296726931019[/C][/ROW]
[ROW][C]56[/C][C]6000[/C][C]4991.41220925368[/C][C]25.1956584155627[/C][C]926.727663081571[/C][C]0.714064408107432[/C][/ROW]
[ROW][C]57[/C][C]6000[/C][C]4709.59847391[/C][C]12.1711895135762[/C][C]1400.43903295084[/C][C]-0.959839843785264[/C][/ROW]
[ROW][C]58[/C][C]3400[/C][C]4601.50841945912[/C][C]7.07233171255281[/C][C]-1158.40225577983[/C][C]-0.376002790961933[/C][/ROW]
[ROW][C]59[/C][C]2800[/C][C]4453.53987389053[/C][C]0.502491913665148[/C][C]-1597.96450331396[/C][C]-0.484761672827901[/C][/ROW]
[ROW][C]60[/C][C]4900[/C][C]4163.12332671453[/C][C]-11.8189811474789[/C][C]841.163346597651[/C][C]-0.909639766263974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302394&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
153005300000
238004110.63933182253-341.182104507436-282.071172387331-0.680378916117956
339003994.64427267692-290.669507687907-133.0558234319440.428326816137182
454004588.63115764696-151.150708761998542.6603065889332.42535540396693
561004950.59052186233-143.456093712423941.5772410529161.71956444149553
642004852.99493134869-139.636033192133-667.8693064538840.130647697913972
740004638.38499667779-147.356308114967-615.69650845802-0.207819591533801
846004407.3494398371-154.739827411048219.968608091703-0.245056224235321
973005089.9165764839-107.849979766381913.889073633282.57847474940788
1044005147.05144044611-97.263221775834-803.3657493268650.495327616223063
1140004943.99958945023-104.778934014065-908.734519606821-0.313841767179693
1253005103.4512593633-87.1485443498541106.8808698246210.794742238633787
1393006041.79453730157-28.17928183221162901.44148287933.13295866895902
1443005823.03568742823-39.0861065387168-1456.94386911672-0.580817358678747
1534005289.76364866299-67.9998918519453-1719.27804296462-1.50229604675062
1660005605.83920339813-46.1649242992738260.9408008147621.17262222487987
1765004760.87864354408-89.05977293620072018.5415047949-2.45234716228631
1834004535.34763192304-96.2444213115163-1087.5337895882-0.419411207515178
1929004505.25329549349-92.7766428655704-1628.425152337220.203334819542868
2050004377.97731140545-94.5545214513584634.135958243075-0.106242982396169
2158004053.76210733416-106.0856346524261827.14882502595-0.708906368854486
2230003974.81166890057-104.744998608551-984.3874184403710.0838572433641297
2323003872.895084992-104.606571852963-1573.894044698780.00874693193056243
2440003562.73844231804-114.548106547318509.957879802903-0.636335230488315
2558003627.42690903118-106.0014921160072109.078449679420.555529979889523
2629003681.51295727432-98.4537147788256-838.2908150649920.496600384972143
2722003658.13688781071-94.9440532094524-1484.78685755120.233044294377766
2839003557.20327975485-95.2216805658892344.924707665967-0.0186044342267392
2953003392.35602955354-98.42064382899991932.40409666895-0.21641651891538
3030003513.33186346507-88.4180325359664-591.4148538721370.682341946743878
3120003480.1889320864-85.9142974562408-1499.873966106380.171993189839651
3237003391.09769303645-86.0573296385848310.034399003587-0.00988985804722541
3360003657.29503640244-70.29076652630692217.105375808251.0970561476281
3428003582.01806312083-70.5127626774533-780.239244441287-0.0155350236453873
3518003453.68761502354-73.0748918130801-1633.05179159046-0.180198361241614
3639003526.49525061999-66.6379616309329321.4155098090470.454810245835971
3754003369.83904601005-70.5940180924612062.3158759987-0.280727601969208
3824003235.77612402572-73.3730881522017-813.096601358264-0.197984422372977
3917003242.26973280884-69.887563126159-1570.817882585780.249194925604817
4035003165.06471737959-70.2059471831941337.551653058291-0.0228364112332746
4154003182.95227219183-66.38363468854322185.541207720640.274978550018147
4239003780.99514511036-37.628017248226-118.6848355237262.07434550916496
4329004153.28164303497-19.9284272464395-1399.955706509571.27996816220039
4446004326.83768497839-11.5916558510457203.9163951957970.604251007799844
4554004083.28966752995-21.56672866332611399.74033582791-0.724498443873203
4629003708.31465521211-36.7377964017069-681.788840092594-1.10398339507008
4727003801.53439927118-31.1680134182426-1148.068453345770.406010273940477
4845003925.31025222618-24.5371581969143519.2010066556720.484122514965247
4963004260.62438160014-9.158052654499651910.488539563571.12446361123594
5028004048.68531278678-17.8136764913591-1176.04719149432-0.633705513528648
5119003666.60782078653-33.3445809601471-1636.11103111281-1.13844153679658
5251004003.84134014689-17.5607466818586963.3868233220461.15825969569464
5362004100.33651430181-12.70740319905862058.795541075120.356510887800448
5435004294.10260155745-3.92904969233386-868.0911745141060.645424630825045
5535004747.5053574681315.4993962913391-1411.399736365381.4296726931019
5660004991.4122092536825.1956584155627926.7276630815710.714064408107432
5760004709.5984739112.17118951357621400.43903295084-0.959839843785264
5834004601.508419459127.07233171255281-1158.40225577983-0.376002790961933
5928004453.539873890530.502491913665148-1597.96450331396-0.484761672827901
6049004163.12332671453-11.8189811474789841.163346597651-0.909639766263974







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15812.233538202654180.155117256791632.07842094586
23163.744314868514181.32877837841-1017.5844635099
32735.356305508344182.50243950002-1447.14613399168
45016.328277177364183.67610062164832.652176555718
55816.928182689124184.849761743261632.07842094586
63168.438959354984186.02342286488-1017.5844635099
72740.050949994824187.1970839865-1447.14613399168
85021.022921663834188.37074510812832.652176555718
95821.622827175594189.544406229731632.07842094586
103173.133603841464190.71806735135-1017.5844635099
112744.745594481294191.89172847297-1447.14613399168
125025.717566150314193.06538959459832.652176555718

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5812.23353820265 & 4180.15511725679 & 1632.07842094586 \tabularnewline
2 & 3163.74431486851 & 4181.32877837841 & -1017.5844635099 \tabularnewline
3 & 2735.35630550834 & 4182.50243950002 & -1447.14613399168 \tabularnewline
4 & 5016.32827717736 & 4183.67610062164 & 832.652176555718 \tabularnewline
5 & 5816.92818268912 & 4184.84976174326 & 1632.07842094586 \tabularnewline
6 & 3168.43895935498 & 4186.02342286488 & -1017.5844635099 \tabularnewline
7 & 2740.05094999482 & 4187.1970839865 & -1447.14613399168 \tabularnewline
8 & 5021.02292166383 & 4188.37074510812 & 832.652176555718 \tabularnewline
9 & 5821.62282717559 & 4189.54440622973 & 1632.07842094586 \tabularnewline
10 & 3173.13360384146 & 4190.71806735135 & -1017.5844635099 \tabularnewline
11 & 2744.74559448129 & 4191.89172847297 & -1447.14613399168 \tabularnewline
12 & 5025.71756615031 & 4193.06538959459 & 832.652176555718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302394&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]5812.23353820265[/C][C]4180.15511725679[/C][C]1632.07842094586[/C][/ROW]
[ROW][C]2[/C][C]3163.74431486851[/C][C]4181.32877837841[/C][C]-1017.5844635099[/C][/ROW]
[ROW][C]3[/C][C]2735.35630550834[/C][C]4182.50243950002[/C][C]-1447.14613399168[/C][/ROW]
[ROW][C]4[/C][C]5016.32827717736[/C][C]4183.67610062164[/C][C]832.652176555718[/C][/ROW]
[ROW][C]5[/C][C]5816.92818268912[/C][C]4184.84976174326[/C][C]1632.07842094586[/C][/ROW]
[ROW][C]6[/C][C]3168.43895935498[/C][C]4186.02342286488[/C][C]-1017.5844635099[/C][/ROW]
[ROW][C]7[/C][C]2740.05094999482[/C][C]4187.1970839865[/C][C]-1447.14613399168[/C][/ROW]
[ROW][C]8[/C][C]5021.02292166383[/C][C]4188.37074510812[/C][C]832.652176555718[/C][/ROW]
[ROW][C]9[/C][C]5821.62282717559[/C][C]4189.54440622973[/C][C]1632.07842094586[/C][/ROW]
[ROW][C]10[/C][C]3173.13360384146[/C][C]4190.71806735135[/C][C]-1017.5844635099[/C][/ROW]
[ROW][C]11[/C][C]2744.74559448129[/C][C]4191.89172847297[/C][C]-1447.14613399168[/C][/ROW]
[ROW][C]12[/C][C]5025.71756615031[/C][C]4193.06538959459[/C][C]832.652176555718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302394&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
15812.233538202654180.155117256791632.07842094586
23163.744314868514181.32877837841-1017.5844635099
32735.356305508344182.50243950002-1447.14613399168
45016.328277177364183.67610062164832.652176555718
55816.928182689124184.849761743261632.07842094586
63168.438959354984186.02342286488-1017.5844635099
72740.050949994824187.1970839865-1447.14613399168
85021.022921663834188.37074510812832.652176555718
95821.622827175594189.544406229731632.07842094586
103173.133603841464190.71806735135-1017.5844635099
112744.745594481294191.89172847297-1447.14613399168
125025.717566150314193.06538959459832.652176555718



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 4 ; 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')