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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, 25 Jan 2017 11:05:30 +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/2017/Jan/25/t14853387572cnctdxk31hi33d.htm/, Retrieved Mon, 13 May 2024 21:16:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306559, Retrieved Mon, 13 May 2024 21:16:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2017-01-25 10:05:30] [4b9ab307db0841e06829391b8f16ae7f] [Current]
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Dataseries X:
3035
2552
2704
2554
2014
1655
1721
1524
1596
2074
2199
2512
2933
2889
2938
2497
1870
1726
1607
1545
1396
1787
2076
2837
2787
3891
3179
2011
1636
1580
1489
1300
1356
1653
2013
2823
3102
2294
2385
2444
1748
1554
1498
1361
1346
1564
1640
2293
2815
3137
2679
1969
1870
1633
1529
1366
1357
1570
1535
2491
3084
2605
2573
2143
1693
1504
1461
1354
1333
1492
1781
1915




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=306559&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=306559&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306559&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
130353035000
225522644.88445392747-92.88445392758-92.8844539274746-0.231050155774009
327042787.81467451458-83.8146745145836-83.81467451458380.586141395673977
425542640.17843232405-86.1784323240526-86.1784323240526-0.158526167756034
520141949.70278123806-21.432406248226364.2972187619444-1.69437185657691
616551696.74190506669-41.7419050504633-41.741905066692-0.474528940948056
717211761.03171730681-40.0317173068058-40.03171730680550.260703340158743
815241566.48434499258-42.4843449925798-42.4843449925798-0.379864378437969
915961475.38363631832-40.205454554219120.616363681678-0.126645647569427
1020742079.56122193757-5.56122191913773-5.561221937569821.42946003247202
1121992203.24242229804-4.24242229804445-4.242422298043760.316844388657585
1225122513.0699995076-1.06999950760361-1.06999950760360.769919338566443
1329332895.29359361571-12.568802119585337.70640638429080.976070470436556
1428892900.86566765653-11.8656676310555-11.86566765653060.0414543949013437
1529382949.41481098405-11.4148109840502-11.414810984050.147908890072696
1624972511.57352456107-14.5735245610709-14.5735245610709-1.04395818309626
1718701867.9103454784-0.6965514988447732.08965452160442-1.58439498222769
1817261730.82941049778-4.8294104720762-4.82941049778034-0.316537772269283
1916071612.49707456359-5.49707456359192-5.49707456359106-0.277662367364221
2015451550.82557985792-5.82557985792104-5.82557985792105-0.137417213786895
2113961386.80110726865-3.066297570096879.19889273134801-0.395835620768261
2217871780.203884998896.796115019987576.796115001111550.929014590859415
2320762067.840581481738.159418518266958.159418518268070.686669564641573
2428372825.2211563930111.778843606988211.77884360698821.83186261513893
2527872822.9446929747411.9815643373507-35.9446929747419-0.035016675128186
2638913857.4462872787533.553712752314733.55371272124662.41155629021423
2731793148.5144089619430.485591038057830.485591038058-1.81476274998025
2820111985.4262342490925.573765750911425.5737657509114-2.91727529032423
2916361723.3320002071929.1106667327182-87.3320002071895-0.71448525780607
3015801554.5143926280425.485607364222225.4856073719595-0.468990693221647
3114891463.9319037071825.068096292817325.0680962928189-0.283614830990508
3213001275.6964324998524.303567500154124.303567500154-0.521208399162792
3313561424.8961829950822.9653943268655-68.89618299507520.309496287007918
3416531627.1337616751325.86623830915925.86623832487020.426289416517541
3520131986.0730197379326.926980262065326.92698026206730.813703679699089
3628232793.594940913329.405059086694929.40505908669491.90699857820145
3731023180.0461429916226.0153809986585-78.04614299161550.883199586262583
3822942281.3857159221312.614284088846412.6142840778704-2.20486740429211
3923852372.1623948109512.837605189048712.83760518904960.19092102873883
4024442431.0312516605612.968748339443112.9687483394430.112436399589233
4117481803.2880817201918.429360578424-55.2880817201896-1.58263747040456
4215541539.2772038079314.722796209234314.722796192069-0.674971166396073
4314981483.4599500138314.540049986165714.5400499861667-0.172279644118062
4413611346.8505171079914.149482892011514.1494828920115-0.369150463977153
4513461387.826191711313.942063908087-41.8261917113010.0661873185109634
4615641548.3009495567115.699050455139615.69905044328520.350821605278858
4716401624.1583941230515.841605876947815.8416058769490.146908378535788
4822932275.6556622194917.344337780507417.34433778050741.55228348552483
4928152855.1016124420813.3672041539855-40.10161244207671.38551816230081
5031373120.8471631780516.15283683988316.15283682194710.605155450748683
5126792663.8801757810715.119824218929915.1198242189301-1.15526368619283
5219691955.4565230725613.543476927440813.5434769274408-1.76674380928425
5318701911.7505290246213.916843005829-41.7505290246246-0.140998780231455
5416331622.1862358043210.813764190921110.813764195681-0.728633460923352
5515291518.4181827877510.581817212244910.5818172122458-0.279763597061374
5613661355.768146097610.231853902404410.2318539024044-0.422962987139843
5713571387.3089081774610.1029693888763-30.30890817746250.0524447984963111
5815701558.3641519279611.635848059925611.63584807203660.386863549002347
5915351523.4519783890411.548021610959811.548021610961-0.113644108353618
6024912477.6766928630713.323307136926213.32330713692632.30148261033137
6130843113.439923602529.81330786578648-29.43992360252421.5310050721731
6226052599.851590516725.148409482319975.14840948327649-1.25926009161466
6325732567.917107989985.08289201002035.08289201002009-0.0905301589522143
6421432138.683098937524.316901062476694.31690106247672-1.06029262573919
6516931712.767762748876.58925424752084-19.7677627488654-1.057676999122
6615041499.254153177484.745846818008094.74584682252198-0.529997581105622
6714611456.333333685494.666666314511774.66666631451218-0.116362103259858
6813541349.518212258634.481787741365344.48178774136537-0.272144843827993
6913331346.556279586984.51875985985705-13.5562795869758-0.0182910313033314
7014921486.412226095785.587773895705965.587773904220040.326129724739712
7117811774.968701521496.031298478511126.031298478511740.690740410416038
7219151908.768750439066.231249560937836.231249560937860.311889373524261

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3035 & 3035 & 0 & 0 & 0 \tabularnewline
2 & 2552 & 2644.88445392747 & -92.88445392758 & -92.8844539274746 & -0.231050155774009 \tabularnewline
3 & 2704 & 2787.81467451458 & -83.8146745145836 & -83.8146745145838 & 0.586141395673977 \tabularnewline
4 & 2554 & 2640.17843232405 & -86.1784323240526 & -86.1784323240526 & -0.158526167756034 \tabularnewline
5 & 2014 & 1949.70278123806 & -21.4324062482263 & 64.2972187619444 & -1.69437185657691 \tabularnewline
6 & 1655 & 1696.74190506669 & -41.7419050504633 & -41.741905066692 & -0.474528940948056 \tabularnewline
7 & 1721 & 1761.03171730681 & -40.0317173068058 & -40.0317173068055 & 0.260703340158743 \tabularnewline
8 & 1524 & 1566.48434499258 & -42.4843449925798 & -42.4843449925798 & -0.379864378437969 \tabularnewline
9 & 1596 & 1475.38363631832 & -40.205454554219 & 120.616363681678 & -0.126645647569427 \tabularnewline
10 & 2074 & 2079.56122193757 & -5.56122191913773 & -5.56122193756982 & 1.42946003247202 \tabularnewline
11 & 2199 & 2203.24242229804 & -4.24242229804445 & -4.24242229804376 & 0.316844388657585 \tabularnewline
12 & 2512 & 2513.0699995076 & -1.06999950760361 & -1.0699995076036 & 0.769919338566443 \tabularnewline
13 & 2933 & 2895.29359361571 & -12.5688021195853 & 37.7064063842908 & 0.976070470436556 \tabularnewline
14 & 2889 & 2900.86566765653 & -11.8656676310555 & -11.8656676565306 & 0.0414543949013437 \tabularnewline
15 & 2938 & 2949.41481098405 & -11.4148109840502 & -11.41481098405 & 0.147908890072696 \tabularnewline
16 & 2497 & 2511.57352456107 & -14.5735245610709 & -14.5735245610709 & -1.04395818309626 \tabularnewline
17 & 1870 & 1867.9103454784 & -0.696551498844773 & 2.08965452160442 & -1.58439498222769 \tabularnewline
18 & 1726 & 1730.82941049778 & -4.8294104720762 & -4.82941049778034 & -0.316537772269283 \tabularnewline
19 & 1607 & 1612.49707456359 & -5.49707456359192 & -5.49707456359106 & -0.277662367364221 \tabularnewline
20 & 1545 & 1550.82557985792 & -5.82557985792104 & -5.82557985792105 & -0.137417213786895 \tabularnewline
21 & 1396 & 1386.80110726865 & -3.06629757009687 & 9.19889273134801 & -0.395835620768261 \tabularnewline
22 & 1787 & 1780.20388499889 & 6.79611501998757 & 6.79611500111155 & 0.929014590859415 \tabularnewline
23 & 2076 & 2067.84058148173 & 8.15941851826695 & 8.15941851826807 & 0.686669564641573 \tabularnewline
24 & 2837 & 2825.22115639301 & 11.7788436069882 & 11.7788436069882 & 1.83186261513893 \tabularnewline
25 & 2787 & 2822.94469297474 & 11.9815643373507 & -35.9446929747419 & -0.035016675128186 \tabularnewline
26 & 3891 & 3857.44628727875 & 33.5537127523147 & 33.5537127212466 & 2.41155629021423 \tabularnewline
27 & 3179 & 3148.51440896194 & 30.4855910380578 & 30.485591038058 & -1.81476274998025 \tabularnewline
28 & 2011 & 1985.42623424909 & 25.5737657509114 & 25.5737657509114 & -2.91727529032423 \tabularnewline
29 & 1636 & 1723.33200020719 & 29.1106667327182 & -87.3320002071895 & -0.71448525780607 \tabularnewline
30 & 1580 & 1554.51439262804 & 25.4856073642222 & 25.4856073719595 & -0.468990693221647 \tabularnewline
31 & 1489 & 1463.93190370718 & 25.0680962928173 & 25.0680962928189 & -0.283614830990508 \tabularnewline
32 & 1300 & 1275.69643249985 & 24.3035675001541 & 24.303567500154 & -0.521208399162792 \tabularnewline
33 & 1356 & 1424.89618299508 & 22.9653943268655 & -68.8961829950752 & 0.309496287007918 \tabularnewline
34 & 1653 & 1627.13376167513 & 25.866238309159 & 25.8662383248702 & 0.426289416517541 \tabularnewline
35 & 2013 & 1986.07301973793 & 26.9269802620653 & 26.9269802620673 & 0.813703679699089 \tabularnewline
36 & 2823 & 2793.5949409133 & 29.4050590866949 & 29.4050590866949 & 1.90699857820145 \tabularnewline
37 & 3102 & 3180.04614299162 & 26.0153809986585 & -78.0461429916155 & 0.883199586262583 \tabularnewline
38 & 2294 & 2281.38571592213 & 12.6142840888464 & 12.6142840778704 & -2.20486740429211 \tabularnewline
39 & 2385 & 2372.16239481095 & 12.8376051890487 & 12.8376051890496 & 0.19092102873883 \tabularnewline
40 & 2444 & 2431.03125166056 & 12.9687483394431 & 12.968748339443 & 0.112436399589233 \tabularnewline
41 & 1748 & 1803.28808172019 & 18.429360578424 & -55.2880817201896 & -1.58263747040456 \tabularnewline
42 & 1554 & 1539.27720380793 & 14.7227962092343 & 14.722796192069 & -0.674971166396073 \tabularnewline
43 & 1498 & 1483.45995001383 & 14.5400499861657 & 14.5400499861667 & -0.172279644118062 \tabularnewline
44 & 1361 & 1346.85051710799 & 14.1494828920115 & 14.1494828920115 & -0.369150463977153 \tabularnewline
45 & 1346 & 1387.8261917113 & 13.942063908087 & -41.826191711301 & 0.0661873185109634 \tabularnewline
46 & 1564 & 1548.30094955671 & 15.6990504551396 & 15.6990504432852 & 0.350821605278858 \tabularnewline
47 & 1640 & 1624.15839412305 & 15.8416058769478 & 15.841605876949 & 0.146908378535788 \tabularnewline
48 & 2293 & 2275.65566221949 & 17.3443377805074 & 17.3443377805074 & 1.55228348552483 \tabularnewline
49 & 2815 & 2855.10161244208 & 13.3672041539855 & -40.1016124420767 & 1.38551816230081 \tabularnewline
50 & 3137 & 3120.84716317805 & 16.152836839883 & 16.1528368219471 & 0.605155450748683 \tabularnewline
51 & 2679 & 2663.88017578107 & 15.1198242189299 & 15.1198242189301 & -1.15526368619283 \tabularnewline
52 & 1969 & 1955.45652307256 & 13.5434769274408 & 13.5434769274408 & -1.76674380928425 \tabularnewline
53 & 1870 & 1911.75052902462 & 13.916843005829 & -41.7505290246246 & -0.140998780231455 \tabularnewline
54 & 1633 & 1622.18623580432 & 10.8137641909211 & 10.813764195681 & -0.728633460923352 \tabularnewline
55 & 1529 & 1518.41818278775 & 10.5818172122449 & 10.5818172122458 & -0.279763597061374 \tabularnewline
56 & 1366 & 1355.7681460976 & 10.2318539024044 & 10.2318539024044 & -0.422962987139843 \tabularnewline
57 & 1357 & 1387.30890817746 & 10.1029693888763 & -30.3089081774625 & 0.0524447984963111 \tabularnewline
58 & 1570 & 1558.36415192796 & 11.6358480599256 & 11.6358480720366 & 0.386863549002347 \tabularnewline
59 & 1535 & 1523.45197838904 & 11.5480216109598 & 11.548021610961 & -0.113644108353618 \tabularnewline
60 & 2491 & 2477.67669286307 & 13.3233071369262 & 13.3233071369263 & 2.30148261033137 \tabularnewline
61 & 3084 & 3113.43992360252 & 9.81330786578648 & -29.4399236025242 & 1.5310050721731 \tabularnewline
62 & 2605 & 2599.85159051672 & 5.14840948231997 & 5.14840948327649 & -1.25926009161466 \tabularnewline
63 & 2573 & 2567.91710798998 & 5.0828920100203 & 5.08289201002009 & -0.0905301589522143 \tabularnewline
64 & 2143 & 2138.68309893752 & 4.31690106247669 & 4.31690106247672 & -1.06029262573919 \tabularnewline
65 & 1693 & 1712.76776274887 & 6.58925424752084 & -19.7677627488654 & -1.057676999122 \tabularnewline
66 & 1504 & 1499.25415317748 & 4.74584681800809 & 4.74584682252198 & -0.529997581105622 \tabularnewline
67 & 1461 & 1456.33333368549 & 4.66666631451177 & 4.66666631451218 & -0.116362103259858 \tabularnewline
68 & 1354 & 1349.51821225863 & 4.48178774136534 & 4.48178774136537 & -0.272144843827993 \tabularnewline
69 & 1333 & 1346.55627958698 & 4.51875985985705 & -13.5562795869758 & -0.0182910313033314 \tabularnewline
70 & 1492 & 1486.41222609578 & 5.58777389570596 & 5.58777390422004 & 0.326129724739712 \tabularnewline
71 & 1781 & 1774.96870152149 & 6.03129847851112 & 6.03129847851174 & 0.690740410416038 \tabularnewline
72 & 1915 & 1908.76875043906 & 6.23124956093783 & 6.23124956093786 & 0.311889373524261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306559&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]3035[/C][C]3035[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2552[/C][C]2644.88445392747[/C][C]-92.88445392758[/C][C]-92.8844539274746[/C][C]-0.231050155774009[/C][/ROW]
[ROW][C]3[/C][C]2704[/C][C]2787.81467451458[/C][C]-83.8146745145836[/C][C]-83.8146745145838[/C][C]0.586141395673977[/C][/ROW]
[ROW][C]4[/C][C]2554[/C][C]2640.17843232405[/C][C]-86.1784323240526[/C][C]-86.1784323240526[/C][C]-0.158526167756034[/C][/ROW]
[ROW][C]5[/C][C]2014[/C][C]1949.70278123806[/C][C]-21.4324062482263[/C][C]64.2972187619444[/C][C]-1.69437185657691[/C][/ROW]
[ROW][C]6[/C][C]1655[/C][C]1696.74190506669[/C][C]-41.7419050504633[/C][C]-41.741905066692[/C][C]-0.474528940948056[/C][/ROW]
[ROW][C]7[/C][C]1721[/C][C]1761.03171730681[/C][C]-40.0317173068058[/C][C]-40.0317173068055[/C][C]0.260703340158743[/C][/ROW]
[ROW][C]8[/C][C]1524[/C][C]1566.48434499258[/C][C]-42.4843449925798[/C][C]-42.4843449925798[/C][C]-0.379864378437969[/C][/ROW]
[ROW][C]9[/C][C]1596[/C][C]1475.38363631832[/C][C]-40.205454554219[/C][C]120.616363681678[/C][C]-0.126645647569427[/C][/ROW]
[ROW][C]10[/C][C]2074[/C][C]2079.56122193757[/C][C]-5.56122191913773[/C][C]-5.56122193756982[/C][C]1.42946003247202[/C][/ROW]
[ROW][C]11[/C][C]2199[/C][C]2203.24242229804[/C][C]-4.24242229804445[/C][C]-4.24242229804376[/C][C]0.316844388657585[/C][/ROW]
[ROW][C]12[/C][C]2512[/C][C]2513.0699995076[/C][C]-1.06999950760361[/C][C]-1.0699995076036[/C][C]0.769919338566443[/C][/ROW]
[ROW][C]13[/C][C]2933[/C][C]2895.29359361571[/C][C]-12.5688021195853[/C][C]37.7064063842908[/C][C]0.976070470436556[/C][/ROW]
[ROW][C]14[/C][C]2889[/C][C]2900.86566765653[/C][C]-11.8656676310555[/C][C]-11.8656676565306[/C][C]0.0414543949013437[/C][/ROW]
[ROW][C]15[/C][C]2938[/C][C]2949.41481098405[/C][C]-11.4148109840502[/C][C]-11.41481098405[/C][C]0.147908890072696[/C][/ROW]
[ROW][C]16[/C][C]2497[/C][C]2511.57352456107[/C][C]-14.5735245610709[/C][C]-14.5735245610709[/C][C]-1.04395818309626[/C][/ROW]
[ROW][C]17[/C][C]1870[/C][C]1867.9103454784[/C][C]-0.696551498844773[/C][C]2.08965452160442[/C][C]-1.58439498222769[/C][/ROW]
[ROW][C]18[/C][C]1726[/C][C]1730.82941049778[/C][C]-4.8294104720762[/C][C]-4.82941049778034[/C][C]-0.316537772269283[/C][/ROW]
[ROW][C]19[/C][C]1607[/C][C]1612.49707456359[/C][C]-5.49707456359192[/C][C]-5.49707456359106[/C][C]-0.277662367364221[/C][/ROW]
[ROW][C]20[/C][C]1545[/C][C]1550.82557985792[/C][C]-5.82557985792104[/C][C]-5.82557985792105[/C][C]-0.137417213786895[/C][/ROW]
[ROW][C]21[/C][C]1396[/C][C]1386.80110726865[/C][C]-3.06629757009687[/C][C]9.19889273134801[/C][C]-0.395835620768261[/C][/ROW]
[ROW][C]22[/C][C]1787[/C][C]1780.20388499889[/C][C]6.79611501998757[/C][C]6.79611500111155[/C][C]0.929014590859415[/C][/ROW]
[ROW][C]23[/C][C]2076[/C][C]2067.84058148173[/C][C]8.15941851826695[/C][C]8.15941851826807[/C][C]0.686669564641573[/C][/ROW]
[ROW][C]24[/C][C]2837[/C][C]2825.22115639301[/C][C]11.7788436069882[/C][C]11.7788436069882[/C][C]1.83186261513893[/C][/ROW]
[ROW][C]25[/C][C]2787[/C][C]2822.94469297474[/C][C]11.9815643373507[/C][C]-35.9446929747419[/C][C]-0.035016675128186[/C][/ROW]
[ROW][C]26[/C][C]3891[/C][C]3857.44628727875[/C][C]33.5537127523147[/C][C]33.5537127212466[/C][C]2.41155629021423[/C][/ROW]
[ROW][C]27[/C][C]3179[/C][C]3148.51440896194[/C][C]30.4855910380578[/C][C]30.485591038058[/C][C]-1.81476274998025[/C][/ROW]
[ROW][C]28[/C][C]2011[/C][C]1985.42623424909[/C][C]25.5737657509114[/C][C]25.5737657509114[/C][C]-2.91727529032423[/C][/ROW]
[ROW][C]29[/C][C]1636[/C][C]1723.33200020719[/C][C]29.1106667327182[/C][C]-87.3320002071895[/C][C]-0.71448525780607[/C][/ROW]
[ROW][C]30[/C][C]1580[/C][C]1554.51439262804[/C][C]25.4856073642222[/C][C]25.4856073719595[/C][C]-0.468990693221647[/C][/ROW]
[ROW][C]31[/C][C]1489[/C][C]1463.93190370718[/C][C]25.0680962928173[/C][C]25.0680962928189[/C][C]-0.283614830990508[/C][/ROW]
[ROW][C]32[/C][C]1300[/C][C]1275.69643249985[/C][C]24.3035675001541[/C][C]24.303567500154[/C][C]-0.521208399162792[/C][/ROW]
[ROW][C]33[/C][C]1356[/C][C]1424.89618299508[/C][C]22.9653943268655[/C][C]-68.8961829950752[/C][C]0.309496287007918[/C][/ROW]
[ROW][C]34[/C][C]1653[/C][C]1627.13376167513[/C][C]25.866238309159[/C][C]25.8662383248702[/C][C]0.426289416517541[/C][/ROW]
[ROW][C]35[/C][C]2013[/C][C]1986.07301973793[/C][C]26.9269802620653[/C][C]26.9269802620673[/C][C]0.813703679699089[/C][/ROW]
[ROW][C]36[/C][C]2823[/C][C]2793.5949409133[/C][C]29.4050590866949[/C][C]29.4050590866949[/C][C]1.90699857820145[/C][/ROW]
[ROW][C]37[/C][C]3102[/C][C]3180.04614299162[/C][C]26.0153809986585[/C][C]-78.0461429916155[/C][C]0.883199586262583[/C][/ROW]
[ROW][C]38[/C][C]2294[/C][C]2281.38571592213[/C][C]12.6142840888464[/C][C]12.6142840778704[/C][C]-2.20486740429211[/C][/ROW]
[ROW][C]39[/C][C]2385[/C][C]2372.16239481095[/C][C]12.8376051890487[/C][C]12.8376051890496[/C][C]0.19092102873883[/C][/ROW]
[ROW][C]40[/C][C]2444[/C][C]2431.03125166056[/C][C]12.9687483394431[/C][C]12.968748339443[/C][C]0.112436399589233[/C][/ROW]
[ROW][C]41[/C][C]1748[/C][C]1803.28808172019[/C][C]18.429360578424[/C][C]-55.2880817201896[/C][C]-1.58263747040456[/C][/ROW]
[ROW][C]42[/C][C]1554[/C][C]1539.27720380793[/C][C]14.7227962092343[/C][C]14.722796192069[/C][C]-0.674971166396073[/C][/ROW]
[ROW][C]43[/C][C]1498[/C][C]1483.45995001383[/C][C]14.5400499861657[/C][C]14.5400499861667[/C][C]-0.172279644118062[/C][/ROW]
[ROW][C]44[/C][C]1361[/C][C]1346.85051710799[/C][C]14.1494828920115[/C][C]14.1494828920115[/C][C]-0.369150463977153[/C][/ROW]
[ROW][C]45[/C][C]1346[/C][C]1387.8261917113[/C][C]13.942063908087[/C][C]-41.826191711301[/C][C]0.0661873185109634[/C][/ROW]
[ROW][C]46[/C][C]1564[/C][C]1548.30094955671[/C][C]15.6990504551396[/C][C]15.6990504432852[/C][C]0.350821605278858[/C][/ROW]
[ROW][C]47[/C][C]1640[/C][C]1624.15839412305[/C][C]15.8416058769478[/C][C]15.841605876949[/C][C]0.146908378535788[/C][/ROW]
[ROW][C]48[/C][C]2293[/C][C]2275.65566221949[/C][C]17.3443377805074[/C][C]17.3443377805074[/C][C]1.55228348552483[/C][/ROW]
[ROW][C]49[/C][C]2815[/C][C]2855.10161244208[/C][C]13.3672041539855[/C][C]-40.1016124420767[/C][C]1.38551816230081[/C][/ROW]
[ROW][C]50[/C][C]3137[/C][C]3120.84716317805[/C][C]16.152836839883[/C][C]16.1528368219471[/C][C]0.605155450748683[/C][/ROW]
[ROW][C]51[/C][C]2679[/C][C]2663.88017578107[/C][C]15.1198242189299[/C][C]15.1198242189301[/C][C]-1.15526368619283[/C][/ROW]
[ROW][C]52[/C][C]1969[/C][C]1955.45652307256[/C][C]13.5434769274408[/C][C]13.5434769274408[/C][C]-1.76674380928425[/C][/ROW]
[ROW][C]53[/C][C]1870[/C][C]1911.75052902462[/C][C]13.916843005829[/C][C]-41.7505290246246[/C][C]-0.140998780231455[/C][/ROW]
[ROW][C]54[/C][C]1633[/C][C]1622.18623580432[/C][C]10.8137641909211[/C][C]10.813764195681[/C][C]-0.728633460923352[/C][/ROW]
[ROW][C]55[/C][C]1529[/C][C]1518.41818278775[/C][C]10.5818172122449[/C][C]10.5818172122458[/C][C]-0.279763597061374[/C][/ROW]
[ROW][C]56[/C][C]1366[/C][C]1355.7681460976[/C][C]10.2318539024044[/C][C]10.2318539024044[/C][C]-0.422962987139843[/C][/ROW]
[ROW][C]57[/C][C]1357[/C][C]1387.30890817746[/C][C]10.1029693888763[/C][C]-30.3089081774625[/C][C]0.0524447984963111[/C][/ROW]
[ROW][C]58[/C][C]1570[/C][C]1558.36415192796[/C][C]11.6358480599256[/C][C]11.6358480720366[/C][C]0.386863549002347[/C][/ROW]
[ROW][C]59[/C][C]1535[/C][C]1523.45197838904[/C][C]11.5480216109598[/C][C]11.548021610961[/C][C]-0.113644108353618[/C][/ROW]
[ROW][C]60[/C][C]2491[/C][C]2477.67669286307[/C][C]13.3233071369262[/C][C]13.3233071369263[/C][C]2.30148261033137[/C][/ROW]
[ROW][C]61[/C][C]3084[/C][C]3113.43992360252[/C][C]9.81330786578648[/C][C]-29.4399236025242[/C][C]1.5310050721731[/C][/ROW]
[ROW][C]62[/C][C]2605[/C][C]2599.85159051672[/C][C]5.14840948231997[/C][C]5.14840948327649[/C][C]-1.25926009161466[/C][/ROW]
[ROW][C]63[/C][C]2573[/C][C]2567.91710798998[/C][C]5.0828920100203[/C][C]5.08289201002009[/C][C]-0.0905301589522143[/C][/ROW]
[ROW][C]64[/C][C]2143[/C][C]2138.68309893752[/C][C]4.31690106247669[/C][C]4.31690106247672[/C][C]-1.06029262573919[/C][/ROW]
[ROW][C]65[/C][C]1693[/C][C]1712.76776274887[/C][C]6.58925424752084[/C][C]-19.7677627488654[/C][C]-1.057676999122[/C][/ROW]
[ROW][C]66[/C][C]1504[/C][C]1499.25415317748[/C][C]4.74584681800809[/C][C]4.74584682252198[/C][C]-0.529997581105622[/C][/ROW]
[ROW][C]67[/C][C]1461[/C][C]1456.33333368549[/C][C]4.66666631451177[/C][C]4.66666631451218[/C][C]-0.116362103259858[/C][/ROW]
[ROW][C]68[/C][C]1354[/C][C]1349.51821225863[/C][C]4.48178774136534[/C][C]4.48178774136537[/C][C]-0.272144843827993[/C][/ROW]
[ROW][C]69[/C][C]1333[/C][C]1346.55627958698[/C][C]4.51875985985705[/C][C]-13.5562795869758[/C][C]-0.0182910313033314[/C][/ROW]
[ROW][C]70[/C][C]1492[/C][C]1486.41222609578[/C][C]5.58777389570596[/C][C]5.58777390422004[/C][C]0.326129724739712[/C][/ROW]
[ROW][C]71[/C][C]1781[/C][C]1774.96870152149[/C][C]6.03129847851112[/C][C]6.03129847851174[/C][C]0.690740410416038[/C][/ROW]
[ROW][C]72[/C][C]1915[/C][C]1908.76875043906[/C][C]6.23124956093783[/C][C]6.23124956093786[/C][C]0.311889373524261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306559&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306559&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
130353035000
225522644.88445392747-92.88445392758-92.8844539274746-0.231050155774009
327042787.81467451458-83.8146745145836-83.81467451458380.586141395673977
425542640.17843232405-86.1784323240526-86.1784323240526-0.158526167756034
520141949.70278123806-21.432406248226364.2972187619444-1.69437185657691
616551696.74190506669-41.7419050504633-41.741905066692-0.474528940948056
717211761.03171730681-40.0317173068058-40.03171730680550.260703340158743
815241566.48434499258-42.4843449925798-42.4843449925798-0.379864378437969
915961475.38363631832-40.205454554219120.616363681678-0.126645647569427
1020742079.56122193757-5.56122191913773-5.561221937569821.42946003247202
1121992203.24242229804-4.24242229804445-4.242422298043760.316844388657585
1225122513.0699995076-1.06999950760361-1.06999950760360.769919338566443
1329332895.29359361571-12.568802119585337.70640638429080.976070470436556
1428892900.86566765653-11.8656676310555-11.86566765653060.0414543949013437
1529382949.41481098405-11.4148109840502-11.414810984050.147908890072696
1624972511.57352456107-14.5735245610709-14.5735245610709-1.04395818309626
1718701867.9103454784-0.6965514988447732.08965452160442-1.58439498222769
1817261730.82941049778-4.8294104720762-4.82941049778034-0.316537772269283
1916071612.49707456359-5.49707456359192-5.49707456359106-0.277662367364221
2015451550.82557985792-5.82557985792104-5.82557985792105-0.137417213786895
2113961386.80110726865-3.066297570096879.19889273134801-0.395835620768261
2217871780.203884998896.796115019987576.796115001111550.929014590859415
2320762067.840581481738.159418518266958.159418518268070.686669564641573
2428372825.2211563930111.778843606988211.77884360698821.83186261513893
2527872822.9446929747411.9815643373507-35.9446929747419-0.035016675128186
2638913857.4462872787533.553712752314733.55371272124662.41155629021423
2731793148.5144089619430.485591038057830.485591038058-1.81476274998025
2820111985.4262342490925.573765750911425.5737657509114-2.91727529032423
2916361723.3320002071929.1106667327182-87.3320002071895-0.71448525780607
3015801554.5143926280425.485607364222225.4856073719595-0.468990693221647
3114891463.9319037071825.068096292817325.0680962928189-0.283614830990508
3213001275.6964324998524.303567500154124.303567500154-0.521208399162792
3313561424.8961829950822.9653943268655-68.89618299507520.309496287007918
3416531627.1337616751325.86623830915925.86623832487020.426289416517541
3520131986.0730197379326.926980262065326.92698026206730.813703679699089
3628232793.594940913329.405059086694929.40505908669491.90699857820145
3731023180.0461429916226.0153809986585-78.04614299161550.883199586262583
3822942281.3857159221312.614284088846412.6142840778704-2.20486740429211
3923852372.1623948109512.837605189048712.83760518904960.19092102873883
4024442431.0312516605612.968748339443112.9687483394430.112436399589233
4117481803.2880817201918.429360578424-55.2880817201896-1.58263747040456
4215541539.2772038079314.722796209234314.722796192069-0.674971166396073
4314981483.4599500138314.540049986165714.5400499861667-0.172279644118062
4413611346.8505171079914.149482892011514.1494828920115-0.369150463977153
4513461387.826191711313.942063908087-41.8261917113010.0661873185109634
4615641548.3009495567115.699050455139615.69905044328520.350821605278858
4716401624.1583941230515.841605876947815.8416058769490.146908378535788
4822932275.6556622194917.344337780507417.34433778050741.55228348552483
4928152855.1016124420813.3672041539855-40.10161244207671.38551816230081
5031373120.8471631780516.15283683988316.15283682194710.605155450748683
5126792663.8801757810715.119824218929915.1198242189301-1.15526368619283
5219691955.4565230725613.543476927440813.5434769274408-1.76674380928425
5318701911.7505290246213.916843005829-41.7505290246246-0.140998780231455
5416331622.1862358043210.813764190921110.813764195681-0.728633460923352
5515291518.4181827877510.581817212244910.5818172122458-0.279763597061374
5613661355.768146097610.231853902404410.2318539024044-0.422962987139843
5713571387.3089081774610.1029693888763-30.30890817746250.0524447984963111
5815701558.3641519279611.635848059925611.63584807203660.386863549002347
5915351523.4519783890411.548021610959811.548021610961-0.113644108353618
6024912477.6766928630713.323307136926213.32330713692632.30148261033137
6130843113.439923602529.81330786578648-29.43992360252421.5310050721731
6226052599.851590516725.148409482319975.14840948327649-1.25926009161466
6325732567.917107989985.08289201002035.08289201002009-0.0905301589522143
6421432138.683098937524.316901062476694.31690106247672-1.06029262573919
6516931712.767762748876.58925424752084-19.7677627488654-1.057676999122
6615041499.254153177484.745846818008094.74584682252198-0.529997581105622
6714611456.333333685494.666666314511774.66666631451218-0.116362103259858
6813541349.518212258634.481787741365344.48178774136537-0.272144843827993
6913331346.556279586984.51875985985705-13.5562795869758-0.0182910313033314
7014921486.412226095785.587773895705965.587773904220040.326129724739712
7117811774.968701521496.031298478511126.031298478511740.690740410416038
7219151908.768750439066.231249560937836.231249560937860.311889373524261







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
12047.101439784532077.45524403893-30.353804254406
22253.661450602772250.777798839612.88365176315593
32434.788680048352424.1003536402910.6883264080588
42614.204734524162597.4229084409616.7818260831913
52740.391658987242770.74546324164-30.353804254406
62946.951669805472944.068018042322.88365176315593
73128.078899251053117.3905728429910.6883264080588
83307.494953726863290.7131276436716.7818260831913
93433.681878189943464.03568244435-30.353804254406
103640.241889008183637.358237245022.88365176315593
113821.369118453763810.680792045710.6883264080588
124000.785172929573984.0033468463816.7818260831913

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 2047.10143978453 & 2077.45524403893 & -30.353804254406 \tabularnewline
2 & 2253.66145060277 & 2250.77779883961 & 2.88365176315593 \tabularnewline
3 & 2434.78868004835 & 2424.10035364029 & 10.6883264080588 \tabularnewline
4 & 2614.20473452416 & 2597.42290844096 & 16.7818260831913 \tabularnewline
5 & 2740.39165898724 & 2770.74546324164 & -30.353804254406 \tabularnewline
6 & 2946.95166980547 & 2944.06801804232 & 2.88365176315593 \tabularnewline
7 & 3128.07889925105 & 3117.39057284299 & 10.6883264080588 \tabularnewline
8 & 3307.49495372686 & 3290.71312764367 & 16.7818260831913 \tabularnewline
9 & 3433.68187818994 & 3464.03568244435 & -30.353804254406 \tabularnewline
10 & 3640.24188900818 & 3637.35823724502 & 2.88365176315593 \tabularnewline
11 & 3821.36911845376 & 3810.6807920457 & 10.6883264080588 \tabularnewline
12 & 4000.78517292957 & 3984.00334684638 & 16.7818260831913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306559&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]2047.10143978453[/C][C]2077.45524403893[/C][C]-30.353804254406[/C][/ROW]
[ROW][C]2[/C][C]2253.66145060277[/C][C]2250.77779883961[/C][C]2.88365176315593[/C][/ROW]
[ROW][C]3[/C][C]2434.78868004835[/C][C]2424.10035364029[/C][C]10.6883264080588[/C][/ROW]
[ROW][C]4[/C][C]2614.20473452416[/C][C]2597.42290844096[/C][C]16.7818260831913[/C][/ROW]
[ROW][C]5[/C][C]2740.39165898724[/C][C]2770.74546324164[/C][C]-30.353804254406[/C][/ROW]
[ROW][C]6[/C][C]2946.95166980547[/C][C]2944.06801804232[/C][C]2.88365176315593[/C][/ROW]
[ROW][C]7[/C][C]3128.07889925105[/C][C]3117.39057284299[/C][C]10.6883264080588[/C][/ROW]
[ROW][C]8[/C][C]3307.49495372686[/C][C]3290.71312764367[/C][C]16.7818260831913[/C][/ROW]
[ROW][C]9[/C][C]3433.68187818994[/C][C]3464.03568244435[/C][C]-30.353804254406[/C][/ROW]
[ROW][C]10[/C][C]3640.24188900818[/C][C]3637.35823724502[/C][C]2.88365176315593[/C][/ROW]
[ROW][C]11[/C][C]3821.36911845376[/C][C]3810.6807920457[/C][C]10.6883264080588[/C][/ROW]
[ROW][C]12[/C][C]4000.78517292957[/C][C]3984.00334684638[/C][C]16.7818260831913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306559&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306559&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
12047.101439784532077.45524403893-30.353804254406
22253.661450602772250.777798839612.88365176315593
32434.788680048352424.1003536402910.6883264080588
42614.204734524162597.4229084409616.7818260831913
52740.391658987242770.74546324164-30.353804254406
62946.951669805472944.068018042322.88365176315593
73128.078899251053117.3905728429910.6883264080588
83307.494953726863290.7131276436716.7818260831913
93433.681878189943464.03568244435-30.353804254406
103640.241889008183637.358237245022.88365176315593
113821.369118453763810.680792045710.6883264080588
124000.785172929573984.0033468463816.7818260831913



Parameters (Session):
par1 = 4 ; par2 = 12 ; par3 = BFGS ;
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')