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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 computationWed, 07 Dec 2016 11:22:21 +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/07/t14811062573c0b798snw7orar.htm/, Retrieved Tue, 07 May 2024 20:48:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297971, Retrieved Tue, 07 May 2024 20:48:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
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...] [2016-12-07 10:22:21] [fd005a509166a1985dac46f39e8d81c5] [Current]
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Dataseries X:
6908
6694
6564
6800
6820
6752
6632
6756
6898
6844
6750
6892
7104
7022
6858
7018
7218
7134
7006
7160
7374
7276
7128
7272
7462
7366
7218
7366
7546
7464
7332
7502
7736
7628
7494
7668
7888
7774
7644
7826
8056
7990
7814
7978
8238
8138
8000
8176
8412
8332
8194
8354
8576
8500
8376
8538




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=297971&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=297971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297971&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
169086908000
266946763.34812045212-6.93186684852988-69.3481204521156-2.8065099589123
365646625.3159065816-16.5329254889295-61.3159065815965-2.68149073778077
468006697.56483495248-9.91797298895097102.4351650475232.16942654161871
568206779.1235707492-2.8458512177033540.87642925080412.28254627412352
667526785.69119987277-2.04477816522139-33.69119987277110.231255866039928
766326707.92132389531-9.20809168019775-75.9213238953093-1.83374104272824
867566720.08117657185-7.0025613300945635.9188234281530.511842485125328
968986822.833841283145.077121595392675.16615871685842.60710272060282
1068446861.765864580668.97749095594416-17.76586458065580.79896868158579
1167506815.099025195152.35403261505839-65.0990251951503-1.30654854017017
1268926852.693681187066.6491006806374139.30631881293760.824192703025829
1371046928.078246909914.384830483674175.9217530900991.68774417345868
1470227000.6632580250621.546263409452821.33674197493641.37126840763356
1568587007.2080478020919.6359485730745-149.208047802087-0.327097293825565
1670186989.8296606454114.916036517844728.1703393545907-0.826880906029952
1772187087.8060324928525.4956586061408130.1939675071471.90494562211418
1871347137.0660502997628.5224054614155-3.066050299764710.545724607143898
1970067137.781738559324.9787992917697-131.781738559297-0.635578611065617
2071607167.3645631589925.566296766029-7.364563158993480.105008763200739
2173747254.1705897754433.3939456844662119.8294102245581.39635141407925
2272767288.2867199350433.4863564792413-12.28671993504260.0164607564832788
2371287266.9940177471426.4815977871438-138.994017747144-1.2467943315816
2472727273.7702361912623.9690173624316-1.77023619126143-0.449226616368125
2574627300.4744106266724.3172595509078161.5255893733280.0632947388819119
2673667328.8924810673924.842425528180337.10751893260570.0943665521712735
2772187358.3862982410825.4384758295728-140.3862982410840.10442171658287
2873667382.1800836050625.2283424837913-16.1800836050626-0.0368832486011872
2975467414.9531789334526.191880518894131.0468210665470.171281715073083
3074647450.2754458203927.359590829639513.72455417960580.20830840316008
3173327478.661005245427.4909223470045-146.66100524540.0233583260248253
3275027523.7119480315829.7386582104348-21.71194803157720.398590127888936
3377367584.8526437023433.7563293070715151.1473562976620.711463201944265
3476287618.8755365497833.79040819220399.124463450215520.00603272480219238
3574947637.5295795357131.8574636761782-143.529579535711-0.342633284702296
3676687668.6660047667531.7654633402109-0.666004766746844-0.0163867151924211
3778887715.2701513031333.6601573750575172.7298486968670.339228136599723
3877747745.3116692221333.197411097806928.6883307778667-0.082473205223167
3976447780.8257175699533.4934673503392-136.8257175699540.0522604787995583
4078267831.6681493225535.7060417996914-5.668149322550750.390281385071125
4180567902.5845772119440.1931729552456153.4154227880570.796504226137666
4279907967.3259556663243.324215911928422.67404433368170.557878436244461
4378147994.6789730831841.2850597750307-180.678973083185-0.362905168584095
4479788022.311252297639.5414008335259-44.3112522975986-0.309387096907097
4582388071.8037584034240.8117736656532166.1962415965810.224904290184395
4681388118.45615905941.55678777241919.54384094099560.131833190314531
4780008152.455498394740.5935660866282-152.455498394705-0.170758726486997
4881768186.371567567439.7426804409503-10.3715675674021-0.151392807654538
4984128231.5714923465740.438549376205180.4285076534330.124076229715909
5083328292.2332427076443.019141294738339.76675729235990.458839974455799
5181948343.9452319052744.1279169538245-149.9452319052690.196188744846885
5283548385.2558628441743.7690149368857-31.2558628441713-0.0634516494724225
5385768429.9842459180943.8911500106701146.0157540819050.0216665746380891
5485008470.7590258971243.494261687457629.240974102881-0.0706182260954908
5583768533.6853871301645.9708923680474-157.685387130160.440598571866735
5685388586.4581837485446.8380869699779-48.45818374854260.153926020390593

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 6908 & 6908 & 0 & 0 & 0 \tabularnewline
2 & 6694 & 6763.34812045212 & -6.93186684852988 & -69.3481204521156 & -2.8065099589123 \tabularnewline
3 & 6564 & 6625.3159065816 & -16.5329254889295 & -61.3159065815965 & -2.68149073778077 \tabularnewline
4 & 6800 & 6697.56483495248 & -9.91797298895097 & 102.435165047523 & 2.16942654161871 \tabularnewline
5 & 6820 & 6779.1235707492 & -2.84585121770335 & 40.8764292508041 & 2.28254627412352 \tabularnewline
6 & 6752 & 6785.69119987277 & -2.04477816522139 & -33.6911998727711 & 0.231255866039928 \tabularnewline
7 & 6632 & 6707.92132389531 & -9.20809168019775 & -75.9213238953093 & -1.83374104272824 \tabularnewline
8 & 6756 & 6720.08117657185 & -7.00256133009456 & 35.918823428153 & 0.511842485125328 \tabularnewline
9 & 6898 & 6822.83384128314 & 5.0771215953926 & 75.1661587168584 & 2.60710272060282 \tabularnewline
10 & 6844 & 6861.76586458066 & 8.97749095594416 & -17.7658645806558 & 0.79896868158579 \tabularnewline
11 & 6750 & 6815.09902519515 & 2.35403261505839 & -65.0990251951503 & -1.30654854017017 \tabularnewline
12 & 6892 & 6852.69368118706 & 6.64910068063741 & 39.3063188129376 & 0.824192703025829 \tabularnewline
13 & 7104 & 6928.0782469099 & 14.384830483674 & 175.921753090099 & 1.68774417345868 \tabularnewline
14 & 7022 & 7000.66325802506 & 21.5462634094528 & 21.3367419749364 & 1.37126840763356 \tabularnewline
15 & 6858 & 7007.20804780209 & 19.6359485730745 & -149.208047802087 & -0.327097293825565 \tabularnewline
16 & 7018 & 6989.82966064541 & 14.9160365178447 & 28.1703393545907 & -0.826880906029952 \tabularnewline
17 & 7218 & 7087.80603249285 & 25.4956586061408 & 130.193967507147 & 1.90494562211418 \tabularnewline
18 & 7134 & 7137.06605029976 & 28.5224054614155 & -3.06605029976471 & 0.545724607143898 \tabularnewline
19 & 7006 & 7137.7817385593 & 24.9787992917697 & -131.781738559297 & -0.635578611065617 \tabularnewline
20 & 7160 & 7167.36456315899 & 25.566296766029 & -7.36456315899348 & 0.105008763200739 \tabularnewline
21 & 7374 & 7254.17058977544 & 33.3939456844662 & 119.829410224558 & 1.39635141407925 \tabularnewline
22 & 7276 & 7288.28671993504 & 33.4863564792413 & -12.2867199350426 & 0.0164607564832788 \tabularnewline
23 & 7128 & 7266.99401774714 & 26.4815977871438 & -138.994017747144 & -1.2467943315816 \tabularnewline
24 & 7272 & 7273.77023619126 & 23.9690173624316 & -1.77023619126143 & -0.449226616368125 \tabularnewline
25 & 7462 & 7300.47441062667 & 24.3172595509078 & 161.525589373328 & 0.0632947388819119 \tabularnewline
26 & 7366 & 7328.89248106739 & 24.8424255281803 & 37.1075189326057 & 0.0943665521712735 \tabularnewline
27 & 7218 & 7358.38629824108 & 25.4384758295728 & -140.386298241084 & 0.10442171658287 \tabularnewline
28 & 7366 & 7382.18008360506 & 25.2283424837913 & -16.1800836050626 & -0.0368832486011872 \tabularnewline
29 & 7546 & 7414.95317893345 & 26.191880518894 & 131.046821066547 & 0.171281715073083 \tabularnewline
30 & 7464 & 7450.27544582039 & 27.3595908296395 & 13.7245541796058 & 0.20830840316008 \tabularnewline
31 & 7332 & 7478.6610052454 & 27.4909223470045 & -146.6610052454 & 0.0233583260248253 \tabularnewline
32 & 7502 & 7523.71194803158 & 29.7386582104348 & -21.7119480315772 & 0.398590127888936 \tabularnewline
33 & 7736 & 7584.85264370234 & 33.7563293070715 & 151.147356297662 & 0.711463201944265 \tabularnewline
34 & 7628 & 7618.87553654978 & 33.7904081922039 & 9.12446345021552 & 0.00603272480219238 \tabularnewline
35 & 7494 & 7637.52957953571 & 31.8574636761782 & -143.529579535711 & -0.342633284702296 \tabularnewline
36 & 7668 & 7668.66600476675 & 31.7654633402109 & -0.666004766746844 & -0.0163867151924211 \tabularnewline
37 & 7888 & 7715.27015130313 & 33.6601573750575 & 172.729848696867 & 0.339228136599723 \tabularnewline
38 & 7774 & 7745.31166922213 & 33.1974110978069 & 28.6883307778667 & -0.082473205223167 \tabularnewline
39 & 7644 & 7780.82571756995 & 33.4934673503392 & -136.825717569954 & 0.0522604787995583 \tabularnewline
40 & 7826 & 7831.66814932255 & 35.7060417996914 & -5.66814932255075 & 0.390281385071125 \tabularnewline
41 & 8056 & 7902.58457721194 & 40.1931729552456 & 153.415422788057 & 0.796504226137666 \tabularnewline
42 & 7990 & 7967.32595566632 & 43.3242159119284 & 22.6740443336817 & 0.557878436244461 \tabularnewline
43 & 7814 & 7994.67897308318 & 41.2850597750307 & -180.678973083185 & -0.362905168584095 \tabularnewline
44 & 7978 & 8022.3112522976 & 39.5414008335259 & -44.3112522975986 & -0.309387096907097 \tabularnewline
45 & 8238 & 8071.80375840342 & 40.8117736656532 & 166.196241596581 & 0.224904290184395 \tabularnewline
46 & 8138 & 8118.456159059 & 41.556787772419 & 19.5438409409956 & 0.131833190314531 \tabularnewline
47 & 8000 & 8152.4554983947 & 40.5935660866282 & -152.455498394705 & -0.170758726486997 \tabularnewline
48 & 8176 & 8186.3715675674 & 39.7426804409503 & -10.3715675674021 & -0.151392807654538 \tabularnewline
49 & 8412 & 8231.57149234657 & 40.438549376205 & 180.428507653433 & 0.124076229715909 \tabularnewline
50 & 8332 & 8292.23324270764 & 43.0191412947383 & 39.7667572923599 & 0.458839974455799 \tabularnewline
51 & 8194 & 8343.94523190527 & 44.1279169538245 & -149.945231905269 & 0.196188744846885 \tabularnewline
52 & 8354 & 8385.25586284417 & 43.7690149368857 & -31.2558628441713 & -0.0634516494724225 \tabularnewline
53 & 8576 & 8429.98424591809 & 43.8911500106701 & 146.015754081905 & 0.0216665746380891 \tabularnewline
54 & 8500 & 8470.75902589712 & 43.4942616874576 & 29.240974102881 & -0.0706182260954908 \tabularnewline
55 & 8376 & 8533.68538713016 & 45.9708923680474 & -157.68538713016 & 0.440598571866735 \tabularnewline
56 & 8538 & 8586.45818374854 & 46.8380869699779 & -48.4581837485426 & 0.153926020390593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297971&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]6908[/C][C]6908[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]6694[/C][C]6763.34812045212[/C][C]-6.93186684852988[/C][C]-69.3481204521156[/C][C]-2.8065099589123[/C][/ROW]
[ROW][C]3[/C][C]6564[/C][C]6625.3159065816[/C][C]-16.5329254889295[/C][C]-61.3159065815965[/C][C]-2.68149073778077[/C][/ROW]
[ROW][C]4[/C][C]6800[/C][C]6697.56483495248[/C][C]-9.91797298895097[/C][C]102.435165047523[/C][C]2.16942654161871[/C][/ROW]
[ROW][C]5[/C][C]6820[/C][C]6779.1235707492[/C][C]-2.84585121770335[/C][C]40.8764292508041[/C][C]2.28254627412352[/C][/ROW]
[ROW][C]6[/C][C]6752[/C][C]6785.69119987277[/C][C]-2.04477816522139[/C][C]-33.6911998727711[/C][C]0.231255866039928[/C][/ROW]
[ROW][C]7[/C][C]6632[/C][C]6707.92132389531[/C][C]-9.20809168019775[/C][C]-75.9213238953093[/C][C]-1.83374104272824[/C][/ROW]
[ROW][C]8[/C][C]6756[/C][C]6720.08117657185[/C][C]-7.00256133009456[/C][C]35.918823428153[/C][C]0.511842485125328[/C][/ROW]
[ROW][C]9[/C][C]6898[/C][C]6822.83384128314[/C][C]5.0771215953926[/C][C]75.1661587168584[/C][C]2.60710272060282[/C][/ROW]
[ROW][C]10[/C][C]6844[/C][C]6861.76586458066[/C][C]8.97749095594416[/C][C]-17.7658645806558[/C][C]0.79896868158579[/C][/ROW]
[ROW][C]11[/C][C]6750[/C][C]6815.09902519515[/C][C]2.35403261505839[/C][C]-65.0990251951503[/C][C]-1.30654854017017[/C][/ROW]
[ROW][C]12[/C][C]6892[/C][C]6852.69368118706[/C][C]6.64910068063741[/C][C]39.3063188129376[/C][C]0.824192703025829[/C][/ROW]
[ROW][C]13[/C][C]7104[/C][C]6928.0782469099[/C][C]14.384830483674[/C][C]175.921753090099[/C][C]1.68774417345868[/C][/ROW]
[ROW][C]14[/C][C]7022[/C][C]7000.66325802506[/C][C]21.5462634094528[/C][C]21.3367419749364[/C][C]1.37126840763356[/C][/ROW]
[ROW][C]15[/C][C]6858[/C][C]7007.20804780209[/C][C]19.6359485730745[/C][C]-149.208047802087[/C][C]-0.327097293825565[/C][/ROW]
[ROW][C]16[/C][C]7018[/C][C]6989.82966064541[/C][C]14.9160365178447[/C][C]28.1703393545907[/C][C]-0.826880906029952[/C][/ROW]
[ROW][C]17[/C][C]7218[/C][C]7087.80603249285[/C][C]25.4956586061408[/C][C]130.193967507147[/C][C]1.90494562211418[/C][/ROW]
[ROW][C]18[/C][C]7134[/C][C]7137.06605029976[/C][C]28.5224054614155[/C][C]-3.06605029976471[/C][C]0.545724607143898[/C][/ROW]
[ROW][C]19[/C][C]7006[/C][C]7137.7817385593[/C][C]24.9787992917697[/C][C]-131.781738559297[/C][C]-0.635578611065617[/C][/ROW]
[ROW][C]20[/C][C]7160[/C][C]7167.36456315899[/C][C]25.566296766029[/C][C]-7.36456315899348[/C][C]0.105008763200739[/C][/ROW]
[ROW][C]21[/C][C]7374[/C][C]7254.17058977544[/C][C]33.3939456844662[/C][C]119.829410224558[/C][C]1.39635141407925[/C][/ROW]
[ROW][C]22[/C][C]7276[/C][C]7288.28671993504[/C][C]33.4863564792413[/C][C]-12.2867199350426[/C][C]0.0164607564832788[/C][/ROW]
[ROW][C]23[/C][C]7128[/C][C]7266.99401774714[/C][C]26.4815977871438[/C][C]-138.994017747144[/C][C]-1.2467943315816[/C][/ROW]
[ROW][C]24[/C][C]7272[/C][C]7273.77023619126[/C][C]23.9690173624316[/C][C]-1.77023619126143[/C][C]-0.449226616368125[/C][/ROW]
[ROW][C]25[/C][C]7462[/C][C]7300.47441062667[/C][C]24.3172595509078[/C][C]161.525589373328[/C][C]0.0632947388819119[/C][/ROW]
[ROW][C]26[/C][C]7366[/C][C]7328.89248106739[/C][C]24.8424255281803[/C][C]37.1075189326057[/C][C]0.0943665521712735[/C][/ROW]
[ROW][C]27[/C][C]7218[/C][C]7358.38629824108[/C][C]25.4384758295728[/C][C]-140.386298241084[/C][C]0.10442171658287[/C][/ROW]
[ROW][C]28[/C][C]7366[/C][C]7382.18008360506[/C][C]25.2283424837913[/C][C]-16.1800836050626[/C][C]-0.0368832486011872[/C][/ROW]
[ROW][C]29[/C][C]7546[/C][C]7414.95317893345[/C][C]26.191880518894[/C][C]131.046821066547[/C][C]0.171281715073083[/C][/ROW]
[ROW][C]30[/C][C]7464[/C][C]7450.27544582039[/C][C]27.3595908296395[/C][C]13.7245541796058[/C][C]0.20830840316008[/C][/ROW]
[ROW][C]31[/C][C]7332[/C][C]7478.6610052454[/C][C]27.4909223470045[/C][C]-146.6610052454[/C][C]0.0233583260248253[/C][/ROW]
[ROW][C]32[/C][C]7502[/C][C]7523.71194803158[/C][C]29.7386582104348[/C][C]-21.7119480315772[/C][C]0.398590127888936[/C][/ROW]
[ROW][C]33[/C][C]7736[/C][C]7584.85264370234[/C][C]33.7563293070715[/C][C]151.147356297662[/C][C]0.711463201944265[/C][/ROW]
[ROW][C]34[/C][C]7628[/C][C]7618.87553654978[/C][C]33.7904081922039[/C][C]9.12446345021552[/C][C]0.00603272480219238[/C][/ROW]
[ROW][C]35[/C][C]7494[/C][C]7637.52957953571[/C][C]31.8574636761782[/C][C]-143.529579535711[/C][C]-0.342633284702296[/C][/ROW]
[ROW][C]36[/C][C]7668[/C][C]7668.66600476675[/C][C]31.7654633402109[/C][C]-0.666004766746844[/C][C]-0.0163867151924211[/C][/ROW]
[ROW][C]37[/C][C]7888[/C][C]7715.27015130313[/C][C]33.6601573750575[/C][C]172.729848696867[/C][C]0.339228136599723[/C][/ROW]
[ROW][C]38[/C][C]7774[/C][C]7745.31166922213[/C][C]33.1974110978069[/C][C]28.6883307778667[/C][C]-0.082473205223167[/C][/ROW]
[ROW][C]39[/C][C]7644[/C][C]7780.82571756995[/C][C]33.4934673503392[/C][C]-136.825717569954[/C][C]0.0522604787995583[/C][/ROW]
[ROW][C]40[/C][C]7826[/C][C]7831.66814932255[/C][C]35.7060417996914[/C][C]-5.66814932255075[/C][C]0.390281385071125[/C][/ROW]
[ROW][C]41[/C][C]8056[/C][C]7902.58457721194[/C][C]40.1931729552456[/C][C]153.415422788057[/C][C]0.796504226137666[/C][/ROW]
[ROW][C]42[/C][C]7990[/C][C]7967.32595566632[/C][C]43.3242159119284[/C][C]22.6740443336817[/C][C]0.557878436244461[/C][/ROW]
[ROW][C]43[/C][C]7814[/C][C]7994.67897308318[/C][C]41.2850597750307[/C][C]-180.678973083185[/C][C]-0.362905168584095[/C][/ROW]
[ROW][C]44[/C][C]7978[/C][C]8022.3112522976[/C][C]39.5414008335259[/C][C]-44.3112522975986[/C][C]-0.309387096907097[/C][/ROW]
[ROW][C]45[/C][C]8238[/C][C]8071.80375840342[/C][C]40.8117736656532[/C][C]166.196241596581[/C][C]0.224904290184395[/C][/ROW]
[ROW][C]46[/C][C]8138[/C][C]8118.456159059[/C][C]41.556787772419[/C][C]19.5438409409956[/C][C]0.131833190314531[/C][/ROW]
[ROW][C]47[/C][C]8000[/C][C]8152.4554983947[/C][C]40.5935660866282[/C][C]-152.455498394705[/C][C]-0.170758726486997[/C][/ROW]
[ROW][C]48[/C][C]8176[/C][C]8186.3715675674[/C][C]39.7426804409503[/C][C]-10.3715675674021[/C][C]-0.151392807654538[/C][/ROW]
[ROW][C]49[/C][C]8412[/C][C]8231.57149234657[/C][C]40.438549376205[/C][C]180.428507653433[/C][C]0.124076229715909[/C][/ROW]
[ROW][C]50[/C][C]8332[/C][C]8292.23324270764[/C][C]43.0191412947383[/C][C]39.7667572923599[/C][C]0.458839974455799[/C][/ROW]
[ROW][C]51[/C][C]8194[/C][C]8343.94523190527[/C][C]44.1279169538245[/C][C]-149.945231905269[/C][C]0.196188744846885[/C][/ROW]
[ROW][C]52[/C][C]8354[/C][C]8385.25586284417[/C][C]43.7690149368857[/C][C]-31.2558628441713[/C][C]-0.0634516494724225[/C][/ROW]
[ROW][C]53[/C][C]8576[/C][C]8429.98424591809[/C][C]43.8911500106701[/C][C]146.015754081905[/C][C]0.0216665746380891[/C][/ROW]
[ROW][C]54[/C][C]8500[/C][C]8470.75902589712[/C][C]43.4942616874576[/C][C]29.240974102881[/C][C]-0.0706182260954908[/C][/ROW]
[ROW][C]55[/C][C]8376[/C][C]8533.68538713016[/C][C]45.9708923680474[/C][C]-157.68538713016[/C][C]0.440598571866735[/C][/ROW]
[ROW][C]56[/C][C]8538[/C][C]8586.45818374854[/C][C]46.8380869699779[/C][C]-48.4581837485426[/C][C]0.153926020390593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297971&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
169086908000
266946763.34812045212-6.93186684852988-69.3481204521156-2.8065099589123
365646625.3159065816-16.5329254889295-61.3159065815965-2.68149073778077
468006697.56483495248-9.91797298895097102.4351650475232.16942654161871
568206779.1235707492-2.8458512177033540.87642925080412.28254627412352
667526785.69119987277-2.04477816522139-33.69119987277110.231255866039928
766326707.92132389531-9.20809168019775-75.9213238953093-1.83374104272824
867566720.08117657185-7.0025613300945635.9188234281530.511842485125328
968986822.833841283145.077121595392675.16615871685842.60710272060282
1068446861.765864580668.97749095594416-17.76586458065580.79896868158579
1167506815.099025195152.35403261505839-65.0990251951503-1.30654854017017
1268926852.693681187066.6491006806374139.30631881293760.824192703025829
1371046928.078246909914.384830483674175.9217530900991.68774417345868
1470227000.6632580250621.546263409452821.33674197493641.37126840763356
1568587007.2080478020919.6359485730745-149.208047802087-0.327097293825565
1670186989.8296606454114.916036517844728.1703393545907-0.826880906029952
1772187087.8060324928525.4956586061408130.1939675071471.90494562211418
1871347137.0660502997628.5224054614155-3.066050299764710.545724607143898
1970067137.781738559324.9787992917697-131.781738559297-0.635578611065617
2071607167.3645631589925.566296766029-7.364563158993480.105008763200739
2173747254.1705897754433.3939456844662119.8294102245581.39635141407925
2272767288.2867199350433.4863564792413-12.28671993504260.0164607564832788
2371287266.9940177471426.4815977871438-138.994017747144-1.2467943315816
2472727273.7702361912623.9690173624316-1.77023619126143-0.449226616368125
2574627300.4744106266724.3172595509078161.5255893733280.0632947388819119
2673667328.8924810673924.842425528180337.10751893260570.0943665521712735
2772187358.3862982410825.4384758295728-140.3862982410840.10442171658287
2873667382.1800836050625.2283424837913-16.1800836050626-0.0368832486011872
2975467414.9531789334526.191880518894131.0468210665470.171281715073083
3074647450.2754458203927.359590829639513.72455417960580.20830840316008
3173327478.661005245427.4909223470045-146.66100524540.0233583260248253
3275027523.7119480315829.7386582104348-21.71194803157720.398590127888936
3377367584.8526437023433.7563293070715151.1473562976620.711463201944265
3476287618.8755365497833.79040819220399.124463450215520.00603272480219238
3574947637.5295795357131.8574636761782-143.529579535711-0.342633284702296
3676687668.6660047667531.7654633402109-0.666004766746844-0.0163867151924211
3778887715.2701513031333.6601573750575172.7298486968670.339228136599723
3877747745.3116692221333.197411097806928.6883307778667-0.082473205223167
3976447780.8257175699533.4934673503392-136.8257175699540.0522604787995583
4078267831.6681493225535.7060417996914-5.668149322550750.390281385071125
4180567902.5845772119440.1931729552456153.4154227880570.796504226137666
4279907967.3259556663243.324215911928422.67404433368170.557878436244461
4378147994.6789730831841.2850597750307-180.678973083185-0.362905168584095
4479788022.311252297639.5414008335259-44.3112522975986-0.309387096907097
4582388071.8037584034240.8117736656532166.1962415965810.224904290184395
4681388118.45615905941.55678777241919.54384094099560.131833190314531
4780008152.455498394740.5935660866282-152.455498394705-0.170758726486997
4881768186.371567567439.7426804409503-10.3715675674021-0.151392807654538
4984128231.5714923465740.438549376205180.4285076534330.124076229715909
5083328292.2332427076443.019141294738339.76675729235990.458839974455799
5181948343.9452319052744.1279169538245-149.9452319052690.196188744846885
5283548385.2558628441743.7690149368857-31.2558628441713-0.0634516494724225
5385768429.9842459180943.8911500106701146.0157540819050.0216665746380891
5485008470.7590258971243.494261687457629.240974102881-0.0706182260954908
5583768533.6853871301645.9708923680474-157.685387130160.440598571866735
5685388586.4581837485446.8380869699779-48.45818374854260.153926020390593







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
18793.187605296758626.84110580022166.346499496526
28696.661148122878671.4256938591125.2354542637598
38566.623785310158716.01028191799-149.386496607848
48743.862378945358760.59486997688-16.7324910315275
58971.90643601648805.17945803577166.726977980626
68881.715902576298849.7640460946631.951856481634
78743.460021245438894.34863415354-150.888612908118
88906.445030520378938.93322221243-32.4881916920659
99126.881141172238983.51781027132143.363330900913
109047.876171073219028.1023983302119.773772743006
118913.041404503529072.6869863891-159.645581885576
129073.015056706659117.27157444798-44.2565177413305

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 8793.18760529675 & 8626.84110580022 & 166.346499496526 \tabularnewline
2 & 8696.66114812287 & 8671.42569385911 & 25.2354542637598 \tabularnewline
3 & 8566.62378531015 & 8716.01028191799 & -149.386496607848 \tabularnewline
4 & 8743.86237894535 & 8760.59486997688 & -16.7324910315275 \tabularnewline
5 & 8971.9064360164 & 8805.17945803577 & 166.726977980626 \tabularnewline
6 & 8881.71590257629 & 8849.76404609466 & 31.951856481634 \tabularnewline
7 & 8743.46002124543 & 8894.34863415354 & -150.888612908118 \tabularnewline
8 & 8906.44503052037 & 8938.93322221243 & -32.4881916920659 \tabularnewline
9 & 9126.88114117223 & 8983.51781027132 & 143.363330900913 \tabularnewline
10 & 9047.87617107321 & 9028.10239833021 & 19.773772743006 \tabularnewline
11 & 8913.04140450352 & 9072.6869863891 & -159.645581885576 \tabularnewline
12 & 9073.01505670665 & 9117.27157444798 & -44.2565177413305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297971&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]8793.18760529675[/C][C]8626.84110580022[/C][C]166.346499496526[/C][/ROW]
[ROW][C]2[/C][C]8696.66114812287[/C][C]8671.42569385911[/C][C]25.2354542637598[/C][/ROW]
[ROW][C]3[/C][C]8566.62378531015[/C][C]8716.01028191799[/C][C]-149.386496607848[/C][/ROW]
[ROW][C]4[/C][C]8743.86237894535[/C][C]8760.59486997688[/C][C]-16.7324910315275[/C][/ROW]
[ROW][C]5[/C][C]8971.9064360164[/C][C]8805.17945803577[/C][C]166.726977980626[/C][/ROW]
[ROW][C]6[/C][C]8881.71590257629[/C][C]8849.76404609466[/C][C]31.951856481634[/C][/ROW]
[ROW][C]7[/C][C]8743.46002124543[/C][C]8894.34863415354[/C][C]-150.888612908118[/C][/ROW]
[ROW][C]8[/C][C]8906.44503052037[/C][C]8938.93322221243[/C][C]-32.4881916920659[/C][/ROW]
[ROW][C]9[/C][C]9126.88114117223[/C][C]8983.51781027132[/C][C]143.363330900913[/C][/ROW]
[ROW][C]10[/C][C]9047.87617107321[/C][C]9028.10239833021[/C][C]19.773772743006[/C][/ROW]
[ROW][C]11[/C][C]8913.04140450352[/C][C]9072.6869863891[/C][C]-159.645581885576[/C][/ROW]
[ROW][C]12[/C][C]9073.01505670665[/C][C]9117.27157444798[/C][C]-44.2565177413305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297971&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
18793.187605296758626.84110580022166.346499496526
28696.661148122878671.4256938591125.2354542637598
38566.623785310158716.01028191799-149.386496607848
48743.862378945358760.59486997688-16.7324910315275
58971.90643601648805.17945803577166.726977980626
68881.715902576298849.7640460946631.951856481634
78743.460021245438894.34863415354-150.888612908118
88906.445030520378938.93322221243-32.4881916920659
99126.881141172238983.51781027132143.363330900913
109047.876171073219028.1023983302119.773772743006
118913.041404503529072.6869863891-159.645581885576
129073.015056706659117.27157444798-44.2565177413305



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