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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 computationTue, 20 Dec 2016 20:43:42 +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/20/t1482263055lk613p9uum4cj4d.htm/, Retrieved Sun, 28 Apr 2024 18:06:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301791, Retrieved Sun, 28 Apr 2024 18:06:51 +0000
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Original text written by user:
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User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-20 19:43:42] [672675941468e072e71d9fb024f2b817] [Current]
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Dataseries X:
1932.8
1861.4
2170.2
1999.6
2225.5
2195.7
2713.1
2412
2568.3
2623.7
3185.5
2722.6
3046.3
2854.2
3337.6
2920.3
3058.3
2933.7
3773.4
3193.5
3472.2
3345.5
4028.4
3463.1
3675.4
3500.8
4142.1
3598
3765.3
3557.7
4303.6
3620.1
3691.1
3678.1
4505.8
3695
3894.1
3718.9
4749.8
3855.9
4011.7
3907.6
4812.5
4071.3
4163.4
4077.6
5109.2
4207.6
4320.8
4396.9
5358.8




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=301791&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=301791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301791&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
11932.81932.8000
21861.41873.87410703104-15.196875715239-12.4741070310398-0.206208873238619
32170.22036.7384999725620.7620716497043133.4615000274412.21432134313713
41999.62034.5224827821418.0116257137511-34.9224827821375-0.366443002212689
52225.52146.6837262567816.080167909105278.81627374321631.59012001618031
62195.72250.970546649720.4968938406073-55.27054664969951.3480125253531
72713.12452.7199250529635.6995804547597260.3800749470382.6579221146377
824122515.0085033869637.5103594943403-103.0085033869620.409586349613737
92568.32559.9555207637737.79929980697758.344479236234240.117720011013487
102623.72690.5215216923141.6430102087934-66.82152169231081.45206439714328
113185.52855.2624599768247.8837014961778330.2375400231771.90206431995916
122722.62887.7810841609147.1351278684896-165.181084160906-0.239182387564298
133046.33019.5197890844850.605939887606726.78021091551971.32961940124348
142854.23033.6377179056949.1995225391334-179.43771790569-0.573870369893391
153337.63040.3676464465947.5214033724018297.232353553414-0.666536609386609
162920.33098.7935744956447.9447317306224-178.4935744956350.171406311618141
173058.33075.3614119610845.3522782114013-17.0614119610816-1.1256305003476
182933.73096.4944503945444.5164760147503-162.794450394536-0.382567108863067
193773.43310.7955515830750.2520526268053462.6044484169342.68309318905705
203193.53371.9857548494650.6130510279379-178.4857548494610.173012656018432
213472.23466.2642826571152.00125176871285.935717342888370.691679773075483
223345.53562.743945517753.3636571785218-217.2439455177030.705409118866001
234028.43602.4111213171952.9559194346617425.988878682806-0.217399098571404
243463.13660.484550090953.1043525928019-197.38455009090.08129339221388
253675.43701.280924154952.7575419367722-25.8809241549018-0.195694964536315
263500.83730.3433942187352.109313692221-229.543394218734-0.377076453836449
274142.13744.5350697543951.099716723523397.564930245607-0.603862388447634
2835983784.9570517212750.8225349049851-186.957051721269-0.170167622052963
293765.33801.9900276906649.9674287139259-36.6900276906622-0.538866112582474
303557.73802.7858004576848.7542941822104-245.085800457677-0.784701269869758
314303.63867.4050935836149.1362189972544436.1949064163920.253337821681431
323620.13849.4070961859347.5577441396116-229.307096185929-1.07264911843118
333691.13787.5207658575945.0432915260592-96.4207658575897-1.74964748656701
343678.13862.2869008658745.7107733569848-184.186900865870.475427520068479
354505.83971.4923523011647.1052446203091534.3076476988391.01614456860549
3636953953.8347936018745.7134426812647-258.834793601868-1.03694804496473
373894.13997.5460458445345.6713175354518-103.446045844527-0.0320731125460532
383718.93980.5973947747444.3809845172579-261.697394774738-1.00356398198953
394749.84098.6488202491945.8683368512365651.1511797508111.18117408425554
403855.94134.6179024752345.6724329573603-278.717902475234-0.158782877267804
414011.74134.9566073920444.7926879203944-123.256607392042-0.727438046080029
423907.64185.1342406437544.8951988047758-277.5342406437520.0864415920254453
434812.54189.0078926283644.1288822780966623.492107371643-0.658740101082253
444071.34276.9862390858444.9330037367162-205.6862390858410.704402578719834
454163.44308.2605774670644.6870378386692-144.86057746706-0.219489537883746
464077.64345.2226090158144.5503862101317-267.622609015813-0.124178959731707
475109.24448.4728190403945.5707073133923660.7271809596120.943896903010377
484207.64456.7940172425744.9342984860365-249.19401724257-0.599159023321117
494320.84480.0168390212244.5695882146307-159.21683902122-0.349333427128358
504396.94605.9243775643445.9133348433972-209.0243775643411.30908825324124
515358.84677.1493268744746.3247002425086681.6506731255350.407489452883644

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 1932.8 & 1932.8 & 0 & 0 & 0 \tabularnewline
2 & 1861.4 & 1873.87410703104 & -15.196875715239 & -12.4741070310398 & -0.206208873238619 \tabularnewline
3 & 2170.2 & 2036.73849997256 & 20.7620716497043 & 133.461500027441 & 2.21432134313713 \tabularnewline
4 & 1999.6 & 2034.52248278214 & 18.0116257137511 & -34.9224827821375 & -0.366443002212689 \tabularnewline
5 & 2225.5 & 2146.68372625678 & 16.0801679091052 & 78.8162737432163 & 1.59012001618031 \tabularnewline
6 & 2195.7 & 2250.9705466497 & 20.4968938406073 & -55.2705466496995 & 1.3480125253531 \tabularnewline
7 & 2713.1 & 2452.71992505296 & 35.6995804547597 & 260.380074947038 & 2.6579221146377 \tabularnewline
8 & 2412 & 2515.00850338696 & 37.5103594943403 & -103.008503386962 & 0.409586349613737 \tabularnewline
9 & 2568.3 & 2559.95552076377 & 37.7992998069775 & 8.34447923623424 & 0.117720011013487 \tabularnewline
10 & 2623.7 & 2690.52152169231 & 41.6430102087934 & -66.8215216923108 & 1.45206439714328 \tabularnewline
11 & 3185.5 & 2855.26245997682 & 47.8837014961778 & 330.237540023177 & 1.90206431995916 \tabularnewline
12 & 2722.6 & 2887.78108416091 & 47.1351278684896 & -165.181084160906 & -0.239182387564298 \tabularnewline
13 & 3046.3 & 3019.51978908448 & 50.6059398876067 & 26.7802109155197 & 1.32961940124348 \tabularnewline
14 & 2854.2 & 3033.63771790569 & 49.1995225391334 & -179.43771790569 & -0.573870369893391 \tabularnewline
15 & 3337.6 & 3040.36764644659 & 47.5214033724018 & 297.232353553414 & -0.666536609386609 \tabularnewline
16 & 2920.3 & 3098.79357449564 & 47.9447317306224 & -178.493574495635 & 0.171406311618141 \tabularnewline
17 & 3058.3 & 3075.36141196108 & 45.3522782114013 & -17.0614119610816 & -1.1256305003476 \tabularnewline
18 & 2933.7 & 3096.49445039454 & 44.5164760147503 & -162.794450394536 & -0.382567108863067 \tabularnewline
19 & 3773.4 & 3310.79555158307 & 50.2520526268053 & 462.604448416934 & 2.68309318905705 \tabularnewline
20 & 3193.5 & 3371.98575484946 & 50.6130510279379 & -178.485754849461 & 0.173012656018432 \tabularnewline
21 & 3472.2 & 3466.26428265711 & 52.0012517687128 & 5.93571734288837 & 0.691679773075483 \tabularnewline
22 & 3345.5 & 3562.7439455177 & 53.3636571785218 & -217.243945517703 & 0.705409118866001 \tabularnewline
23 & 4028.4 & 3602.41112131719 & 52.9559194346617 & 425.988878682806 & -0.217399098571404 \tabularnewline
24 & 3463.1 & 3660.4845500909 & 53.1043525928019 & -197.3845500909 & 0.08129339221388 \tabularnewline
25 & 3675.4 & 3701.2809241549 & 52.7575419367722 & -25.8809241549018 & -0.195694964536315 \tabularnewline
26 & 3500.8 & 3730.34339421873 & 52.109313692221 & -229.543394218734 & -0.377076453836449 \tabularnewline
27 & 4142.1 & 3744.53506975439 & 51.099716723523 & 397.564930245607 & -0.603862388447634 \tabularnewline
28 & 3598 & 3784.95705172127 & 50.8225349049851 & -186.957051721269 & -0.170167622052963 \tabularnewline
29 & 3765.3 & 3801.99002769066 & 49.9674287139259 & -36.6900276906622 & -0.538866112582474 \tabularnewline
30 & 3557.7 & 3802.78580045768 & 48.7542941822104 & -245.085800457677 & -0.784701269869758 \tabularnewline
31 & 4303.6 & 3867.40509358361 & 49.1362189972544 & 436.194906416392 & 0.253337821681431 \tabularnewline
32 & 3620.1 & 3849.40709618593 & 47.5577441396116 & -229.307096185929 & -1.07264911843118 \tabularnewline
33 & 3691.1 & 3787.52076585759 & 45.0432915260592 & -96.4207658575897 & -1.74964748656701 \tabularnewline
34 & 3678.1 & 3862.28690086587 & 45.7107733569848 & -184.18690086587 & 0.475427520068479 \tabularnewline
35 & 4505.8 & 3971.49235230116 & 47.1052446203091 & 534.307647698839 & 1.01614456860549 \tabularnewline
36 & 3695 & 3953.83479360187 & 45.7134426812647 & -258.834793601868 & -1.03694804496473 \tabularnewline
37 & 3894.1 & 3997.54604584453 & 45.6713175354518 & -103.446045844527 & -0.0320731125460532 \tabularnewline
38 & 3718.9 & 3980.59739477474 & 44.3809845172579 & -261.697394774738 & -1.00356398198953 \tabularnewline
39 & 4749.8 & 4098.64882024919 & 45.8683368512365 & 651.151179750811 & 1.18117408425554 \tabularnewline
40 & 3855.9 & 4134.61790247523 & 45.6724329573603 & -278.717902475234 & -0.158782877267804 \tabularnewline
41 & 4011.7 & 4134.95660739204 & 44.7926879203944 & -123.256607392042 & -0.727438046080029 \tabularnewline
42 & 3907.6 & 4185.13424064375 & 44.8951988047758 & -277.534240643752 & 0.0864415920254453 \tabularnewline
43 & 4812.5 & 4189.00789262836 & 44.1288822780966 & 623.492107371643 & -0.658740101082253 \tabularnewline
44 & 4071.3 & 4276.98623908584 & 44.9330037367162 & -205.686239085841 & 0.704402578719834 \tabularnewline
45 & 4163.4 & 4308.26057746706 & 44.6870378386692 & -144.86057746706 & -0.219489537883746 \tabularnewline
46 & 4077.6 & 4345.22260901581 & 44.5503862101317 & -267.622609015813 & -0.124178959731707 \tabularnewline
47 & 5109.2 & 4448.47281904039 & 45.5707073133923 & 660.727180959612 & 0.943896903010377 \tabularnewline
48 & 4207.6 & 4456.79401724257 & 44.9342984860365 & -249.19401724257 & -0.599159023321117 \tabularnewline
49 & 4320.8 & 4480.01683902122 & 44.5695882146307 & -159.21683902122 & -0.349333427128358 \tabularnewline
50 & 4396.9 & 4605.92437756434 & 45.9133348433972 & -209.024377564341 & 1.30908825324124 \tabularnewline
51 & 5358.8 & 4677.14932687447 & 46.3247002425086 & 681.650673125535 & 0.407489452883644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301791&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]1932.8[/C][C]1932.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]1861.4[/C][C]1873.87410703104[/C][C]-15.196875715239[/C][C]-12.4741070310398[/C][C]-0.206208873238619[/C][/ROW]
[ROW][C]3[/C][C]2170.2[/C][C]2036.73849997256[/C][C]20.7620716497043[/C][C]133.461500027441[/C][C]2.21432134313713[/C][/ROW]
[ROW][C]4[/C][C]1999.6[/C][C]2034.52248278214[/C][C]18.0116257137511[/C][C]-34.9224827821375[/C][C]-0.366443002212689[/C][/ROW]
[ROW][C]5[/C][C]2225.5[/C][C]2146.68372625678[/C][C]16.0801679091052[/C][C]78.8162737432163[/C][C]1.59012001618031[/C][/ROW]
[ROW][C]6[/C][C]2195.7[/C][C]2250.9705466497[/C][C]20.4968938406073[/C][C]-55.2705466496995[/C][C]1.3480125253531[/C][/ROW]
[ROW][C]7[/C][C]2713.1[/C][C]2452.71992505296[/C][C]35.6995804547597[/C][C]260.380074947038[/C][C]2.6579221146377[/C][/ROW]
[ROW][C]8[/C][C]2412[/C][C]2515.00850338696[/C][C]37.5103594943403[/C][C]-103.008503386962[/C][C]0.409586349613737[/C][/ROW]
[ROW][C]9[/C][C]2568.3[/C][C]2559.95552076377[/C][C]37.7992998069775[/C][C]8.34447923623424[/C][C]0.117720011013487[/C][/ROW]
[ROW][C]10[/C][C]2623.7[/C][C]2690.52152169231[/C][C]41.6430102087934[/C][C]-66.8215216923108[/C][C]1.45206439714328[/C][/ROW]
[ROW][C]11[/C][C]3185.5[/C][C]2855.26245997682[/C][C]47.8837014961778[/C][C]330.237540023177[/C][C]1.90206431995916[/C][/ROW]
[ROW][C]12[/C][C]2722.6[/C][C]2887.78108416091[/C][C]47.1351278684896[/C][C]-165.181084160906[/C][C]-0.239182387564298[/C][/ROW]
[ROW][C]13[/C][C]3046.3[/C][C]3019.51978908448[/C][C]50.6059398876067[/C][C]26.7802109155197[/C][C]1.32961940124348[/C][/ROW]
[ROW][C]14[/C][C]2854.2[/C][C]3033.63771790569[/C][C]49.1995225391334[/C][C]-179.43771790569[/C][C]-0.573870369893391[/C][/ROW]
[ROW][C]15[/C][C]3337.6[/C][C]3040.36764644659[/C][C]47.5214033724018[/C][C]297.232353553414[/C][C]-0.666536609386609[/C][/ROW]
[ROW][C]16[/C][C]2920.3[/C][C]3098.79357449564[/C][C]47.9447317306224[/C][C]-178.493574495635[/C][C]0.171406311618141[/C][/ROW]
[ROW][C]17[/C][C]3058.3[/C][C]3075.36141196108[/C][C]45.3522782114013[/C][C]-17.0614119610816[/C][C]-1.1256305003476[/C][/ROW]
[ROW][C]18[/C][C]2933.7[/C][C]3096.49445039454[/C][C]44.5164760147503[/C][C]-162.794450394536[/C][C]-0.382567108863067[/C][/ROW]
[ROW][C]19[/C][C]3773.4[/C][C]3310.79555158307[/C][C]50.2520526268053[/C][C]462.604448416934[/C][C]2.68309318905705[/C][/ROW]
[ROW][C]20[/C][C]3193.5[/C][C]3371.98575484946[/C][C]50.6130510279379[/C][C]-178.485754849461[/C][C]0.173012656018432[/C][/ROW]
[ROW][C]21[/C][C]3472.2[/C][C]3466.26428265711[/C][C]52.0012517687128[/C][C]5.93571734288837[/C][C]0.691679773075483[/C][/ROW]
[ROW][C]22[/C][C]3345.5[/C][C]3562.7439455177[/C][C]53.3636571785218[/C][C]-217.243945517703[/C][C]0.705409118866001[/C][/ROW]
[ROW][C]23[/C][C]4028.4[/C][C]3602.41112131719[/C][C]52.9559194346617[/C][C]425.988878682806[/C][C]-0.217399098571404[/C][/ROW]
[ROW][C]24[/C][C]3463.1[/C][C]3660.4845500909[/C][C]53.1043525928019[/C][C]-197.3845500909[/C][C]0.08129339221388[/C][/ROW]
[ROW][C]25[/C][C]3675.4[/C][C]3701.2809241549[/C][C]52.7575419367722[/C][C]-25.8809241549018[/C][C]-0.195694964536315[/C][/ROW]
[ROW][C]26[/C][C]3500.8[/C][C]3730.34339421873[/C][C]52.109313692221[/C][C]-229.543394218734[/C][C]-0.377076453836449[/C][/ROW]
[ROW][C]27[/C][C]4142.1[/C][C]3744.53506975439[/C][C]51.099716723523[/C][C]397.564930245607[/C][C]-0.603862388447634[/C][/ROW]
[ROW][C]28[/C][C]3598[/C][C]3784.95705172127[/C][C]50.8225349049851[/C][C]-186.957051721269[/C][C]-0.170167622052963[/C][/ROW]
[ROW][C]29[/C][C]3765.3[/C][C]3801.99002769066[/C][C]49.9674287139259[/C][C]-36.6900276906622[/C][C]-0.538866112582474[/C][/ROW]
[ROW][C]30[/C][C]3557.7[/C][C]3802.78580045768[/C][C]48.7542941822104[/C][C]-245.085800457677[/C][C]-0.784701269869758[/C][/ROW]
[ROW][C]31[/C][C]4303.6[/C][C]3867.40509358361[/C][C]49.1362189972544[/C][C]436.194906416392[/C][C]0.253337821681431[/C][/ROW]
[ROW][C]32[/C][C]3620.1[/C][C]3849.40709618593[/C][C]47.5577441396116[/C][C]-229.307096185929[/C][C]-1.07264911843118[/C][/ROW]
[ROW][C]33[/C][C]3691.1[/C][C]3787.52076585759[/C][C]45.0432915260592[/C][C]-96.4207658575897[/C][C]-1.74964748656701[/C][/ROW]
[ROW][C]34[/C][C]3678.1[/C][C]3862.28690086587[/C][C]45.7107733569848[/C][C]-184.18690086587[/C][C]0.475427520068479[/C][/ROW]
[ROW][C]35[/C][C]4505.8[/C][C]3971.49235230116[/C][C]47.1052446203091[/C][C]534.307647698839[/C][C]1.01614456860549[/C][/ROW]
[ROW][C]36[/C][C]3695[/C][C]3953.83479360187[/C][C]45.7134426812647[/C][C]-258.834793601868[/C][C]-1.03694804496473[/C][/ROW]
[ROW][C]37[/C][C]3894.1[/C][C]3997.54604584453[/C][C]45.6713175354518[/C][C]-103.446045844527[/C][C]-0.0320731125460532[/C][/ROW]
[ROW][C]38[/C][C]3718.9[/C][C]3980.59739477474[/C][C]44.3809845172579[/C][C]-261.697394774738[/C][C]-1.00356398198953[/C][/ROW]
[ROW][C]39[/C][C]4749.8[/C][C]4098.64882024919[/C][C]45.8683368512365[/C][C]651.151179750811[/C][C]1.18117408425554[/C][/ROW]
[ROW][C]40[/C][C]3855.9[/C][C]4134.61790247523[/C][C]45.6724329573603[/C][C]-278.717902475234[/C][C]-0.158782877267804[/C][/ROW]
[ROW][C]41[/C][C]4011.7[/C][C]4134.95660739204[/C][C]44.7926879203944[/C][C]-123.256607392042[/C][C]-0.727438046080029[/C][/ROW]
[ROW][C]42[/C][C]3907.6[/C][C]4185.13424064375[/C][C]44.8951988047758[/C][C]-277.534240643752[/C][C]0.0864415920254453[/C][/ROW]
[ROW][C]43[/C][C]4812.5[/C][C]4189.00789262836[/C][C]44.1288822780966[/C][C]623.492107371643[/C][C]-0.658740101082253[/C][/ROW]
[ROW][C]44[/C][C]4071.3[/C][C]4276.98623908584[/C][C]44.9330037367162[/C][C]-205.686239085841[/C][C]0.704402578719834[/C][/ROW]
[ROW][C]45[/C][C]4163.4[/C][C]4308.26057746706[/C][C]44.6870378386692[/C][C]-144.86057746706[/C][C]-0.219489537883746[/C][/ROW]
[ROW][C]46[/C][C]4077.6[/C][C]4345.22260901581[/C][C]44.5503862101317[/C][C]-267.622609015813[/C][C]-0.124178959731707[/C][/ROW]
[ROW][C]47[/C][C]5109.2[/C][C]4448.47281904039[/C][C]45.5707073133923[/C][C]660.727180959612[/C][C]0.943896903010377[/C][/ROW]
[ROW][C]48[/C][C]4207.6[/C][C]4456.79401724257[/C][C]44.9342984860365[/C][C]-249.19401724257[/C][C]-0.599159023321117[/C][/ROW]
[ROW][C]49[/C][C]4320.8[/C][C]4480.01683902122[/C][C]44.5695882146307[/C][C]-159.21683902122[/C][C]-0.349333427128358[/C][/ROW]
[ROW][C]50[/C][C]4396.9[/C][C]4605.92437756434[/C][C]45.9133348433972[/C][C]-209.024377564341[/C][C]1.30908825324124[/C][/ROW]
[ROW][C]51[/C][C]5358.8[/C][C]4677.14932687447[/C][C]46.3247002425086[/C][C]681.650673125535[/C][C]0.407489452883644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301791&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
11932.81932.8000
21861.41873.87410703104-15.196875715239-12.4741070310398-0.206208873238619
32170.22036.7384999725620.7620716497043133.4615000274412.21432134313713
41999.62034.5224827821418.0116257137511-34.9224827821375-0.366443002212689
52225.52146.6837262567816.080167909105278.81627374321631.59012001618031
62195.72250.970546649720.4968938406073-55.27054664969951.3480125253531
72713.12452.7199250529635.6995804547597260.3800749470382.6579221146377
824122515.0085033869637.5103594943403-103.0085033869620.409586349613737
92568.32559.9555207637737.79929980697758.344479236234240.117720011013487
102623.72690.5215216923141.6430102087934-66.82152169231081.45206439714328
113185.52855.2624599768247.8837014961778330.2375400231771.90206431995916
122722.62887.7810841609147.1351278684896-165.181084160906-0.239182387564298
133046.33019.5197890844850.605939887606726.78021091551971.32961940124348
142854.23033.6377179056949.1995225391334-179.43771790569-0.573870369893391
153337.63040.3676464465947.5214033724018297.232353553414-0.666536609386609
162920.33098.7935744956447.9447317306224-178.4935744956350.171406311618141
173058.33075.3614119610845.3522782114013-17.0614119610816-1.1256305003476
182933.73096.4944503945444.5164760147503-162.794450394536-0.382567108863067
193773.43310.7955515830750.2520526268053462.6044484169342.68309318905705
203193.53371.9857548494650.6130510279379-178.4857548494610.173012656018432
213472.23466.2642826571152.00125176871285.935717342888370.691679773075483
223345.53562.743945517753.3636571785218-217.2439455177030.705409118866001
234028.43602.4111213171952.9559194346617425.988878682806-0.217399098571404
243463.13660.484550090953.1043525928019-197.38455009090.08129339221388
253675.43701.280924154952.7575419367722-25.8809241549018-0.195694964536315
263500.83730.3433942187352.109313692221-229.543394218734-0.377076453836449
274142.13744.5350697543951.099716723523397.564930245607-0.603862388447634
2835983784.9570517212750.8225349049851-186.957051721269-0.170167622052963
293765.33801.9900276906649.9674287139259-36.6900276906622-0.538866112582474
303557.73802.7858004576848.7542941822104-245.085800457677-0.784701269869758
314303.63867.4050935836149.1362189972544436.1949064163920.253337821681431
323620.13849.4070961859347.5577441396116-229.307096185929-1.07264911843118
333691.13787.5207658575945.0432915260592-96.4207658575897-1.74964748656701
343678.13862.2869008658745.7107733569848-184.186900865870.475427520068479
354505.83971.4923523011647.1052446203091534.3076476988391.01614456860549
3636953953.8347936018745.7134426812647-258.834793601868-1.03694804496473
373894.13997.5460458445345.6713175354518-103.446045844527-0.0320731125460532
383718.93980.5973947747444.3809845172579-261.697394774738-1.00356398198953
394749.84098.6488202491945.8683368512365651.1511797508111.18117408425554
403855.94134.6179024752345.6724329573603-278.717902475234-0.158782877267804
414011.74134.9566073920444.7926879203944-123.256607392042-0.727438046080029
423907.64185.1342406437544.8951988047758-277.5342406437520.0864415920254453
434812.54189.0078926283644.1288822780966623.492107371643-0.658740101082253
444071.34276.9862390858444.9330037367162-205.6862390858410.704402578719834
454163.44308.2605774670644.6870378386692-144.86057746706-0.219489537883746
464077.64345.2226090158144.5503862101317-267.622609015813-0.124178959731707
475109.24448.4728190403945.5707073133923660.7271809596120.943896903010377
484207.64456.7940172425744.9342984860365-249.19401724257-0.599159023321117
494320.84480.0168390212244.5695882146307-159.21683902122-0.349333427128358
504396.94605.9243775643445.9133348433972-209.0243775643411.30908825324124
515358.84677.1493268744746.3247002425086681.6506731255350.407489452883644







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14481.582591441774736.41014237497-254.827550933192
24591.388403319824791.82698190936-200.438578589535
34625.168519547064847.24382144375-222.075301896687
45580.002092397564902.66066097814677.341431419415
54703.249949579344958.07750051253-254.827550933192
64813.055761457395013.49434004692-200.438578589535
74846.835877684635068.91117958131-222.075301896687
85801.669450535125124.32801911571677.341431419415
94924.91730771695179.7448586501-254.827550933192
105034.723119594955235.16169818449-200.438578589535
115068.503235822195290.57853771888-222.075301896687
126023.336808672695345.99537725327677.341431419415

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4481.58259144177 & 4736.41014237497 & -254.827550933192 \tabularnewline
2 & 4591.38840331982 & 4791.82698190936 & -200.438578589535 \tabularnewline
3 & 4625.16851954706 & 4847.24382144375 & -222.075301896687 \tabularnewline
4 & 5580.00209239756 & 4902.66066097814 & 677.341431419415 \tabularnewline
5 & 4703.24994957934 & 4958.07750051253 & -254.827550933192 \tabularnewline
6 & 4813.05576145739 & 5013.49434004692 & -200.438578589535 \tabularnewline
7 & 4846.83587768463 & 5068.91117958131 & -222.075301896687 \tabularnewline
8 & 5801.66945053512 & 5124.32801911571 & 677.341431419415 \tabularnewline
9 & 4924.9173077169 & 5179.7448586501 & -254.827550933192 \tabularnewline
10 & 5034.72311959495 & 5235.16169818449 & -200.438578589535 \tabularnewline
11 & 5068.50323582219 & 5290.57853771888 & -222.075301896687 \tabularnewline
12 & 6023.33680867269 & 5345.99537725327 & 677.341431419415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301791&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]4481.58259144177[/C][C]4736.41014237497[/C][C]-254.827550933192[/C][/ROW]
[ROW][C]2[/C][C]4591.38840331982[/C][C]4791.82698190936[/C][C]-200.438578589535[/C][/ROW]
[ROW][C]3[/C][C]4625.16851954706[/C][C]4847.24382144375[/C][C]-222.075301896687[/C][/ROW]
[ROW][C]4[/C][C]5580.00209239756[/C][C]4902.66066097814[/C][C]677.341431419415[/C][/ROW]
[ROW][C]5[/C][C]4703.24994957934[/C][C]4958.07750051253[/C][C]-254.827550933192[/C][/ROW]
[ROW][C]6[/C][C]4813.05576145739[/C][C]5013.49434004692[/C][C]-200.438578589535[/C][/ROW]
[ROW][C]7[/C][C]4846.83587768463[/C][C]5068.91117958131[/C][C]-222.075301896687[/C][/ROW]
[ROW][C]8[/C][C]5801.66945053512[/C][C]5124.32801911571[/C][C]677.341431419415[/C][/ROW]
[ROW][C]9[/C][C]4924.9173077169[/C][C]5179.7448586501[/C][C]-254.827550933192[/C][/ROW]
[ROW][C]10[/C][C]5034.72311959495[/C][C]5235.16169818449[/C][C]-200.438578589535[/C][/ROW]
[ROW][C]11[/C][C]5068.50323582219[/C][C]5290.57853771888[/C][C]-222.075301896687[/C][/ROW]
[ROW][C]12[/C][C]6023.33680867269[/C][C]5345.99537725327[/C][C]677.341431419415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301791&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
14481.582591441774736.41014237497-254.827550933192
24591.388403319824791.82698190936-200.438578589535
34625.168519547064847.24382144375-222.075301896687
45580.002092397564902.66066097814677.341431419415
54703.249949579344958.07750051253-254.827550933192
64813.055761457395013.49434004692-200.438578589535
74846.835877684635068.91117958131-222.075301896687
85801.669450535125124.32801911571677.341431419415
94924.91730771695179.7448586501-254.827550933192
105034.723119594955235.16169818449-200.438578589535
115068.503235822195290.57853771888-222.075301896687
126023.336808672695345.99537725327677.341431419415



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 12 ;
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')