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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 computationSat, 17 Dec 2016 18:08:21 +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/17/t148199452660a2sdnv4cmmm02.htm/, Retrieved Thu, 02 May 2024 09:28:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300890, Retrieved Thu, 02 May 2024 09:28:54 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Histogram] [2016-12-02 11:39:44] [937b9e6718912fc8986df66e31b6c342]
- RMP   [Histogram] [HISTO&FREQ STATPAP] [2016-12-11 13:44:30] [937b9e6718912fc8986df66e31b6c342]
- RMP       [Structural Time Series Models] [structural time s...] [2016-12-17 17:08:21] [863feeaf19a0ddfce7bd9c25059c4d8a] [Current]
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Dataseries X:
4790.92
4795.33
4822.62
4797.52
4822.17
4843.08
4850.79
4827.02
4796.65
4854.96
4870.81
4891.06
4881.38
4921.43
4956.21
4962.81
4949.38
4977.99
4992.73
5009.02
4990.98
5014.96
5022.23
5028.83
4894.36
4918.13
4936.4
4899.87
4862.89
4882.69
4895.46
4883.8
4855.4
4874.33
4880.94
4861.79
4851.44
4840.22
4842.42
4827.02
4749.77
4866.63
4734.37
4726.44
4753.51
4867.29
4793.35
4822.4
4865.09
4987.67
4900.96
4904.71
4889.52
5015.63
4938.81
4924.73
4871.48
4998.24
4891.06
4876.54
4824.15




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=300890&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=300890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300890&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
14790.924790.92000
24795.334794.681262109160.2051677674528050.4665112479426420.0805073677339686
34822.624815.05221426640.802474555715215.684207361698450.648655303887345
44797.524803.177174202940.660898117081259-4.34712093379176-0.42878207652763
54822.174815.877028936620.7446467521470975.040897314737130.407739296738925
64843.084836.278376254510.8781140583530664.757685469691480.665521848709992
74850.794847.86647129140.9529698206492341.810312116501480.362550333104772
84827.024832.925765677920.841226003024407-4.25392667508894-0.538003112879819
94796.654804.883950722490.639204219828133-5.23211751054616-0.977684199747048
104854.964839.198326800370.87304184941755312.2617300099481.13988660520842
114870.814864.282344880891.039963926608124.01131119576770.819520102328013
124891.064885.08961531391.175308530806143.915862575517060.669098488192715
134881.384890.473652818660.990962445407661-9.536946565710150.165509072212042
144921.434916.904597934121.426703075900212.352803050223280.780330403595603
154956.214939.983214481071.8407846161800214.30110148052250.69710193928114
164962.814961.317740145012.03992397522259-0.3725469263891150.656060720171442
174949.384954.005796388061.98985805690149-3.71925109423518-0.316454368847767
184977.994968.245079008232.040822120279218.556152891579230.41447081289975
194992.734982.199657566382.090834713801189.374524707956680.40300010694434
205009.024999.764126990162.158584949643767.755177453766240.523344704814751
214990.985002.353667233722.16053664869454-11.41545751855990.0145760673038113
225014.965005.401622978612.164698123546559.472319419351010.0300214464997771
235022.235016.383647562782.202078560084734.990958624573350.298275308370509
245028.835024.30686487192.20164043531253.967507120923340.193435350119437
254894.364957.473345139333.22230831568781-56.2598509954394-2.45325935887009
264918.134930.336832943872.99257104780975-9.42916980518243-0.990515608937646
274936.44925.109180272062.8816374579101812.0273122167307-0.267460119110835
284899.874905.653981459582.66554011769536-3.69804988813303-0.748694784434498
294862.894879.961885534552.50552583101031-14.380526745086-0.95868527509191
304882.694876.318697084712.481802597372776.95653676460919-0.208026460586045
314895.464885.10602463582.503904379991789.753742074187570.213287638143519
324883.84879.938344218892.475792690161444.59170086172915-0.259456121292589
334855.44872.038855633762.43524461590007-15.6517018935642-0.35092092343981
344874.334869.932255998562.417625533499774.82994613387297-0.153639074611782
354880.944875.083561114722.424785183632275.596193546210770.092415907714829
364861.794852.062306725742.46059915935512.1540966551948-0.861526187158598
374851.444880.750143862142.29582219253703-31.84309525380450.904400523572427
384840.224859.296200674842.19026503982826-16.870717827596-0.788560757322384
394842.424834.39140268421.9213540547431310.4871034900013-0.890347562958625
404827.024825.993332073341.831638790380681.98319886538816-0.34522692906043
414749.774784.126271699241.57748167899492-30.2444554574096-1.47549432287252
424866.634833.64878489971.7682584025455428.45057988155221.62178397816992
434734.374763.070903472941.5260873043829-21.8596227373662-2.4473136101725
444726.444730.497157473191.41170610741655-0.832849642015832-1.15343765840363
454753.514754.04292207481.48850339026449-2.625606657563960.748710821091524
464867.294828.180674853461.7166729892266632.23974524119482.45700574216764
474793.354803.089577382931.67276411013476-7.20408894470092-0.905977807932177
484822.44811.685482505261.6641493747801210.05848715232950.234448383834095
494865.094863.552227517061.52776160629689-3.245245327928581.71091829152047
504987.674956.606783989651.8316292956334122.53323680465553.05740885303423
514900.964916.395386282951.50999165725608-11.5857184782527-1.39132829797654
524904.714900.710584879291.378486539013195.59053023825407-0.575038324280155
534889.524920.00467314561.48156929542521-32.16297494786090.604235421706406
545015.634951.381452625271.6050812648428361.43400535102511.01091285271152
554938.814953.615331135911.60719475546416-14.86460690183050.0212719310163363
564924.734941.253394623871.56289864057774-15.2062808248324-0.472576079084563
574871.484908.076625725421.45618184524394-33.3211047269918-1.17513821757552
584998.244939.342906805941.531637912485856.08633236747531.00793487481168
594891.064916.172463784431.50378619307019-22.783015610038-0.834733590120257
604876.544893.831366732251.52210198053299-15.0391486086469-0.807102219456249
614824.154863.825010691351.55259441733513-36.6926381175151-1.06882022232229

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 4790.92 & 4790.92 & 0 & 0 & 0 \tabularnewline
2 & 4795.33 & 4794.68126210916 & 0.205167767452805 & 0.466511247942642 & 0.0805073677339686 \tabularnewline
3 & 4822.62 & 4815.0522142664 & 0.80247455571521 & 5.68420736169845 & 0.648655303887345 \tabularnewline
4 & 4797.52 & 4803.17717420294 & 0.660898117081259 & -4.34712093379176 & -0.42878207652763 \tabularnewline
5 & 4822.17 & 4815.87702893662 & 0.744646752147097 & 5.04089731473713 & 0.407739296738925 \tabularnewline
6 & 4843.08 & 4836.27837625451 & 0.878114058353066 & 4.75768546969148 & 0.665521848709992 \tabularnewline
7 & 4850.79 & 4847.8664712914 & 0.952969820649234 & 1.81031211650148 & 0.362550333104772 \tabularnewline
8 & 4827.02 & 4832.92576567792 & 0.841226003024407 & -4.25392667508894 & -0.538003112879819 \tabularnewline
9 & 4796.65 & 4804.88395072249 & 0.639204219828133 & -5.23211751054616 & -0.977684199747048 \tabularnewline
10 & 4854.96 & 4839.19832680037 & 0.873041849417553 & 12.261730009948 & 1.13988660520842 \tabularnewline
11 & 4870.81 & 4864.28234488089 & 1.03996392660812 & 4.0113111957677 & 0.819520102328013 \tabularnewline
12 & 4891.06 & 4885.0896153139 & 1.17530853080614 & 3.91586257551706 & 0.669098488192715 \tabularnewline
13 & 4881.38 & 4890.47365281866 & 0.990962445407661 & -9.53694656571015 & 0.165509072212042 \tabularnewline
14 & 4921.43 & 4916.90459793412 & 1.42670307590021 & 2.35280305022328 & 0.780330403595603 \tabularnewline
15 & 4956.21 & 4939.98321448107 & 1.84078461618002 & 14.3011014805225 & 0.69710193928114 \tabularnewline
16 & 4962.81 & 4961.31774014501 & 2.03992397522259 & -0.372546926389115 & 0.656060720171442 \tabularnewline
17 & 4949.38 & 4954.00579638806 & 1.98985805690149 & -3.71925109423518 & -0.316454368847767 \tabularnewline
18 & 4977.99 & 4968.24507900823 & 2.04082212027921 & 8.55615289157923 & 0.41447081289975 \tabularnewline
19 & 4992.73 & 4982.19965756638 & 2.09083471380118 & 9.37452470795668 & 0.40300010694434 \tabularnewline
20 & 5009.02 & 4999.76412699016 & 2.15858494964376 & 7.75517745376624 & 0.523344704814751 \tabularnewline
21 & 4990.98 & 5002.35366723372 & 2.16053664869454 & -11.4154575185599 & 0.0145760673038113 \tabularnewline
22 & 5014.96 & 5005.40162297861 & 2.16469812354655 & 9.47231941935101 & 0.0300214464997771 \tabularnewline
23 & 5022.23 & 5016.38364756278 & 2.20207856008473 & 4.99095862457335 & 0.298275308370509 \tabularnewline
24 & 5028.83 & 5024.3068648719 & 2.2016404353125 & 3.96750712092334 & 0.193435350119437 \tabularnewline
25 & 4894.36 & 4957.47334513933 & 3.22230831568781 & -56.2598509954394 & -2.45325935887009 \tabularnewline
26 & 4918.13 & 4930.33683294387 & 2.99257104780975 & -9.42916980518243 & -0.990515608937646 \tabularnewline
27 & 4936.4 & 4925.10918027206 & 2.88163745791018 & 12.0273122167307 & -0.267460119110835 \tabularnewline
28 & 4899.87 & 4905.65398145958 & 2.66554011769536 & -3.69804988813303 & -0.748694784434498 \tabularnewline
29 & 4862.89 & 4879.96188553455 & 2.50552583101031 & -14.380526745086 & -0.95868527509191 \tabularnewline
30 & 4882.69 & 4876.31869708471 & 2.48180259737277 & 6.95653676460919 & -0.208026460586045 \tabularnewline
31 & 4895.46 & 4885.1060246358 & 2.50390437999178 & 9.75374207418757 & 0.213287638143519 \tabularnewline
32 & 4883.8 & 4879.93834421889 & 2.47579269016144 & 4.59170086172915 & -0.259456121292589 \tabularnewline
33 & 4855.4 & 4872.03885563376 & 2.43524461590007 & -15.6517018935642 & -0.35092092343981 \tabularnewline
34 & 4874.33 & 4869.93225599856 & 2.41762553349977 & 4.82994613387297 & -0.153639074611782 \tabularnewline
35 & 4880.94 & 4875.08356111472 & 2.42478518363227 & 5.59619354621077 & 0.092415907714829 \tabularnewline
36 & 4861.79 & 4852.06230672574 & 2.460599159355 & 12.1540966551948 & -0.861526187158598 \tabularnewline
37 & 4851.44 & 4880.75014386214 & 2.29582219253703 & -31.8430952538045 & 0.904400523572427 \tabularnewline
38 & 4840.22 & 4859.29620067484 & 2.19026503982826 & -16.870717827596 & -0.788560757322384 \tabularnewline
39 & 4842.42 & 4834.3914026842 & 1.92135405474313 & 10.4871034900013 & -0.890347562958625 \tabularnewline
40 & 4827.02 & 4825.99333207334 & 1.83163879038068 & 1.98319886538816 & -0.34522692906043 \tabularnewline
41 & 4749.77 & 4784.12627169924 & 1.57748167899492 & -30.2444554574096 & -1.47549432287252 \tabularnewline
42 & 4866.63 & 4833.6487848997 & 1.76825840254554 & 28.4505798815522 & 1.62178397816992 \tabularnewline
43 & 4734.37 & 4763.07090347294 & 1.5260873043829 & -21.8596227373662 & -2.4473136101725 \tabularnewline
44 & 4726.44 & 4730.49715747319 & 1.41170610741655 & -0.832849642015832 & -1.15343765840363 \tabularnewline
45 & 4753.51 & 4754.0429220748 & 1.48850339026449 & -2.62560665756396 & 0.748710821091524 \tabularnewline
46 & 4867.29 & 4828.18067485346 & 1.71667298922666 & 32.2397452411948 & 2.45700574216764 \tabularnewline
47 & 4793.35 & 4803.08957738293 & 1.67276411013476 & -7.20408894470092 & -0.905977807932177 \tabularnewline
48 & 4822.4 & 4811.68548250526 & 1.66414937478012 & 10.0584871523295 & 0.234448383834095 \tabularnewline
49 & 4865.09 & 4863.55222751706 & 1.52776160629689 & -3.24524532792858 & 1.71091829152047 \tabularnewline
50 & 4987.67 & 4956.60678398965 & 1.83162929563341 & 22.5332368046555 & 3.05740885303423 \tabularnewline
51 & 4900.96 & 4916.39538628295 & 1.50999165725608 & -11.5857184782527 & -1.39132829797654 \tabularnewline
52 & 4904.71 & 4900.71058487929 & 1.37848653901319 & 5.59053023825407 & -0.575038324280155 \tabularnewline
53 & 4889.52 & 4920.0046731456 & 1.48156929542521 & -32.1629749478609 & 0.604235421706406 \tabularnewline
54 & 5015.63 & 4951.38145262527 & 1.60508126484283 & 61.4340053510251 & 1.01091285271152 \tabularnewline
55 & 4938.81 & 4953.61533113591 & 1.60719475546416 & -14.8646069018305 & 0.0212719310163363 \tabularnewline
56 & 4924.73 & 4941.25339462387 & 1.56289864057774 & -15.2062808248324 & -0.472576079084563 \tabularnewline
57 & 4871.48 & 4908.07662572542 & 1.45618184524394 & -33.3211047269918 & -1.17513821757552 \tabularnewline
58 & 4998.24 & 4939.34290680594 & 1.5316379124858 & 56.0863323674753 & 1.00793487481168 \tabularnewline
59 & 4891.06 & 4916.17246378443 & 1.50378619307019 & -22.783015610038 & -0.834733590120257 \tabularnewline
60 & 4876.54 & 4893.83136673225 & 1.52210198053299 & -15.0391486086469 & -0.807102219456249 \tabularnewline
61 & 4824.15 & 4863.82501069135 & 1.55259441733513 & -36.6926381175151 & -1.06882022232229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300890&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]4790.92[/C][C]4790.92[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]4795.33[/C][C]4794.68126210916[/C][C]0.205167767452805[/C][C]0.466511247942642[/C][C]0.0805073677339686[/C][/ROW]
[ROW][C]3[/C][C]4822.62[/C][C]4815.0522142664[/C][C]0.80247455571521[/C][C]5.68420736169845[/C][C]0.648655303887345[/C][/ROW]
[ROW][C]4[/C][C]4797.52[/C][C]4803.17717420294[/C][C]0.660898117081259[/C][C]-4.34712093379176[/C][C]-0.42878207652763[/C][/ROW]
[ROW][C]5[/C][C]4822.17[/C][C]4815.87702893662[/C][C]0.744646752147097[/C][C]5.04089731473713[/C][C]0.407739296738925[/C][/ROW]
[ROW][C]6[/C][C]4843.08[/C][C]4836.27837625451[/C][C]0.878114058353066[/C][C]4.75768546969148[/C][C]0.665521848709992[/C][/ROW]
[ROW][C]7[/C][C]4850.79[/C][C]4847.8664712914[/C][C]0.952969820649234[/C][C]1.81031211650148[/C][C]0.362550333104772[/C][/ROW]
[ROW][C]8[/C][C]4827.02[/C][C]4832.92576567792[/C][C]0.841226003024407[/C][C]-4.25392667508894[/C][C]-0.538003112879819[/C][/ROW]
[ROW][C]9[/C][C]4796.65[/C][C]4804.88395072249[/C][C]0.639204219828133[/C][C]-5.23211751054616[/C][C]-0.977684199747048[/C][/ROW]
[ROW][C]10[/C][C]4854.96[/C][C]4839.19832680037[/C][C]0.873041849417553[/C][C]12.261730009948[/C][C]1.13988660520842[/C][/ROW]
[ROW][C]11[/C][C]4870.81[/C][C]4864.28234488089[/C][C]1.03996392660812[/C][C]4.0113111957677[/C][C]0.819520102328013[/C][/ROW]
[ROW][C]12[/C][C]4891.06[/C][C]4885.0896153139[/C][C]1.17530853080614[/C][C]3.91586257551706[/C][C]0.669098488192715[/C][/ROW]
[ROW][C]13[/C][C]4881.38[/C][C]4890.47365281866[/C][C]0.990962445407661[/C][C]-9.53694656571015[/C][C]0.165509072212042[/C][/ROW]
[ROW][C]14[/C][C]4921.43[/C][C]4916.90459793412[/C][C]1.42670307590021[/C][C]2.35280305022328[/C][C]0.780330403595603[/C][/ROW]
[ROW][C]15[/C][C]4956.21[/C][C]4939.98321448107[/C][C]1.84078461618002[/C][C]14.3011014805225[/C][C]0.69710193928114[/C][/ROW]
[ROW][C]16[/C][C]4962.81[/C][C]4961.31774014501[/C][C]2.03992397522259[/C][C]-0.372546926389115[/C][C]0.656060720171442[/C][/ROW]
[ROW][C]17[/C][C]4949.38[/C][C]4954.00579638806[/C][C]1.98985805690149[/C][C]-3.71925109423518[/C][C]-0.316454368847767[/C][/ROW]
[ROW][C]18[/C][C]4977.99[/C][C]4968.24507900823[/C][C]2.04082212027921[/C][C]8.55615289157923[/C][C]0.41447081289975[/C][/ROW]
[ROW][C]19[/C][C]4992.73[/C][C]4982.19965756638[/C][C]2.09083471380118[/C][C]9.37452470795668[/C][C]0.40300010694434[/C][/ROW]
[ROW][C]20[/C][C]5009.02[/C][C]4999.76412699016[/C][C]2.15858494964376[/C][C]7.75517745376624[/C][C]0.523344704814751[/C][/ROW]
[ROW][C]21[/C][C]4990.98[/C][C]5002.35366723372[/C][C]2.16053664869454[/C][C]-11.4154575185599[/C][C]0.0145760673038113[/C][/ROW]
[ROW][C]22[/C][C]5014.96[/C][C]5005.40162297861[/C][C]2.16469812354655[/C][C]9.47231941935101[/C][C]0.0300214464997771[/C][/ROW]
[ROW][C]23[/C][C]5022.23[/C][C]5016.38364756278[/C][C]2.20207856008473[/C][C]4.99095862457335[/C][C]0.298275308370509[/C][/ROW]
[ROW][C]24[/C][C]5028.83[/C][C]5024.3068648719[/C][C]2.2016404353125[/C][C]3.96750712092334[/C][C]0.193435350119437[/C][/ROW]
[ROW][C]25[/C][C]4894.36[/C][C]4957.47334513933[/C][C]3.22230831568781[/C][C]-56.2598509954394[/C][C]-2.45325935887009[/C][/ROW]
[ROW][C]26[/C][C]4918.13[/C][C]4930.33683294387[/C][C]2.99257104780975[/C][C]-9.42916980518243[/C][C]-0.990515608937646[/C][/ROW]
[ROW][C]27[/C][C]4936.4[/C][C]4925.10918027206[/C][C]2.88163745791018[/C][C]12.0273122167307[/C][C]-0.267460119110835[/C][/ROW]
[ROW][C]28[/C][C]4899.87[/C][C]4905.65398145958[/C][C]2.66554011769536[/C][C]-3.69804988813303[/C][C]-0.748694784434498[/C][/ROW]
[ROW][C]29[/C][C]4862.89[/C][C]4879.96188553455[/C][C]2.50552583101031[/C][C]-14.380526745086[/C][C]-0.95868527509191[/C][/ROW]
[ROW][C]30[/C][C]4882.69[/C][C]4876.31869708471[/C][C]2.48180259737277[/C][C]6.95653676460919[/C][C]-0.208026460586045[/C][/ROW]
[ROW][C]31[/C][C]4895.46[/C][C]4885.1060246358[/C][C]2.50390437999178[/C][C]9.75374207418757[/C][C]0.213287638143519[/C][/ROW]
[ROW][C]32[/C][C]4883.8[/C][C]4879.93834421889[/C][C]2.47579269016144[/C][C]4.59170086172915[/C][C]-0.259456121292589[/C][/ROW]
[ROW][C]33[/C][C]4855.4[/C][C]4872.03885563376[/C][C]2.43524461590007[/C][C]-15.6517018935642[/C][C]-0.35092092343981[/C][/ROW]
[ROW][C]34[/C][C]4874.33[/C][C]4869.93225599856[/C][C]2.41762553349977[/C][C]4.82994613387297[/C][C]-0.153639074611782[/C][/ROW]
[ROW][C]35[/C][C]4880.94[/C][C]4875.08356111472[/C][C]2.42478518363227[/C][C]5.59619354621077[/C][C]0.092415907714829[/C][/ROW]
[ROW][C]36[/C][C]4861.79[/C][C]4852.06230672574[/C][C]2.460599159355[/C][C]12.1540966551948[/C][C]-0.861526187158598[/C][/ROW]
[ROW][C]37[/C][C]4851.44[/C][C]4880.75014386214[/C][C]2.29582219253703[/C][C]-31.8430952538045[/C][C]0.904400523572427[/C][/ROW]
[ROW][C]38[/C][C]4840.22[/C][C]4859.29620067484[/C][C]2.19026503982826[/C][C]-16.870717827596[/C][C]-0.788560757322384[/C][/ROW]
[ROW][C]39[/C][C]4842.42[/C][C]4834.3914026842[/C][C]1.92135405474313[/C][C]10.4871034900013[/C][C]-0.890347562958625[/C][/ROW]
[ROW][C]40[/C][C]4827.02[/C][C]4825.99333207334[/C][C]1.83163879038068[/C][C]1.98319886538816[/C][C]-0.34522692906043[/C][/ROW]
[ROW][C]41[/C][C]4749.77[/C][C]4784.12627169924[/C][C]1.57748167899492[/C][C]-30.2444554574096[/C][C]-1.47549432287252[/C][/ROW]
[ROW][C]42[/C][C]4866.63[/C][C]4833.6487848997[/C][C]1.76825840254554[/C][C]28.4505798815522[/C][C]1.62178397816992[/C][/ROW]
[ROW][C]43[/C][C]4734.37[/C][C]4763.07090347294[/C][C]1.5260873043829[/C][C]-21.8596227373662[/C][C]-2.4473136101725[/C][/ROW]
[ROW][C]44[/C][C]4726.44[/C][C]4730.49715747319[/C][C]1.41170610741655[/C][C]-0.832849642015832[/C][C]-1.15343765840363[/C][/ROW]
[ROW][C]45[/C][C]4753.51[/C][C]4754.0429220748[/C][C]1.48850339026449[/C][C]-2.62560665756396[/C][C]0.748710821091524[/C][/ROW]
[ROW][C]46[/C][C]4867.29[/C][C]4828.18067485346[/C][C]1.71667298922666[/C][C]32.2397452411948[/C][C]2.45700574216764[/C][/ROW]
[ROW][C]47[/C][C]4793.35[/C][C]4803.08957738293[/C][C]1.67276411013476[/C][C]-7.20408894470092[/C][C]-0.905977807932177[/C][/ROW]
[ROW][C]48[/C][C]4822.4[/C][C]4811.68548250526[/C][C]1.66414937478012[/C][C]10.0584871523295[/C][C]0.234448383834095[/C][/ROW]
[ROW][C]49[/C][C]4865.09[/C][C]4863.55222751706[/C][C]1.52776160629689[/C][C]-3.24524532792858[/C][C]1.71091829152047[/C][/ROW]
[ROW][C]50[/C][C]4987.67[/C][C]4956.60678398965[/C][C]1.83162929563341[/C][C]22.5332368046555[/C][C]3.05740885303423[/C][/ROW]
[ROW][C]51[/C][C]4900.96[/C][C]4916.39538628295[/C][C]1.50999165725608[/C][C]-11.5857184782527[/C][C]-1.39132829797654[/C][/ROW]
[ROW][C]52[/C][C]4904.71[/C][C]4900.71058487929[/C][C]1.37848653901319[/C][C]5.59053023825407[/C][C]-0.575038324280155[/C][/ROW]
[ROW][C]53[/C][C]4889.52[/C][C]4920.0046731456[/C][C]1.48156929542521[/C][C]-32.1629749478609[/C][C]0.604235421706406[/C][/ROW]
[ROW][C]54[/C][C]5015.63[/C][C]4951.38145262527[/C][C]1.60508126484283[/C][C]61.4340053510251[/C][C]1.01091285271152[/C][/ROW]
[ROW][C]55[/C][C]4938.81[/C][C]4953.61533113591[/C][C]1.60719475546416[/C][C]-14.8646069018305[/C][C]0.0212719310163363[/C][/ROW]
[ROW][C]56[/C][C]4924.73[/C][C]4941.25339462387[/C][C]1.56289864057774[/C][C]-15.2062808248324[/C][C]-0.472576079084563[/C][/ROW]
[ROW][C]57[/C][C]4871.48[/C][C]4908.07662572542[/C][C]1.45618184524394[/C][C]-33.3211047269918[/C][C]-1.17513821757552[/C][/ROW]
[ROW][C]58[/C][C]4998.24[/C][C]4939.34290680594[/C][C]1.5316379124858[/C][C]56.0863323674753[/C][C]1.00793487481168[/C][/ROW]
[ROW][C]59[/C][C]4891.06[/C][C]4916.17246378443[/C][C]1.50378619307019[/C][C]-22.783015610038[/C][C]-0.834733590120257[/C][/ROW]
[ROW][C]60[/C][C]4876.54[/C][C]4893.83136673225[/C][C]1.52210198053299[/C][C]-15.0391486086469[/C][C]-0.807102219456249[/C][/ROW]
[ROW][C]61[/C][C]4824.15[/C][C]4863.82501069135[/C][C]1.55259441733513[/C][C]-36.6926381175151[/C][C]-1.06882022232229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300890&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
14790.924790.92000
24795.334794.681262109160.2051677674528050.4665112479426420.0805073677339686
34822.624815.05221426640.802474555715215.684207361698450.648655303887345
44797.524803.177174202940.660898117081259-4.34712093379176-0.42878207652763
54822.174815.877028936620.7446467521470975.040897314737130.407739296738925
64843.084836.278376254510.8781140583530664.757685469691480.665521848709992
74850.794847.86647129140.9529698206492341.810312116501480.362550333104772
84827.024832.925765677920.841226003024407-4.25392667508894-0.538003112879819
94796.654804.883950722490.639204219828133-5.23211751054616-0.977684199747048
104854.964839.198326800370.87304184941755312.2617300099481.13988660520842
114870.814864.282344880891.039963926608124.01131119576770.819520102328013
124891.064885.08961531391.175308530806143.915862575517060.669098488192715
134881.384890.473652818660.990962445407661-9.536946565710150.165509072212042
144921.434916.904597934121.426703075900212.352803050223280.780330403595603
154956.214939.983214481071.8407846161800214.30110148052250.69710193928114
164962.814961.317740145012.03992397522259-0.3725469263891150.656060720171442
174949.384954.005796388061.98985805690149-3.71925109423518-0.316454368847767
184977.994968.245079008232.040822120279218.556152891579230.41447081289975
194992.734982.199657566382.090834713801189.374524707956680.40300010694434
205009.024999.764126990162.158584949643767.755177453766240.523344704814751
214990.985002.353667233722.16053664869454-11.41545751855990.0145760673038113
225014.965005.401622978612.164698123546559.472319419351010.0300214464997771
235022.235016.383647562782.202078560084734.990958624573350.298275308370509
245028.835024.30686487192.20164043531253.967507120923340.193435350119437
254894.364957.473345139333.22230831568781-56.2598509954394-2.45325935887009
264918.134930.336832943872.99257104780975-9.42916980518243-0.990515608937646
274936.44925.109180272062.8816374579101812.0273122167307-0.267460119110835
284899.874905.653981459582.66554011769536-3.69804988813303-0.748694784434498
294862.894879.961885534552.50552583101031-14.380526745086-0.95868527509191
304882.694876.318697084712.481802597372776.95653676460919-0.208026460586045
314895.464885.10602463582.503904379991789.753742074187570.213287638143519
324883.84879.938344218892.475792690161444.59170086172915-0.259456121292589
334855.44872.038855633762.43524461590007-15.6517018935642-0.35092092343981
344874.334869.932255998562.417625533499774.82994613387297-0.153639074611782
354880.944875.083561114722.424785183632275.596193546210770.092415907714829
364861.794852.062306725742.46059915935512.1540966551948-0.861526187158598
374851.444880.750143862142.29582219253703-31.84309525380450.904400523572427
384840.224859.296200674842.19026503982826-16.870717827596-0.788560757322384
394842.424834.39140268421.9213540547431310.4871034900013-0.890347562958625
404827.024825.993332073341.831638790380681.98319886538816-0.34522692906043
414749.774784.126271699241.57748167899492-30.2444554574096-1.47549432287252
424866.634833.64878489971.7682584025455428.45057988155221.62178397816992
434734.374763.070903472941.5260873043829-21.8596227373662-2.4473136101725
444726.444730.497157473191.41170610741655-0.832849642015832-1.15343765840363
454753.514754.04292207481.48850339026449-2.625606657563960.748710821091524
464867.294828.180674853461.7166729892266632.23974524119482.45700574216764
474793.354803.089577382931.67276411013476-7.20408894470092-0.905977807932177
484822.44811.685482505261.6641493747801210.05848715232950.234448383834095
494865.094863.552227517061.52776160629689-3.245245327928581.71091829152047
504987.674956.606783989651.8316292956334122.53323680465553.05740885303423
514900.964916.395386282951.50999165725608-11.5857184782527-1.39132829797654
524904.714900.710584879291.378486539013195.59053023825407-0.575038324280155
534889.524920.00467314561.48156929542521-32.16297494786090.604235421706406
545015.634951.381452625271.6050812648428361.43400535102511.01091285271152
554938.814953.615331135911.60719475546416-14.86460690183050.0212719310163363
564924.734941.253394623871.56289864057774-15.2062808248324-0.472576079084563
574871.484908.076625725421.45618184524394-33.3211047269918-1.17513821757552
584998.244939.342906805941.531637912485856.08633236747531.00793487481168
594891.064916.172463784431.50378619307019-22.783015610038-0.834733590120257
604876.544893.831366732251.52210198053299-15.0391486086469-0.807102219456249
614824.154863.825010691351.55259441733513-36.6926381175151-1.06882022232229







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14900.797000692094858.2320685912842.5649321008049
24852.111046094484859.04503555291-6.93398945843224
34857.513563810734859.85800251454-2.34443870381376
44817.293951829224860.67096947617-43.3770176469583
54921.644746716734861.483936437860.1608102789246
64848.60076265754862.29690339943-13.6961407419327
74849.445260807594863.10987036106-13.6646095534718
84817.299927635644863.92283732269-46.6229096870526
94929.76998341354864.7358042843265.0341791291732
104855.540805906364865.54877124595-10.0079653395935
114866.419203060894866.361738207580.0574648533103606
124836.004389938264867.17470516921-31.1703152309581

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4900.79700069209 & 4858.23206859128 & 42.5649321008049 \tabularnewline
2 & 4852.11104609448 & 4859.04503555291 & -6.93398945843224 \tabularnewline
3 & 4857.51356381073 & 4859.85800251454 & -2.34443870381376 \tabularnewline
4 & 4817.29395182922 & 4860.67096947617 & -43.3770176469583 \tabularnewline
5 & 4921.64474671673 & 4861.4839364378 & 60.1608102789246 \tabularnewline
6 & 4848.6007626575 & 4862.29690339943 & -13.6961407419327 \tabularnewline
7 & 4849.44526080759 & 4863.10987036106 & -13.6646095534718 \tabularnewline
8 & 4817.29992763564 & 4863.92283732269 & -46.6229096870526 \tabularnewline
9 & 4929.7699834135 & 4864.73580428432 & 65.0341791291732 \tabularnewline
10 & 4855.54080590636 & 4865.54877124595 & -10.0079653395935 \tabularnewline
11 & 4866.41920306089 & 4866.36173820758 & 0.0574648533103606 \tabularnewline
12 & 4836.00438993826 & 4867.17470516921 & -31.1703152309581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300890&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]4900.79700069209[/C][C]4858.23206859128[/C][C]42.5649321008049[/C][/ROW]
[ROW][C]2[/C][C]4852.11104609448[/C][C]4859.04503555291[/C][C]-6.93398945843224[/C][/ROW]
[ROW][C]3[/C][C]4857.51356381073[/C][C]4859.85800251454[/C][C]-2.34443870381376[/C][/ROW]
[ROW][C]4[/C][C]4817.29395182922[/C][C]4860.67096947617[/C][C]-43.3770176469583[/C][/ROW]
[ROW][C]5[/C][C]4921.64474671673[/C][C]4861.4839364378[/C][C]60.1608102789246[/C][/ROW]
[ROW][C]6[/C][C]4848.6007626575[/C][C]4862.29690339943[/C][C]-13.6961407419327[/C][/ROW]
[ROW][C]7[/C][C]4849.44526080759[/C][C]4863.10987036106[/C][C]-13.6646095534718[/C][/ROW]
[ROW][C]8[/C][C]4817.29992763564[/C][C]4863.92283732269[/C][C]-46.6229096870526[/C][/ROW]
[ROW][C]9[/C][C]4929.7699834135[/C][C]4864.73580428432[/C][C]65.0341791291732[/C][/ROW]
[ROW][C]10[/C][C]4855.54080590636[/C][C]4865.54877124595[/C][C]-10.0079653395935[/C][/ROW]
[ROW][C]11[/C][C]4866.41920306089[/C][C]4866.36173820758[/C][C]0.0574648533103606[/C][/ROW]
[ROW][C]12[/C][C]4836.00438993826[/C][C]4867.17470516921[/C][C]-31.1703152309581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300890&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300890&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
14900.797000692094858.2320685912842.5649321008049
24852.111046094484859.04503555291-6.93398945843224
34857.513563810734859.85800251454-2.34443870381376
44817.293951829224860.67096947617-43.3770176469583
54921.644746716734861.483936437860.1608102789246
64848.60076265754862.29690339943-13.6961407419327
74849.445260807594863.10987036106-13.6646095534718
84817.299927635644863.92283732269-46.6229096870526
94929.76998341354864.7358042843265.0341791291732
104855.540805906364865.54877124595-10.0079653395935
114866.419203060894866.361738207580.0574648533103606
124836.004389938264867.17470516921-31.1703152309581



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