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*The author of this computation has been verified*

R Software Module

rwasp_structuraltimeseries.wasp

Title produced by software

Structural Time Series Models

Date of computation

Thu, 22 Dec 2011 13:01:39 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324577071psag60oibrd33lo.htm/, Retrieved Fri, 03 May 2024 15:02:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159795, Retrieved Fri, 03 May 2024 15:02:46 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

101

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D    [(Partial) Autocorrelation Function] [] [2011-12-22 15:18:49] [5a05da414fd67612c3b80d44effe0727]
- R         [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [5a05da414fd67612c3b80d44effe0727]
-             [(Partial) Autocorrelation Function] [] [2011-12-22 15:29:46] [5a05da414fd67612c3b80d44effe0727]
- RM            [Exponential Smoothing] [] [2011-12-22 16:47:54] [5a05da414fd67612c3b80d44effe0727]
- RM              [Classical Decomposition] [] [2011-12-22 16:54:59] [5a05da414fd67612c3b80d44effe0727]
- RM                  [Structural Time Series Models] [] [2011-12-22 18:01:39] [95610e892c4b5c84ff80f4c898567a9d] [Current]

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Dataseries X:

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Histogram

Boxplots

7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159795&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159795&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 Output	view raw output of R engine
Computing time	3 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	7.9	7.9	0	0	0
2	7.9	7.9	0	0	0
3	8	7.99098783723296	0.00102456581915253	0.00901216276704411	0.307411232507945
4	8	8.00082759696501	0.00105933907219604	-0.000827596965005893	0.0298708355948673
5	7.9	7.90764701758227	0.000652163499576684	-0.00764701758227057	-0.319272558799416
6	8	7.98929676606908	0.00101959347633178	0.0107032339309204	0.274402539041742
7	7.7	7.72518400885614	-0.00018143913342023	-0.0251840088561354	-0.898208049870083
8	7.2	7.23627469316286	-0.00238300924049594	-0.036274693162857	-1.65568569308891
9	7.5	7.46706253501293	-0.00133756247158843	0.0329374649870718	0.789916448250384
10	7.3	7.32117639329977	-0.00198277407385268	-0.0211763932997667	-0.489685076959809
11	7	7.02420521212762	-0.00329365055656567	-0.0242052121276239	-0.999319080135188
12	7	6.99677791701724	-0.00340042179308946	0.00322208298276472	-0.0817557612828028
13	7	6.97328486846187	-0.00258063329713146	0.0267151315381289	-0.080538100624212
14	7.2	7.18475563019096	0.0019760076690628	0.0152443698090423	0.632844436975831
15	7.3	7.28477584293738	0.0029241316634193	0.01522415706262	0.32888098629791
16	7.1	7.11971173058552	0.0024587038713824	-0.0197117305855178	-0.568830207378783
17	6.8	6.85054994913242	0.00187680021783967	-0.0505499491324166	-0.919370061882964
18	6.4	6.42390133410201	0.000838103283618726	-0.0239013341020127	-1.45032884003474
19	6.1	6.10703584477694	3.87532174752332e-05	-0.00703584477693785	-1.07524642529827
20	6.5	6.48693761036966	0.000993158234325194	0.0130623896303363	1.28562199919763
21	7.7	7.5275365781074	0.00359850872215919	0.172463421892597	3.51848304685733
22	7.9	7.88908926278563	0.00452423716222908	0.0109107372143703	1.21157249839315
23	7.5	7.57706795670162	0.00365329601323917	-0.077067956701622	-1.07170019023211
24	6.9	6.96326186956977	0.00353155874368284	-0.0632618695697681	-2.0878544588136
25	6.6	6.69667927781282	0.00793129141671023	-0.0966792778128158	-0.978537899251588
26	6.9	6.87196399505581	0.0098644311731182	0.0280360049441885	0.531197649452878
27	7.7	7.55597435614516	0.0156751926600236	0.144025643854838	2.25197934442126
28	8	7.94903605331415	0.0168492538131329	0.0509639466858521	1.27748431712848
29	8	8.00020038293075	0.0169081856122872	-0.000200382930747692	0.116133674751087
30	7.7	7.70701200203572	0.0163463886845023	-0.00701200203572311	-1.04929135564265
31	7.3	7.3607074937911	0.0156333403776823	-0.0607074937910997	-1.22706196956589
32	7.4	7.46334754287304	0.0158079498961154	-0.063347542873041	0.294394057152584
33	8.1	7.9020228001174	0.01667441936297	0.197977199882607	1.43086637572354
34	8.3	8.22029752053408	0.017337637753848	0.0797024794659232	1.02073554253251
35	8.1	8.12505128618713	0.0171132104859526	-0.0250512861871317	-0.381031555069578
36	7.9	7.95467220782447	0.0173472033307872	-0.0546722078244735	-0.634334133178222
37	7.9	8.03991145541141	0.0167624636448687	-0.139911455411409	0.237631564902217
38	8.3	8.33511839421914	0.0187528866350998	-0.035118394219143	0.909109062795593
39	8.6	8.49785557817271	0.0198298721647814	0.102144421827284	0.480400058091249
40	8.7	8.64479309532545	0.0202700404259387	0.0552069046745462	0.429997200801626
41	8.5	8.49261364601093	0.0199727124641275	0.00738635398907085	-0.583636004389723
42	8.3	8.2800553442429	0.0196130001945905	0.0199446557571058	-0.786789960220803
43	8	8.08670941168318	0.0192535492004775	-0.0867094116831757	-0.72049921344479
44	8	8.1063597603182	0.0192542588198317	-0.106359760318206	0.00134247308891664
45	8.8	8.56461057003087	0.0200859240919063	0.235389429969134	1.48539002367714
46	8.7	8.61348164712198	0.020143239537402	0.0865183528780179	0.097419355053658
47	8.5	8.5172721001643	0.0199838519838819	-0.0172721001643076	-0.393630507267621
48	8.1	8.21723421717573	0.0205141032244595	-0.117234217175728	-1.08357277712438
49	7.8	8.02813911530479	0.0215613071895101	-0.228139115304785	-0.722188482052962
50	7.6	7.70936082219973	0.0199039543927136	-0.109360822199732	-1.12613506289814
51	7.4	7.37121309080674	0.01760561843531	0.0287869091932622	-1.19518359079252
52	7.1	7.06833905892566	0.0164402211701429	0.0316609410743393	-1.08328935880633
53	6.9	6.88106913008516	0.0160624428003844	0.018930869914838	-0.689434269438328
54	6.7	6.6735481731755	0.0157395680862473	0.0264518268244968	-0.756516581354674
55	6.6	6.67781377075321	0.0157220893439141	-0.0778137707532073	-0.0388186371879963
56	6.5	6.67793920755814	0.0156961114447233	-0.177939207558144	-0.0527662840292818
57	7.1	6.85028577074093	0.0159785669257867	0.249714229259071	0.530051372399314
58	7.2	7.0754747220096	0.016351038049291	0.124525277990406	0.70799554788789
59	6.9	6.9207401985509	0.0161973389540574	-0.0207401985508993	-0.578625114936945
60	6.7	6.80805665689144	0.0164064926167986	-0.108056656891443	-0.436560242023417

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 7.9 & 7.9 & 0 & 0 & 0 \tabularnewline
2 & 7.9 & 7.9 & 0 & 0 & 0 \tabularnewline
3 & 8 & 7.99098783723296 & 0.00102456581915253 & 0.00901216276704411 & 0.307411232507945 \tabularnewline
4 & 8 & 8.00082759696501 & 0.00105933907219604 & -0.000827596965005893 & 0.0298708355948673 \tabularnewline
5 & 7.9 & 7.90764701758227 & 0.000652163499576684 & -0.00764701758227057 & -0.319272558799416 \tabularnewline
6 & 8 & 7.98929676606908 & 0.00101959347633178 & 0.0107032339309204 & 0.274402539041742 \tabularnewline
7 & 7.7 & 7.72518400885614 & -0.00018143913342023 & -0.0251840088561354 & -0.898208049870083 \tabularnewline
8 & 7.2 & 7.23627469316286 & -0.00238300924049594 & -0.036274693162857 & -1.65568569308891 \tabularnewline
9 & 7.5 & 7.46706253501293 & -0.00133756247158843 & 0.0329374649870718 & 0.789916448250384 \tabularnewline
10 & 7.3 & 7.32117639329977 & -0.00198277407385268 & -0.0211763932997667 & -0.489685076959809 \tabularnewline
11 & 7 & 7.02420521212762 & -0.00329365055656567 & -0.0242052121276239 & -0.999319080135188 \tabularnewline
12 & 7 & 6.99677791701724 & -0.00340042179308946 & 0.00322208298276472 & -0.0817557612828028 \tabularnewline
13 & 7 & 6.97328486846187 & -0.00258063329713146 & 0.0267151315381289 & -0.080538100624212 \tabularnewline
14 & 7.2 & 7.18475563019096 & 0.0019760076690628 & 0.0152443698090423 & 0.632844436975831 \tabularnewline
15 & 7.3 & 7.28477584293738 & 0.0029241316634193 & 0.01522415706262 & 0.32888098629791 \tabularnewline
16 & 7.1 & 7.11971173058552 & 0.0024587038713824 & -0.0197117305855178 & -0.568830207378783 \tabularnewline
17 & 6.8 & 6.85054994913242 & 0.00187680021783967 & -0.0505499491324166 & -0.919370061882964 \tabularnewline
18 & 6.4 & 6.42390133410201 & 0.000838103283618726 & -0.0239013341020127 & -1.45032884003474 \tabularnewline
19 & 6.1 & 6.10703584477694 & 3.87532174752332e-05 & -0.00703584477693785 & -1.07524642529827 \tabularnewline
20 & 6.5 & 6.48693761036966 & 0.000993158234325194 & 0.0130623896303363 & 1.28562199919763 \tabularnewline
21 & 7.7 & 7.5275365781074 & 0.00359850872215919 & 0.172463421892597 & 3.51848304685733 \tabularnewline
22 & 7.9 & 7.88908926278563 & 0.00452423716222908 & 0.0109107372143703 & 1.21157249839315 \tabularnewline
23 & 7.5 & 7.57706795670162 & 0.00365329601323917 & -0.077067956701622 & -1.07170019023211 \tabularnewline
24 & 6.9 & 6.96326186956977 & 0.00353155874368284 & -0.0632618695697681 & -2.0878544588136 \tabularnewline
25 & 6.6 & 6.69667927781282 & 0.00793129141671023 & -0.0966792778128158 & -0.978537899251588 \tabularnewline
26 & 6.9 & 6.87196399505581 & 0.0098644311731182 & 0.0280360049441885 & 0.531197649452878 \tabularnewline
27 & 7.7 & 7.55597435614516 & 0.0156751926600236 & 0.144025643854838 & 2.25197934442126 \tabularnewline
28 & 8 & 7.94903605331415 & 0.0168492538131329 & 0.0509639466858521 & 1.27748431712848 \tabularnewline
29 & 8 & 8.00020038293075 & 0.0169081856122872 & -0.000200382930747692 & 0.116133674751087 \tabularnewline
30 & 7.7 & 7.70701200203572 & 0.0163463886845023 & -0.00701200203572311 & -1.04929135564265 \tabularnewline
31 & 7.3 & 7.3607074937911 & 0.0156333403776823 & -0.0607074937910997 & -1.22706196956589 \tabularnewline
32 & 7.4 & 7.46334754287304 & 0.0158079498961154 & -0.063347542873041 & 0.294394057152584 \tabularnewline
33 & 8.1 & 7.9020228001174 & 0.01667441936297 & 0.197977199882607 & 1.43086637572354 \tabularnewline
34 & 8.3 & 8.22029752053408 & 0.017337637753848 & 0.0797024794659232 & 1.02073554253251 \tabularnewline
35 & 8.1 & 8.12505128618713 & 0.0171132104859526 & -0.0250512861871317 & -0.381031555069578 \tabularnewline
36 & 7.9 & 7.95467220782447 & 0.0173472033307872 & -0.0546722078244735 & -0.634334133178222 \tabularnewline
37 & 7.9 & 8.03991145541141 & 0.0167624636448687 & -0.139911455411409 & 0.237631564902217 \tabularnewline
38 & 8.3 & 8.33511839421914 & 0.0187528866350998 & -0.035118394219143 & 0.909109062795593 \tabularnewline
39 & 8.6 & 8.49785557817271 & 0.0198298721647814 & 0.102144421827284 & 0.480400058091249 \tabularnewline
40 & 8.7 & 8.64479309532545 & 0.0202700404259387 & 0.0552069046745462 & 0.429997200801626 \tabularnewline
41 & 8.5 & 8.49261364601093 & 0.0199727124641275 & 0.00738635398907085 & -0.583636004389723 \tabularnewline
42 & 8.3 & 8.2800553442429 & 0.0196130001945905 & 0.0199446557571058 & -0.786789960220803 \tabularnewline
43 & 8 & 8.08670941168318 & 0.0192535492004775 & -0.0867094116831757 & -0.72049921344479 \tabularnewline
44 & 8 & 8.1063597603182 & 0.0192542588198317 & -0.106359760318206 & 0.00134247308891664 \tabularnewline
45 & 8.8 & 8.56461057003087 & 0.0200859240919063 & 0.235389429969134 & 1.48539002367714 \tabularnewline
46 & 8.7 & 8.61348164712198 & 0.020143239537402 & 0.0865183528780179 & 0.097419355053658 \tabularnewline
47 & 8.5 & 8.5172721001643 & 0.0199838519838819 & -0.0172721001643076 & -0.393630507267621 \tabularnewline
48 & 8.1 & 8.21723421717573 & 0.0205141032244595 & -0.117234217175728 & -1.08357277712438 \tabularnewline
49 & 7.8 & 8.02813911530479 & 0.0215613071895101 & -0.228139115304785 & -0.722188482052962 \tabularnewline
50 & 7.6 & 7.70936082219973 & 0.0199039543927136 & -0.109360822199732 & -1.12613506289814 \tabularnewline
51 & 7.4 & 7.37121309080674 & 0.01760561843531 & 0.0287869091932622 & -1.19518359079252 \tabularnewline
52 & 7.1 & 7.06833905892566 & 0.0164402211701429 & 0.0316609410743393 & -1.08328935880633 \tabularnewline
53 & 6.9 & 6.88106913008516 & 0.0160624428003844 & 0.018930869914838 & -0.689434269438328 \tabularnewline
54 & 6.7 & 6.6735481731755 & 0.0157395680862473 & 0.0264518268244968 & -0.756516581354674 \tabularnewline
55 & 6.6 & 6.67781377075321 & 0.0157220893439141 & -0.0778137707532073 & -0.0388186371879963 \tabularnewline
56 & 6.5 & 6.67793920755814 & 0.0156961114447233 & -0.177939207558144 & -0.0527662840292818 \tabularnewline
57 & 7.1 & 6.85028577074093 & 0.0159785669257867 & 0.249714229259071 & 0.530051372399314 \tabularnewline
58 & 7.2 & 7.0754747220096 & 0.016351038049291 & 0.124525277990406 & 0.70799554788789 \tabularnewline
59 & 6.9 & 6.9207401985509 & 0.0161973389540574 & -0.0207401985508993 & -0.578625114936945 \tabularnewline
60 & 6.7 & 6.80805665689144 & 0.0164064926167986 & -0.108056656891443 & -0.436560242023417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159795&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/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]7.9[/C][C]7.9[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]7.9[/C][C]7.9[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]8[/C][C]7.99098783723296[/C][C]0.00102456581915253[/C][C]0.00901216276704411[/C][C]0.307411232507945[/C][/ROW]
[ROW][C]4[/C][C]8[/C][C]8.00082759696501[/C][C]0.00105933907219604[/C][C]-0.000827596965005893[/C][C]0.0298708355948673[/C][/ROW]
[ROW][C]5[/C][C]7.9[/C][C]7.90764701758227[/C][C]0.000652163499576684[/C][C]-0.00764701758227057[/C][C]-0.319272558799416[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]7.98929676606908[/C][C]0.00101959347633178[/C][C]0.0107032339309204[/C][C]0.274402539041742[/C][/ROW]
[ROW][C]7[/C][C]7.7[/C][C]7.72518400885614[/C][C]-0.00018143913342023[/C][C]-0.0251840088561354[/C][C]-0.898208049870083[/C][/ROW]
[ROW][C]8[/C][C]7.2[/C][C]7.23627469316286[/C][C]-0.00238300924049594[/C][C]-0.036274693162857[/C][C]-1.65568569308891[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.46706253501293[/C][C]-0.00133756247158843[/C][C]0.0329374649870718[/C][C]0.789916448250384[/C][/ROW]
[ROW][C]10[/C][C]7.3[/C][C]7.32117639329977[/C][C]-0.00198277407385268[/C][C]-0.0211763932997667[/C][C]-0.489685076959809[/C][/ROW]
[ROW][C]11[/C][C]7[/C][C]7.02420521212762[/C][C]-0.00329365055656567[/C][C]-0.0242052121276239[/C][C]-0.999319080135188[/C][/ROW]
[ROW][C]12[/C][C]7[/C][C]6.99677791701724[/C][C]-0.00340042179308946[/C][C]0.00322208298276472[/C][C]-0.0817557612828028[/C][/ROW]
[ROW][C]13[/C][C]7[/C][C]6.97328486846187[/C][C]-0.00258063329713146[/C][C]0.0267151315381289[/C][C]-0.080538100624212[/C][/ROW]
[ROW][C]14[/C][C]7.2[/C][C]7.18475563019096[/C][C]0.0019760076690628[/C][C]0.0152443698090423[/C][C]0.632844436975831[/C][/ROW]
[ROW][C]15[/C][C]7.3[/C][C]7.28477584293738[/C][C]0.0029241316634193[/C][C]0.01522415706262[/C][C]0.32888098629791[/C][/ROW]
[ROW][C]16[/C][C]7.1[/C][C]7.11971173058552[/C][C]0.0024587038713824[/C][C]-0.0197117305855178[/C][C]-0.568830207378783[/C][/ROW]
[ROW][C]17[/C][C]6.8[/C][C]6.85054994913242[/C][C]0.00187680021783967[/C][C]-0.0505499491324166[/C][C]-0.919370061882964[/C][/ROW]
[ROW][C]18[/C][C]6.4[/C][C]6.42390133410201[/C][C]0.000838103283618726[/C][C]-0.0239013341020127[/C][C]-1.45032884003474[/C][/ROW]
[ROW][C]19[/C][C]6.1[/C][C]6.10703584477694[/C][C]3.87532174752332e-05[/C][C]-0.00703584477693785[/C][C]-1.07524642529827[/C][/ROW]
[ROW][C]20[/C][C]6.5[/C][C]6.48693761036966[/C][C]0.000993158234325194[/C][C]0.0130623896303363[/C][C]1.28562199919763[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.5275365781074[/C][C]0.00359850872215919[/C][C]0.172463421892597[/C][C]3.51848304685733[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.88908926278563[/C][C]0.00452423716222908[/C][C]0.0109107372143703[/C][C]1.21157249839315[/C][/ROW]
[ROW][C]23[/C][C]7.5[/C][C]7.57706795670162[/C][C]0.00365329601323917[/C][C]-0.077067956701622[/C][C]-1.07170019023211[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]6.96326186956977[/C][C]0.00353155874368284[/C][C]-0.0632618695697681[/C][C]-2.0878544588136[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.69667927781282[/C][C]0.00793129141671023[/C][C]-0.0966792778128158[/C][C]-0.978537899251588[/C][/ROW]
[ROW][C]26[/C][C]6.9[/C][C]6.87196399505581[/C][C]0.0098644311731182[/C][C]0.0280360049441885[/C][C]0.531197649452878[/C][/ROW]
[ROW][C]27[/C][C]7.7[/C][C]7.55597435614516[/C][C]0.0156751926600236[/C][C]0.144025643854838[/C][C]2.25197934442126[/C][/ROW]
[ROW][C]28[/C][C]8[/C][C]7.94903605331415[/C][C]0.0168492538131329[/C][C]0.0509639466858521[/C][C]1.27748431712848[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]8.00020038293075[/C][C]0.0169081856122872[/C][C]-0.000200382930747692[/C][C]0.116133674751087[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.70701200203572[/C][C]0.0163463886845023[/C][C]-0.00701200203572311[/C][C]-1.04929135564265[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]7.3607074937911[/C][C]0.0156333403776823[/C][C]-0.0607074937910997[/C][C]-1.22706196956589[/C][/ROW]
[ROW][C]32[/C][C]7.4[/C][C]7.46334754287304[/C][C]0.0158079498961154[/C][C]-0.063347542873041[/C][C]0.294394057152584[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]7.9020228001174[/C][C]0.01667441936297[/C][C]0.197977199882607[/C][C]1.43086637572354[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]8.22029752053408[/C][C]0.017337637753848[/C][C]0.0797024794659232[/C][C]1.02073554253251[/C][/ROW]
[ROW][C]35[/C][C]8.1[/C][C]8.12505128618713[/C][C]0.0171132104859526[/C][C]-0.0250512861871317[/C][C]-0.381031555069578[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.95467220782447[/C][C]0.0173472033307872[/C][C]-0.0546722078244735[/C][C]-0.634334133178222[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]8.03991145541141[/C][C]0.0167624636448687[/C][C]-0.139911455411409[/C][C]0.237631564902217[/C][/ROW]
[ROW][C]38[/C][C]8.3[/C][C]8.33511839421914[/C][C]0.0187528866350998[/C][C]-0.035118394219143[/C][C]0.909109062795593[/C][/ROW]
[ROW][C]39[/C][C]8.6[/C][C]8.49785557817271[/C][C]0.0198298721647814[/C][C]0.102144421827284[/C][C]0.480400058091249[/C][/ROW]
[ROW][C]40[/C][C]8.7[/C][C]8.64479309532545[/C][C]0.0202700404259387[/C][C]0.0552069046745462[/C][C]0.429997200801626[/C][/ROW]
[ROW][C]41[/C][C]8.5[/C][C]8.49261364601093[/C][C]0.0199727124641275[/C][C]0.00738635398907085[/C][C]-0.583636004389723[/C][/ROW]
[ROW][C]42[/C][C]8.3[/C][C]8.2800553442429[/C][C]0.0196130001945905[/C][C]0.0199446557571058[/C][C]-0.786789960220803[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]8.08670941168318[/C][C]0.0192535492004775[/C][C]-0.0867094116831757[/C][C]-0.72049921344479[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]8.1063597603182[/C][C]0.0192542588198317[/C][C]-0.106359760318206[/C][C]0.00134247308891664[/C][/ROW]
[ROW][C]45[/C][C]8.8[/C][C]8.56461057003087[/C][C]0.0200859240919063[/C][C]0.235389429969134[/C][C]1.48539002367714[/C][/ROW]
[ROW][C]46[/C][C]8.7[/C][C]8.61348164712198[/C][C]0.020143239537402[/C][C]0.0865183528780179[/C][C]0.097419355053658[/C][/ROW]
[ROW][C]47[/C][C]8.5[/C][C]8.5172721001643[/C][C]0.0199838519838819[/C][C]-0.0172721001643076[/C][C]-0.393630507267621[/C][/ROW]
[ROW][C]48[/C][C]8.1[/C][C]8.21723421717573[/C][C]0.0205141032244595[/C][C]-0.117234217175728[/C][C]-1.08357277712438[/C][/ROW]
[ROW][C]49[/C][C]7.8[/C][C]8.02813911530479[/C][C]0.0215613071895101[/C][C]-0.228139115304785[/C][C]-0.722188482052962[/C][/ROW]
[ROW][C]50[/C][C]7.6[/C][C]7.70936082219973[/C][C]0.0199039543927136[/C][C]-0.109360822199732[/C][C]-1.12613506289814[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]7.37121309080674[/C][C]0.01760561843531[/C][C]0.0287869091932622[/C][C]-1.19518359079252[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]7.06833905892566[/C][C]0.0164402211701429[/C][C]0.0316609410743393[/C][C]-1.08328935880633[/C][/ROW]
[ROW][C]53[/C][C]6.9[/C][C]6.88106913008516[/C][C]0.0160624428003844[/C][C]0.018930869914838[/C][C]-0.689434269438328[/C][/ROW]
[ROW][C]54[/C][C]6.7[/C][C]6.6735481731755[/C][C]0.0157395680862473[/C][C]0.0264518268244968[/C][C]-0.756516581354674[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.67781377075321[/C][C]0.0157220893439141[/C][C]-0.0778137707532073[/C][C]-0.0388186371879963[/C][/ROW]
[ROW][C]56[/C][C]6.5[/C][C]6.67793920755814[/C][C]0.0156961114447233[/C][C]-0.177939207558144[/C][C]-0.0527662840292818[/C][/ROW]
[ROW][C]57[/C][C]7.1[/C][C]6.85028577074093[/C][C]0.0159785669257867[/C][C]0.249714229259071[/C][C]0.530051372399314[/C][/ROW]
[ROW][C]58[/C][C]7.2[/C][C]7.0754747220096[/C][C]0.016351038049291[/C][C]0.124525277990406[/C][C]0.70799554788789[/C][/ROW]
[ROW][C]59[/C][C]6.9[/C][C]6.9207401985509[/C][C]0.0161973389540574[/C][C]-0.0207401985508993[/C][C]-0.578625114936945[/C][/ROW]
[ROW][C]60[/C][C]6.7[/C][C]6.80805665689144[/C][C]0.0164064926167986[/C][C]-0.108056656891443[/C][C]-0.436560242023417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159795&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
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	7.9	7.9	0	0	0
2	7.9	7.9	0	0	0
3	8	7.99098783723296	0.00102456581915253	0.00901216276704411	0.307411232507945
4	8	8.00082759696501	0.00105933907219604	-0.000827596965005893	0.0298708355948673
5	7.9	7.90764701758227	0.000652163499576684	-0.00764701758227057	-0.319272558799416
6	8	7.98929676606908	0.00101959347633178	0.0107032339309204	0.274402539041742
7	7.7	7.72518400885614	-0.00018143913342023	-0.0251840088561354	-0.898208049870083
8	7.2	7.23627469316286	-0.00238300924049594	-0.036274693162857	-1.65568569308891
9	7.5	7.46706253501293	-0.00133756247158843	0.0329374649870718	0.789916448250384
10	7.3	7.32117639329977	-0.00198277407385268	-0.0211763932997667	-0.489685076959809
11	7	7.02420521212762	-0.00329365055656567	-0.0242052121276239	-0.999319080135188
12	7	6.99677791701724	-0.00340042179308946	0.00322208298276472	-0.0817557612828028
13	7	6.97328486846187	-0.00258063329713146	0.0267151315381289	-0.080538100624212
14	7.2	7.18475563019096	0.0019760076690628	0.0152443698090423	0.632844436975831
15	7.3	7.28477584293738	0.0029241316634193	0.01522415706262	0.32888098629791
16	7.1	7.11971173058552	0.0024587038713824	-0.0197117305855178	-0.568830207378783
17	6.8	6.85054994913242	0.00187680021783967	-0.0505499491324166	-0.919370061882964
18	6.4	6.42390133410201	0.000838103283618726	-0.0239013341020127	-1.45032884003474
19	6.1	6.10703584477694	3.87532174752332e-05	-0.00703584477693785	-1.07524642529827
20	6.5	6.48693761036966	0.000993158234325194	0.0130623896303363	1.28562199919763
21	7.7	7.5275365781074	0.00359850872215919	0.172463421892597	3.51848304685733
22	7.9	7.88908926278563	0.00452423716222908	0.0109107372143703	1.21157249839315
23	7.5	7.57706795670162	0.00365329601323917	-0.077067956701622	-1.07170019023211
24	6.9	6.96326186956977	0.00353155874368284	-0.0632618695697681	-2.0878544588136
25	6.6	6.69667927781282	0.00793129141671023	-0.0966792778128158	-0.978537899251588
26	6.9	6.87196399505581	0.0098644311731182	0.0280360049441885	0.531197649452878
27	7.7	7.55597435614516	0.0156751926600236	0.144025643854838	2.25197934442126
28	8	7.94903605331415	0.0168492538131329	0.0509639466858521	1.27748431712848
29	8	8.00020038293075	0.0169081856122872	-0.000200382930747692	0.116133674751087
30	7.7	7.70701200203572	0.0163463886845023	-0.00701200203572311	-1.04929135564265
31	7.3	7.3607074937911	0.0156333403776823	-0.0607074937910997	-1.22706196956589
32	7.4	7.46334754287304	0.0158079498961154	-0.063347542873041	0.294394057152584
33	8.1	7.9020228001174	0.01667441936297	0.197977199882607	1.43086637572354
34	8.3	8.22029752053408	0.017337637753848	0.0797024794659232	1.02073554253251
35	8.1	8.12505128618713	0.0171132104859526	-0.0250512861871317	-0.381031555069578
36	7.9	7.95467220782447	0.0173472033307872	-0.0546722078244735	-0.634334133178222
37	7.9	8.03991145541141	0.0167624636448687	-0.139911455411409	0.237631564902217
38	8.3	8.33511839421914	0.0187528866350998	-0.035118394219143	0.909109062795593
39	8.6	8.49785557817271	0.0198298721647814	0.102144421827284	0.480400058091249
40	8.7	8.64479309532545	0.0202700404259387	0.0552069046745462	0.429997200801626
41	8.5	8.49261364601093	0.0199727124641275	0.00738635398907085	-0.583636004389723
42	8.3	8.2800553442429	0.0196130001945905	0.0199446557571058	-0.786789960220803
43	8	8.08670941168318	0.0192535492004775	-0.0867094116831757	-0.72049921344479
44	8	8.1063597603182	0.0192542588198317	-0.106359760318206	0.00134247308891664
45	8.8	8.56461057003087	0.0200859240919063	0.235389429969134	1.48539002367714
46	8.7	8.61348164712198	0.020143239537402	0.0865183528780179	0.097419355053658
47	8.5	8.5172721001643	0.0199838519838819	-0.0172721001643076	-0.393630507267621
48	8.1	8.21723421717573	0.0205141032244595	-0.117234217175728	-1.08357277712438
49	7.8	8.02813911530479	0.0215613071895101	-0.228139115304785	-0.722188482052962
50	7.6	7.70936082219973	0.0199039543927136	-0.109360822199732	-1.12613506289814
51	7.4	7.37121309080674	0.01760561843531	0.0287869091932622	-1.19518359079252
52	7.1	7.06833905892566	0.0164402211701429	0.0316609410743393	-1.08328935880633
53	6.9	6.88106913008516	0.0160624428003844	0.018930869914838	-0.689434269438328
54	6.7	6.6735481731755	0.0157395680862473	0.0264518268244968	-0.756516581354674
55	6.6	6.67781377075321	0.0157220893439141	-0.0778137707532073	-0.0388186371879963
56	6.5	6.67793920755814	0.0156961114447233	-0.177939207558144	-0.0527662840292818
57	7.1	6.85028577074093	0.0159785669257867	0.249714229259071	0.530051372399314
58	7.2	7.0754747220096	0.016351038049291	0.124525277990406	0.70799554788789
59	6.9	6.9207401985509	0.0161973389540574	-0.0207401985508993	-0.578625114936945
60	6.7	6.80805665689144	0.0164064926167986	-0.108056656891443	-0.436560242023417

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$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()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code