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rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Thu, 01 Dec 2011 13:41:55 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t1322764948fs8znj1x1gcrq8m.htm/, Retrieved Fri, 26 Apr 2024 14:04:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149942, Retrieved Fri, 26 Apr 2024 14:04:17 +0000

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105

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-       [Structural Time Series Models] [Brutoindex van de...] [2011-12-01 18:41:55] [22ff23eaefab118cb5de5c6132878e2b] [Current]

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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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149942&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149942&T=0

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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	'Gwilym Jenkins' @ jenkins.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	101.5	101.5	0	0	0
2	100.7	101.110914728874	-0.00798407021648019	-0.410914728873969	-0.190866113760831
3	110.6	105.801649268374	0.294948272708542	4.79835073162565	1.77793341107671
4	96.8	102.819705412202	0.103397965374441	-6.01970541220163	-1.5416659996985
5	100	100.994312024367	0.0254652812002814	-0.994312024367041	-1.02250675877947
6	104.8	102.022496207592	0.0514457379228577	2.77750379240826	0.549340851606076
7	86.8	96.2219196608434	-0.0556418670967111	-9.4219196608434	-3.22596596120342
8	92	92.9004685520394	-0.106360429329745	-0.900468552039409	-1.80068872754125
9	100.2	94.8999815840349	-0.0745876688248249	5.3000184159651	1.15983349891299
10	106.6	100.166896591191	0.00741559297661347	6.43310340880913	2.93856542931115
11	102.1	102.426798039419	0.0425499719507616	-0.326798039418552	1.23833291569953
12	93.7	99.5551425041882	-0.0030242499890409	-5.85514250418821	-1.6017280808444
13	97.6	98.3601572984398	0.0192207383707748	-0.760157298439834	-0.689941536140337
14	96.9	98.4103260176414	0.0190144529994933	-1.51032601764137	0.0176710012643789
15	105.6	98.422826971078	0.0189120087793836	7.17717302892199	-0.00338260617742581
16	102.8	102.149536815964	0.118315919068003	0.650463184036144	1.87823197323937
17	101.7	102.737143926952	0.131279290580172	-1.03714392695238	0.245195337284679
18	104.2	100.693093361817	0.0805000727157606	3.50690663818281	-1.17203087967141
19	92.7	100.312351943107	0.072033521915747	-7.61235194310654	-0.252391665613037
20	91.9	98.3653214681869	0.0423792472164244	-6.46532146818689	-1.11126900169209
21	106.5	100.326706189228	0.0661463849293835	6.17329381077155	1.05791294141102
22	112.3	103.116130439438	0.0947678279353965	9.18386956056156	1.50096287505103
23	102.8	103.006019323546	0.0931434813805423	-0.20601932354639	-0.112826285006804
24	96.5	102.526118382342	0.0907785496705155	-6.02611838234246	-0.315953859966049
25	101	102.366726110395	0.0906349717090661	-1.36672611039506	-0.138693072819252
26	98.9	102.071593033771	0.0894645828975912	-3.1715930337707	-0.212086602262207
27	105.1	101.264939777305	0.080708600039079	3.83506022269535	-0.480451269886664
28	103	101.331750616573	0.0804887508722171	1.66824938342685	-0.00733288449571652
29	99	100.198215925729	0.0578787074467842	-1.198215925729	-0.643589053485383
30	104.3	99.9362324541426	0.0520179219573324	4.36376754585745	-0.172067500134939
31	94.6	100.60527406106	0.0620245850144505	-6.00527406105998	0.336166638341445
32	90.4	100.08875957123	0.0541883193561983	-9.68875957122985	-0.317472545654792
33	108.9	101.609799688302	0.0702114783908292	7.29020031169785	0.80720541355292
34	111.4	102.123949118696	0.0739638458695379	9.27605088130399	0.244406860600834
35	100.8	101.673264021534	0.0707450079516713	-0.873264021533966	-0.288786892639873
36	102.5	104.100920452895	0.0809060269361568	-1.60092045289483	1.29745271441448
37	98.2	102.759316494522	0.0755082190508372	-4.55931649452203	-0.782096056914791
38	98.7	101.856388151057	0.0702886950493028	-3.15638815105681	-0.534481228499955
39	113.3	104.489595902644	0.0919110786984478	8.81040409735621	1.38492314633933
40	104.6	104.21308092027	0.0876155370666936	0.386919079730323	-0.197520279701741
41	99.3	102.695334620724	0.0655297969364819	-3.39533462072433	-0.860968621095262
42	111.8	104.352756434001	0.0882536923091506	7.44724356599899	0.859531697625339
43	97.3	104.396204448006	0.0876519977743917	-7.09620444800587	-0.0243870729635218
44	97.7	105.95971015044	0.104972891973451	-8.25971015044001	0.807957335990527
45	115.6	107.362823008904	0.117558384100905	8.2371769910958	0.712761046831337
46	111.9	105.968516927719	0.105951070611873	5.9314830722814	-0.830937616285717
47	107	106.799388231392	0.110293843259496	0.200611768608183	0.398474158575944
48	107.1	107.42972567292	0.112874399107033	-0.329725672920014	0.285714868423134
49	100.6	106.77106111679	0.10909180995271	-6.17106111679006	-0.423037384918288
50	99.2	105.476965550527	0.100803132649058	-6.27696555052726	-0.765970306194247
51	108.4	102.747330200611	0.0791123881178475	5.65266979938889	-1.53608731243452
52	103	101.933460907278	0.0705875159626745	1.06653909272196	-0.482569184515659
53	99.8	102.738519544733	0.0786188074351042	-2.93851954473314	0.396789374787888
54	115	105.009288153982	0.103759054620692	9.99071184601841	1.18824778731402
55	90.8	103.258328353177	0.0831495625340426	-12.4583283531769	-1.01014230562517
56	95.9	103.416653901326	0.0839066863203075	-7.51665390132604	0.041109944986303
57	114.4	104.301345306542	0.0908444208652733	10.0986546934585	0.439003281040356
58	108.2	103.942453573362	0.0875973552997235	4.25754642663777	-0.246832973818508
59	112.6	107.066983407285	0.105942183667801	5.53301659271506	1.66719885809041
60	109.1	108.240704600939	0.111677847093507	0.859295399061066	0.585860173333068
61	105	108.970473468295	0.114991171958746	-3.97047346829475	0.338561019956043
62	105	109.341212319097	0.116523828190554	-4.34121231909707	0.139677020287179
63	118.5	110.76496881612	0.125754338033006	7.73503118387984	0.711504428207517
64	103.7	108.338745331769	0.104768687086392	-4.63874533176943	-1.38558461298983
65	112.5	110.886747582812	0.127072276894256	1.61325241718814	1.32608982103777
66	116.6	109.472752010262	0.112374471509111	7.12724798973751	-0.837904169637812
67	96.6	109.152457768685	0.108317188469096	-12.5524577686854	-0.235916191864126
68	101.9	109.517806686835	0.110562227955183	-7.61780668683539	0.140528746782067
69	116.5	108.747326042364	0.103689012733759	7.75267395763564	-0.482619248414312
70	119.3	111.894645308775	0.124428700251512	7.40535469122542	1.6689489721079
71	115.4	112.216378186994	0.125612620421748	3.18362181300614	0.10822009631475
72	108.5	110.762431733474	0.116868235744461	-2.26243173347433	-0.866007892667615
73	111.5	112.407513817931	0.125286903503982	-0.90751381793149	0.836842674610217
74	108.8	113.224189127818	0.129362562925236	-4.42418912781763	0.377879384196783
75	121.8	113.366926850816	0.129450291259601	8.43307314918361	0.00729489519162625
76	109.6	114.161026501295	0.134298243731241	-4.56102650129502	0.361962886688326
77	112.2	112.604386108122	0.120964939881822	-0.404386108121774	-0.920615418437235
78	119.6	112.181108765687	0.11651614200472	7.41889123431271	-0.296595234425069
79	104.1	113.958371906122	0.129965622467148	-9.85837190612178	0.906606389332122
80	105.3	114.138195959418	0.13034930991225	-8.83819595941763	0.0272664052496418
81	115	112.269419614238	0.116190851594383	2.7305803857619	-1.09479043792397
82	124.1	113.538716199016	0.123590138374985	10.5612838009837	0.632000765247875
83	116.8	113.75130202574	0.124111422958527	3.04869797426031	0.048790116003608
84	107.5	112.757812861906	0.117934958912487	-5.25781286190578	-0.61252779132921
85	115.6	114.187567345379	0.12512873987581	1.41243265462055	0.718381811177091
86	116.2	117.032241776597	0.140665206192519	-0.832241776596874	1.48744397952436
87	116.3	114.149766076153	0.122141601178783	2.15023392384664	-1.65132379675596
88	119	116.750918604534	0.138493295429606	2.24908139546596	1.35284093683125
89	111.9	115.732648044881	0.130416568937675	-3.83264804488106	-0.631134446482959
90	118.6	114.119711361128	0.117898793526824	4.48028863887171	-0.951706313954253
91	106.9	114.664902600848	0.120950713725183	-7.76490260084795	0.233507565036805
92	103.2	113.501018431976	0.112103796080564	-10.3010184319762	-0.702962717764913
93	118.6	114.457826932327	0.117578641425988	4.14217306767253	0.462610278101363
94	118.7	112.295293398809	0.103822839499088	6.40470660119088	-1.24950910738666
95	102.8	107.030547486234	0.0735044595963799	-4.23054748623386	-2.94267042386132
96	100.6	105.991254620548	0.0674854046597414	-5.39125462054799	-0.60985240104681
97	94.9	101.452037478405	0.0427949452633875	-6.55203747840549	-2.52327019128589
98	94.5	97.6411036658358	0.0216341741921853	-3.14110366583582	-2.10915295992929
99	102.9	98.4342101381903	0.0260687157572324	4.46578986180976	0.421876497796053
100	95.3	96.1396135949516	0.0120353347412972	-0.839613594951578	-1.26829203474018
101	92.5	95.3029015220238	0.00668948303700552	-2.80290152202383	-0.463787779609454
102	102.7	96.2123628844734	0.0124956493958672	6.48763711552656	0.493469157964951
103	91.5	97.2153817287346	0.0188459165383239	-5.71538172873458	0.541794268442599
104	89.5	98.0962260914344	0.0242284415681362	-8.59622609143437	0.471859895716036
105	104.2	97.7596543323489	0.0220725523675258	6.44034566765112	-0.197638101411453
106	105.2	96.4213116364071	0.0143571514042342	8.77868836359291	-0.745551806446163
107	99	97.7784306015476	0.0216133549090135	1.22156939845241	0.73601819989275
108	95.5	97.7604017489756	0.0214060003585525	-2.26040174897555	-0.0217273689041073
109	90.5	96.545315423633	0.0149991037274387	-6.04531542363301	-0.677470386988509
110	96.1	97.2097222497158	0.0184103905052445	-1.10972224971584	0.355626074200345
111	113	101.127000230831	0.0395053563353804	11.8729997691693	2.13394577122698
112	101.9	102.57593415522	0.0473981626672908	-0.675934155220106	0.771119958428032
113	101.4	103.847199131574	0.054450543314066	-2.44719913157401	0.669525001261498
114	113.6	105.668748532017	0.0647876265945888	7.93125146798273	0.966893942921447
115	96.6	104.904971177748	0.0599513712253673	-8.30497117774795	-0.453553625944709
116	97.8	105.118332353001	0.0608298282890074	-7.31833235300054	0.0840194374506019
117	114.9	106.282543511438	0.0669481292867581	8.61745648856189	0.604587808434621
118	112.5	105.862851342518	0.0643509072727006	6.6371486574823	-0.266741148533286
119	108.4	106.228672329749	0.0659034402645493	2.17132767025125	0.165269877745043
120	107	107.482865677663	0.071872003598929	-0.482865677662638	0.651408789763586
121	103.5	109.262084967575	0.0803699953960795	-5.76208496757534	0.935748699062502
122	107.5	110.584498416857	0.0865957836616631	-3.08449841685709	0.68050614768621
123	122.3	111.36923039469	0.0901611945316595	10.9307696053098	0.382373210408552

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 101.5 & 101.5 & 0 & 0 & 0 \tabularnewline
2 & 100.7 & 101.110914728874 & -0.00798407021648019 & -0.410914728873969 & -0.190866113760831 \tabularnewline
3 & 110.6 & 105.801649268374 & 0.294948272708542 & 4.79835073162565 & 1.77793341107671 \tabularnewline
4 & 96.8 & 102.819705412202 & 0.103397965374441 & -6.01970541220163 & -1.5416659996985 \tabularnewline
5 & 100 & 100.994312024367 & 0.0254652812002814 & -0.994312024367041 & -1.02250675877947 \tabularnewline
6 & 104.8 & 102.022496207592 & 0.0514457379228577 & 2.77750379240826 & 0.549340851606076 \tabularnewline
7 & 86.8 & 96.2219196608434 & -0.0556418670967111 & -9.4219196608434 & -3.22596596120342 \tabularnewline
8 & 92 & 92.9004685520394 & -0.106360429329745 & -0.900468552039409 & -1.80068872754125 \tabularnewline
9 & 100.2 & 94.8999815840349 & -0.0745876688248249 & 5.3000184159651 & 1.15983349891299 \tabularnewline
10 & 106.6 & 100.166896591191 & 0.00741559297661347 & 6.43310340880913 & 2.93856542931115 \tabularnewline
11 & 102.1 & 102.426798039419 & 0.0425499719507616 & -0.326798039418552 & 1.23833291569953 \tabularnewline
12 & 93.7 & 99.5551425041882 & -0.0030242499890409 & -5.85514250418821 & -1.6017280808444 \tabularnewline
13 & 97.6 & 98.3601572984398 & 0.0192207383707748 & -0.760157298439834 & -0.689941536140337 \tabularnewline
14 & 96.9 & 98.4103260176414 & 0.0190144529994933 & -1.51032601764137 & 0.0176710012643789 \tabularnewline
15 & 105.6 & 98.422826971078 & 0.0189120087793836 & 7.17717302892199 & -0.00338260617742581 \tabularnewline
16 & 102.8 & 102.149536815964 & 0.118315919068003 & 0.650463184036144 & 1.87823197323937 \tabularnewline
17 & 101.7 & 102.737143926952 & 0.131279290580172 & -1.03714392695238 & 0.245195337284679 \tabularnewline
18 & 104.2 & 100.693093361817 & 0.0805000727157606 & 3.50690663818281 & -1.17203087967141 \tabularnewline
19 & 92.7 & 100.312351943107 & 0.072033521915747 & -7.61235194310654 & -0.252391665613037 \tabularnewline
20 & 91.9 & 98.3653214681869 & 0.0423792472164244 & -6.46532146818689 & -1.11126900169209 \tabularnewline
21 & 106.5 & 100.326706189228 & 0.0661463849293835 & 6.17329381077155 & 1.05791294141102 \tabularnewline
22 & 112.3 & 103.116130439438 & 0.0947678279353965 & 9.18386956056156 & 1.50096287505103 \tabularnewline
23 & 102.8 & 103.006019323546 & 0.0931434813805423 & -0.20601932354639 & -0.112826285006804 \tabularnewline
24 & 96.5 & 102.526118382342 & 0.0907785496705155 & -6.02611838234246 & -0.315953859966049 \tabularnewline
25 & 101 & 102.366726110395 & 0.0906349717090661 & -1.36672611039506 & -0.138693072819252 \tabularnewline
26 & 98.9 & 102.071593033771 & 0.0894645828975912 & -3.1715930337707 & -0.212086602262207 \tabularnewline
27 & 105.1 & 101.264939777305 & 0.080708600039079 & 3.83506022269535 & -0.480451269886664 \tabularnewline
28 & 103 & 101.331750616573 & 0.0804887508722171 & 1.66824938342685 & -0.00733288449571652 \tabularnewline
29 & 99 & 100.198215925729 & 0.0578787074467842 & -1.198215925729 & -0.643589053485383 \tabularnewline
30 & 104.3 & 99.9362324541426 & 0.0520179219573324 & 4.36376754585745 & -0.172067500134939 \tabularnewline
31 & 94.6 & 100.60527406106 & 0.0620245850144505 & -6.00527406105998 & 0.336166638341445 \tabularnewline
32 & 90.4 & 100.08875957123 & 0.0541883193561983 & -9.68875957122985 & -0.317472545654792 \tabularnewline
33 & 108.9 & 101.609799688302 & 0.0702114783908292 & 7.29020031169785 & 0.80720541355292 \tabularnewline
34 & 111.4 & 102.123949118696 & 0.0739638458695379 & 9.27605088130399 & 0.244406860600834 \tabularnewline
35 & 100.8 & 101.673264021534 & 0.0707450079516713 & -0.873264021533966 & -0.288786892639873 \tabularnewline
36 & 102.5 & 104.100920452895 & 0.0809060269361568 & -1.60092045289483 & 1.29745271441448 \tabularnewline
37 & 98.2 & 102.759316494522 & 0.0755082190508372 & -4.55931649452203 & -0.782096056914791 \tabularnewline
38 & 98.7 & 101.856388151057 & 0.0702886950493028 & -3.15638815105681 & -0.534481228499955 \tabularnewline
39 & 113.3 & 104.489595902644 & 0.0919110786984478 & 8.81040409735621 & 1.38492314633933 \tabularnewline
40 & 104.6 & 104.21308092027 & 0.0876155370666936 & 0.386919079730323 & -0.197520279701741 \tabularnewline
41 & 99.3 & 102.695334620724 & 0.0655297969364819 & -3.39533462072433 & -0.860968621095262 \tabularnewline
42 & 111.8 & 104.352756434001 & 0.0882536923091506 & 7.44724356599899 & 0.859531697625339 \tabularnewline
43 & 97.3 & 104.396204448006 & 0.0876519977743917 & -7.09620444800587 & -0.0243870729635218 \tabularnewline
44 & 97.7 & 105.95971015044 & 0.104972891973451 & -8.25971015044001 & 0.807957335990527 \tabularnewline
45 & 115.6 & 107.362823008904 & 0.117558384100905 & 8.2371769910958 & 0.712761046831337 \tabularnewline
46 & 111.9 & 105.968516927719 & 0.105951070611873 & 5.9314830722814 & -0.830937616285717 \tabularnewline
47 & 107 & 106.799388231392 & 0.110293843259496 & 0.200611768608183 & 0.398474158575944 \tabularnewline
48 & 107.1 & 107.42972567292 & 0.112874399107033 & -0.329725672920014 & 0.285714868423134 \tabularnewline
49 & 100.6 & 106.77106111679 & 0.10909180995271 & -6.17106111679006 & -0.423037384918288 \tabularnewline
50 & 99.2 & 105.476965550527 & 0.100803132649058 & -6.27696555052726 & -0.765970306194247 \tabularnewline
51 & 108.4 & 102.747330200611 & 0.0791123881178475 & 5.65266979938889 & -1.53608731243452 \tabularnewline
52 & 103 & 101.933460907278 & 0.0705875159626745 & 1.06653909272196 & -0.482569184515659 \tabularnewline
53 & 99.8 & 102.738519544733 & 0.0786188074351042 & -2.93851954473314 & 0.396789374787888 \tabularnewline
54 & 115 & 105.009288153982 & 0.103759054620692 & 9.99071184601841 & 1.18824778731402 \tabularnewline
55 & 90.8 & 103.258328353177 & 0.0831495625340426 & -12.4583283531769 & -1.01014230562517 \tabularnewline
56 & 95.9 & 103.416653901326 & 0.0839066863203075 & -7.51665390132604 & 0.041109944986303 \tabularnewline
57 & 114.4 & 104.301345306542 & 0.0908444208652733 & 10.0986546934585 & 0.439003281040356 \tabularnewline
58 & 108.2 & 103.942453573362 & 0.0875973552997235 & 4.25754642663777 & -0.246832973818508 \tabularnewline
59 & 112.6 & 107.066983407285 & 0.105942183667801 & 5.53301659271506 & 1.66719885809041 \tabularnewline
60 & 109.1 & 108.240704600939 & 0.111677847093507 & 0.859295399061066 & 0.585860173333068 \tabularnewline
61 & 105 & 108.970473468295 & 0.114991171958746 & -3.97047346829475 & 0.338561019956043 \tabularnewline
62 & 105 & 109.341212319097 & 0.116523828190554 & -4.34121231909707 & 0.139677020287179 \tabularnewline
63 & 118.5 & 110.76496881612 & 0.125754338033006 & 7.73503118387984 & 0.711504428207517 \tabularnewline
64 & 103.7 & 108.338745331769 & 0.104768687086392 & -4.63874533176943 & -1.38558461298983 \tabularnewline
65 & 112.5 & 110.886747582812 & 0.127072276894256 & 1.61325241718814 & 1.32608982103777 \tabularnewline
66 & 116.6 & 109.472752010262 & 0.112374471509111 & 7.12724798973751 & -0.837904169637812 \tabularnewline
67 & 96.6 & 109.152457768685 & 0.108317188469096 & -12.5524577686854 & -0.235916191864126 \tabularnewline
68 & 101.9 & 109.517806686835 & 0.110562227955183 & -7.61780668683539 & 0.140528746782067 \tabularnewline
69 & 116.5 & 108.747326042364 & 0.103689012733759 & 7.75267395763564 & -0.482619248414312 \tabularnewline
70 & 119.3 & 111.894645308775 & 0.124428700251512 & 7.40535469122542 & 1.6689489721079 \tabularnewline
71 & 115.4 & 112.216378186994 & 0.125612620421748 & 3.18362181300614 & 0.10822009631475 \tabularnewline
72 & 108.5 & 110.762431733474 & 0.116868235744461 & -2.26243173347433 & -0.866007892667615 \tabularnewline
73 & 111.5 & 112.407513817931 & 0.125286903503982 & -0.90751381793149 & 0.836842674610217 \tabularnewline
74 & 108.8 & 113.224189127818 & 0.129362562925236 & -4.42418912781763 & 0.377879384196783 \tabularnewline
75 & 121.8 & 113.366926850816 & 0.129450291259601 & 8.43307314918361 & 0.00729489519162625 \tabularnewline
76 & 109.6 & 114.161026501295 & 0.134298243731241 & -4.56102650129502 & 0.361962886688326 \tabularnewline
77 & 112.2 & 112.604386108122 & 0.120964939881822 & -0.404386108121774 & -0.920615418437235 \tabularnewline
78 & 119.6 & 112.181108765687 & 0.11651614200472 & 7.41889123431271 & -0.296595234425069 \tabularnewline
79 & 104.1 & 113.958371906122 & 0.129965622467148 & -9.85837190612178 & 0.906606389332122 \tabularnewline
80 & 105.3 & 114.138195959418 & 0.13034930991225 & -8.83819595941763 & 0.0272664052496418 \tabularnewline
81 & 115 & 112.269419614238 & 0.116190851594383 & 2.7305803857619 & -1.09479043792397 \tabularnewline
82 & 124.1 & 113.538716199016 & 0.123590138374985 & 10.5612838009837 & 0.632000765247875 \tabularnewline
83 & 116.8 & 113.75130202574 & 0.124111422958527 & 3.04869797426031 & 0.048790116003608 \tabularnewline
84 & 107.5 & 112.757812861906 & 0.117934958912487 & -5.25781286190578 & -0.61252779132921 \tabularnewline
85 & 115.6 & 114.187567345379 & 0.12512873987581 & 1.41243265462055 & 0.718381811177091 \tabularnewline
86 & 116.2 & 117.032241776597 & 0.140665206192519 & -0.832241776596874 & 1.48744397952436 \tabularnewline
87 & 116.3 & 114.149766076153 & 0.122141601178783 & 2.15023392384664 & -1.65132379675596 \tabularnewline
88 & 119 & 116.750918604534 & 0.138493295429606 & 2.24908139546596 & 1.35284093683125 \tabularnewline
89 & 111.9 & 115.732648044881 & 0.130416568937675 & -3.83264804488106 & -0.631134446482959 \tabularnewline
90 & 118.6 & 114.119711361128 & 0.117898793526824 & 4.48028863887171 & -0.951706313954253 \tabularnewline
91 & 106.9 & 114.664902600848 & 0.120950713725183 & -7.76490260084795 & 0.233507565036805 \tabularnewline
92 & 103.2 & 113.501018431976 & 0.112103796080564 & -10.3010184319762 & -0.702962717764913 \tabularnewline
93 & 118.6 & 114.457826932327 & 0.117578641425988 & 4.14217306767253 & 0.462610278101363 \tabularnewline
94 & 118.7 & 112.295293398809 & 0.103822839499088 & 6.40470660119088 & -1.24950910738666 \tabularnewline
95 & 102.8 & 107.030547486234 & 0.0735044595963799 & -4.23054748623386 & -2.94267042386132 \tabularnewline
96 & 100.6 & 105.991254620548 & 0.0674854046597414 & -5.39125462054799 & -0.60985240104681 \tabularnewline
97 & 94.9 & 101.452037478405 & 0.0427949452633875 & -6.55203747840549 & -2.52327019128589 \tabularnewline
98 & 94.5 & 97.6411036658358 & 0.0216341741921853 & -3.14110366583582 & -2.10915295992929 \tabularnewline
99 & 102.9 & 98.4342101381903 & 0.0260687157572324 & 4.46578986180976 & 0.421876497796053 \tabularnewline
100 & 95.3 & 96.1396135949516 & 0.0120353347412972 & -0.839613594951578 & -1.26829203474018 \tabularnewline
101 & 92.5 & 95.3029015220238 & 0.00668948303700552 & -2.80290152202383 & -0.463787779609454 \tabularnewline
102 & 102.7 & 96.2123628844734 & 0.0124956493958672 & 6.48763711552656 & 0.493469157964951 \tabularnewline
103 & 91.5 & 97.2153817287346 & 0.0188459165383239 & -5.71538172873458 & 0.541794268442599 \tabularnewline
104 & 89.5 & 98.0962260914344 & 0.0242284415681362 & -8.59622609143437 & 0.471859895716036 \tabularnewline
105 & 104.2 & 97.7596543323489 & 0.0220725523675258 & 6.44034566765112 & -0.197638101411453 \tabularnewline
106 & 105.2 & 96.4213116364071 & 0.0143571514042342 & 8.77868836359291 & -0.745551806446163 \tabularnewline
107 & 99 & 97.7784306015476 & 0.0216133549090135 & 1.22156939845241 & 0.73601819989275 \tabularnewline
108 & 95.5 & 97.7604017489756 & 0.0214060003585525 & -2.26040174897555 & -0.0217273689041073 \tabularnewline
109 & 90.5 & 96.545315423633 & 0.0149991037274387 & -6.04531542363301 & -0.677470386988509 \tabularnewline
110 & 96.1 & 97.2097222497158 & 0.0184103905052445 & -1.10972224971584 & 0.355626074200345 \tabularnewline
111 & 113 & 101.127000230831 & 0.0395053563353804 & 11.8729997691693 & 2.13394577122698 \tabularnewline
112 & 101.9 & 102.57593415522 & 0.0473981626672908 & -0.675934155220106 & 0.771119958428032 \tabularnewline
113 & 101.4 & 103.847199131574 & 0.054450543314066 & -2.44719913157401 & 0.669525001261498 \tabularnewline
114 & 113.6 & 105.668748532017 & 0.0647876265945888 & 7.93125146798273 & 0.966893942921447 \tabularnewline
115 & 96.6 & 104.904971177748 & 0.0599513712253673 & -8.30497117774795 & -0.453553625944709 \tabularnewline
116 & 97.8 & 105.118332353001 & 0.0608298282890074 & -7.31833235300054 & 0.0840194374506019 \tabularnewline
117 & 114.9 & 106.282543511438 & 0.0669481292867581 & 8.61745648856189 & 0.604587808434621 \tabularnewline
118 & 112.5 & 105.862851342518 & 0.0643509072727006 & 6.6371486574823 & -0.266741148533286 \tabularnewline
119 & 108.4 & 106.228672329749 & 0.0659034402645493 & 2.17132767025125 & 0.165269877745043 \tabularnewline
120 & 107 & 107.482865677663 & 0.071872003598929 & -0.482865677662638 & 0.651408789763586 \tabularnewline
121 & 103.5 & 109.262084967575 & 0.0803699953960795 & -5.76208496757534 & 0.935748699062502 \tabularnewline
122 & 107.5 & 110.584498416857 & 0.0865957836616631 & -3.08449841685709 & 0.68050614768621 \tabularnewline
123 & 122.3 & 111.36923039469 & 0.0901611945316595 & 10.9307696053098 & 0.382373210408552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149942&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]101.5[/C][C]101.5[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]100.7[/C][C]101.110914728874[/C][C]-0.00798407021648019[/C][C]-0.410914728873969[/C][C]-0.190866113760831[/C][/ROW]
[ROW][C]3[/C][C]110.6[/C][C]105.801649268374[/C][C]0.294948272708542[/C][C]4.79835073162565[/C][C]1.77793341107671[/C][/ROW]
[ROW][C]4[/C][C]96.8[/C][C]102.819705412202[/C][C]0.103397965374441[/C][C]-6.01970541220163[/C][C]-1.5416659996985[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]100.994312024367[/C][C]0.0254652812002814[/C][C]-0.994312024367041[/C][C]-1.02250675877947[/C][/ROW]
[ROW][C]6[/C][C]104.8[/C][C]102.022496207592[/C][C]0.0514457379228577[/C][C]2.77750379240826[/C][C]0.549340851606076[/C][/ROW]
[ROW][C]7[/C][C]86.8[/C][C]96.2219196608434[/C][C]-0.0556418670967111[/C][C]-9.4219196608434[/C][C]-3.22596596120342[/C][/ROW]
[ROW][C]8[/C][C]92[/C][C]92.9004685520394[/C][C]-0.106360429329745[/C][C]-0.900468552039409[/C][C]-1.80068872754125[/C][/ROW]
[ROW][C]9[/C][C]100.2[/C][C]94.8999815840349[/C][C]-0.0745876688248249[/C][C]5.3000184159651[/C][C]1.15983349891299[/C][/ROW]
[ROW][C]10[/C][C]106.6[/C][C]100.166896591191[/C][C]0.00741559297661347[/C][C]6.43310340880913[/C][C]2.93856542931115[/C][/ROW]
[ROW][C]11[/C][C]102.1[/C][C]102.426798039419[/C][C]0.0425499719507616[/C][C]-0.326798039418552[/C][C]1.23833291569953[/C][/ROW]
[ROW][C]12[/C][C]93.7[/C][C]99.5551425041882[/C][C]-0.0030242499890409[/C][C]-5.85514250418821[/C][C]-1.6017280808444[/C][/ROW]
[ROW][C]13[/C][C]97.6[/C][C]98.3601572984398[/C][C]0.0192207383707748[/C][C]-0.760157298439834[/C][C]-0.689941536140337[/C][/ROW]
[ROW][C]14[/C][C]96.9[/C][C]98.4103260176414[/C][C]0.0190144529994933[/C][C]-1.51032601764137[/C][C]0.0176710012643789[/C][/ROW]
[ROW][C]15[/C][C]105.6[/C][C]98.422826971078[/C][C]0.0189120087793836[/C][C]7.17717302892199[/C][C]-0.00338260617742581[/C][/ROW]
[ROW][C]16[/C][C]102.8[/C][C]102.149536815964[/C][C]0.118315919068003[/C][C]0.650463184036144[/C][C]1.87823197323937[/C][/ROW]
[ROW][C]17[/C][C]101.7[/C][C]102.737143926952[/C][C]0.131279290580172[/C][C]-1.03714392695238[/C][C]0.245195337284679[/C][/ROW]
[ROW][C]18[/C][C]104.2[/C][C]100.693093361817[/C][C]0.0805000727157606[/C][C]3.50690663818281[/C][C]-1.17203087967141[/C][/ROW]
[ROW][C]19[/C][C]92.7[/C][C]100.312351943107[/C][C]0.072033521915747[/C][C]-7.61235194310654[/C][C]-0.252391665613037[/C][/ROW]
[ROW][C]20[/C][C]91.9[/C][C]98.3653214681869[/C][C]0.0423792472164244[/C][C]-6.46532146818689[/C][C]-1.11126900169209[/C][/ROW]
[ROW][C]21[/C][C]106.5[/C][C]100.326706189228[/C][C]0.0661463849293835[/C][C]6.17329381077155[/C][C]1.05791294141102[/C][/ROW]
[ROW][C]22[/C][C]112.3[/C][C]103.116130439438[/C][C]0.0947678279353965[/C][C]9.18386956056156[/C][C]1.50096287505103[/C][/ROW]
[ROW][C]23[/C][C]102.8[/C][C]103.006019323546[/C][C]0.0931434813805423[/C][C]-0.20601932354639[/C][C]-0.112826285006804[/C][/ROW]
[ROW][C]24[/C][C]96.5[/C][C]102.526118382342[/C][C]0.0907785496705155[/C][C]-6.02611838234246[/C][C]-0.315953859966049[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]102.366726110395[/C][C]0.0906349717090661[/C][C]-1.36672611039506[/C][C]-0.138693072819252[/C][/ROW]
[ROW][C]26[/C][C]98.9[/C][C]102.071593033771[/C][C]0.0894645828975912[/C][C]-3.1715930337707[/C][C]-0.212086602262207[/C][/ROW]
[ROW][C]27[/C][C]105.1[/C][C]101.264939777305[/C][C]0.080708600039079[/C][C]3.83506022269535[/C][C]-0.480451269886664[/C][/ROW]
[ROW][C]28[/C][C]103[/C][C]101.331750616573[/C][C]0.0804887508722171[/C][C]1.66824938342685[/C][C]-0.00733288449571652[/C][/ROW]
[ROW][C]29[/C][C]99[/C][C]100.198215925729[/C][C]0.0578787074467842[/C][C]-1.198215925729[/C][C]-0.643589053485383[/C][/ROW]
[ROW][C]30[/C][C]104.3[/C][C]99.9362324541426[/C][C]0.0520179219573324[/C][C]4.36376754585745[/C][C]-0.172067500134939[/C][/ROW]
[ROW][C]31[/C][C]94.6[/C][C]100.60527406106[/C][C]0.0620245850144505[/C][C]-6.00527406105998[/C][C]0.336166638341445[/C][/ROW]
[ROW][C]32[/C][C]90.4[/C][C]100.08875957123[/C][C]0.0541883193561983[/C][C]-9.68875957122985[/C][C]-0.317472545654792[/C][/ROW]
[ROW][C]33[/C][C]108.9[/C][C]101.609799688302[/C][C]0.0702114783908292[/C][C]7.29020031169785[/C][C]0.80720541355292[/C][/ROW]
[ROW][C]34[/C][C]111.4[/C][C]102.123949118696[/C][C]0.0739638458695379[/C][C]9.27605088130399[/C][C]0.244406860600834[/C][/ROW]
[ROW][C]35[/C][C]100.8[/C][C]101.673264021534[/C][C]0.0707450079516713[/C][C]-0.873264021533966[/C][C]-0.288786892639873[/C][/ROW]
[ROW][C]36[/C][C]102.5[/C][C]104.100920452895[/C][C]0.0809060269361568[/C][C]-1.60092045289483[/C][C]1.29745271441448[/C][/ROW]
[ROW][C]37[/C][C]98.2[/C][C]102.759316494522[/C][C]0.0755082190508372[/C][C]-4.55931649452203[/C][C]-0.782096056914791[/C][/ROW]
[ROW][C]38[/C][C]98.7[/C][C]101.856388151057[/C][C]0.0702886950493028[/C][C]-3.15638815105681[/C][C]-0.534481228499955[/C][/ROW]
[ROW][C]39[/C][C]113.3[/C][C]104.489595902644[/C][C]0.0919110786984478[/C][C]8.81040409735621[/C][C]1.38492314633933[/C][/ROW]
[ROW][C]40[/C][C]104.6[/C][C]104.21308092027[/C][C]0.0876155370666936[/C][C]0.386919079730323[/C][C]-0.197520279701741[/C][/ROW]
[ROW][C]41[/C][C]99.3[/C][C]102.695334620724[/C][C]0.0655297969364819[/C][C]-3.39533462072433[/C][C]-0.860968621095262[/C][/ROW]
[ROW][C]42[/C][C]111.8[/C][C]104.352756434001[/C][C]0.0882536923091506[/C][C]7.44724356599899[/C][C]0.859531697625339[/C][/ROW]
[ROW][C]43[/C][C]97.3[/C][C]104.396204448006[/C][C]0.0876519977743917[/C][C]-7.09620444800587[/C][C]-0.0243870729635218[/C][/ROW]
[ROW][C]44[/C][C]97.7[/C][C]105.95971015044[/C][C]0.104972891973451[/C][C]-8.25971015044001[/C][C]0.807957335990527[/C][/ROW]
[ROW][C]45[/C][C]115.6[/C][C]107.362823008904[/C][C]0.117558384100905[/C][C]8.2371769910958[/C][C]0.712761046831337[/C][/ROW]
[ROW][C]46[/C][C]111.9[/C][C]105.968516927719[/C][C]0.105951070611873[/C][C]5.9314830722814[/C][C]-0.830937616285717[/C][/ROW]
[ROW][C]47[/C][C]107[/C][C]106.799388231392[/C][C]0.110293843259496[/C][C]0.200611768608183[/C][C]0.398474158575944[/C][/ROW]
[ROW][C]48[/C][C]107.1[/C][C]107.42972567292[/C][C]0.112874399107033[/C][C]-0.329725672920014[/C][C]0.285714868423134[/C][/ROW]
[ROW][C]49[/C][C]100.6[/C][C]106.77106111679[/C][C]0.10909180995271[/C][C]-6.17106111679006[/C][C]-0.423037384918288[/C][/ROW]
[ROW][C]50[/C][C]99.2[/C][C]105.476965550527[/C][C]0.100803132649058[/C][C]-6.27696555052726[/C][C]-0.765970306194247[/C][/ROW]
[ROW][C]51[/C][C]108.4[/C][C]102.747330200611[/C][C]0.0791123881178475[/C][C]5.65266979938889[/C][C]-1.53608731243452[/C][/ROW]
[ROW][C]52[/C][C]103[/C][C]101.933460907278[/C][C]0.0705875159626745[/C][C]1.06653909272196[/C][C]-0.482569184515659[/C][/ROW]
[ROW][C]53[/C][C]99.8[/C][C]102.738519544733[/C][C]0.0786188074351042[/C][C]-2.93851954473314[/C][C]0.396789374787888[/C][/ROW]
[ROW][C]54[/C][C]115[/C][C]105.009288153982[/C][C]0.103759054620692[/C][C]9.99071184601841[/C][C]1.18824778731402[/C][/ROW]
[ROW][C]55[/C][C]90.8[/C][C]103.258328353177[/C][C]0.0831495625340426[/C][C]-12.4583283531769[/C][C]-1.01014230562517[/C][/ROW]
[ROW][C]56[/C][C]95.9[/C][C]103.416653901326[/C][C]0.0839066863203075[/C][C]-7.51665390132604[/C][C]0.041109944986303[/C][/ROW]
[ROW][C]57[/C][C]114.4[/C][C]104.301345306542[/C][C]0.0908444208652733[/C][C]10.0986546934585[/C][C]0.439003281040356[/C][/ROW]
[ROW][C]58[/C][C]108.2[/C][C]103.942453573362[/C][C]0.0875973552997235[/C][C]4.25754642663777[/C][C]-0.246832973818508[/C][/ROW]
[ROW][C]59[/C][C]112.6[/C][C]107.066983407285[/C][C]0.105942183667801[/C][C]5.53301659271506[/C][C]1.66719885809041[/C][/ROW]
[ROW][C]60[/C][C]109.1[/C][C]108.240704600939[/C][C]0.111677847093507[/C][C]0.859295399061066[/C][C]0.585860173333068[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]108.970473468295[/C][C]0.114991171958746[/C][C]-3.97047346829475[/C][C]0.338561019956043[/C][/ROW]
[ROW][C]62[/C][C]105[/C][C]109.341212319097[/C][C]0.116523828190554[/C][C]-4.34121231909707[/C][C]0.139677020287179[/C][/ROW]
[ROW][C]63[/C][C]118.5[/C][C]110.76496881612[/C][C]0.125754338033006[/C][C]7.73503118387984[/C][C]0.711504428207517[/C][/ROW]
[ROW][C]64[/C][C]103.7[/C][C]108.338745331769[/C][C]0.104768687086392[/C][C]-4.63874533176943[/C][C]-1.38558461298983[/C][/ROW]
[ROW][C]65[/C][C]112.5[/C][C]110.886747582812[/C][C]0.127072276894256[/C][C]1.61325241718814[/C][C]1.32608982103777[/C][/ROW]
[ROW][C]66[/C][C]116.6[/C][C]109.472752010262[/C][C]0.112374471509111[/C][C]7.12724798973751[/C][C]-0.837904169637812[/C][/ROW]
[ROW][C]67[/C][C]96.6[/C][C]109.152457768685[/C][C]0.108317188469096[/C][C]-12.5524577686854[/C][C]-0.235916191864126[/C][/ROW]
[ROW][C]68[/C][C]101.9[/C][C]109.517806686835[/C][C]0.110562227955183[/C][C]-7.61780668683539[/C][C]0.140528746782067[/C][/ROW]
[ROW][C]69[/C][C]116.5[/C][C]108.747326042364[/C][C]0.103689012733759[/C][C]7.75267395763564[/C][C]-0.482619248414312[/C][/ROW]
[ROW][C]70[/C][C]119.3[/C][C]111.894645308775[/C][C]0.124428700251512[/C][C]7.40535469122542[/C][C]1.6689489721079[/C][/ROW]
[ROW][C]71[/C][C]115.4[/C][C]112.216378186994[/C][C]0.125612620421748[/C][C]3.18362181300614[/C][C]0.10822009631475[/C][/ROW]
[ROW][C]72[/C][C]108.5[/C][C]110.762431733474[/C][C]0.116868235744461[/C][C]-2.26243173347433[/C][C]-0.866007892667615[/C][/ROW]
[ROW][C]73[/C][C]111.5[/C][C]112.407513817931[/C][C]0.125286903503982[/C][C]-0.90751381793149[/C][C]0.836842674610217[/C][/ROW]
[ROW][C]74[/C][C]108.8[/C][C]113.224189127818[/C][C]0.129362562925236[/C][C]-4.42418912781763[/C][C]0.377879384196783[/C][/ROW]
[ROW][C]75[/C][C]121.8[/C][C]113.366926850816[/C][C]0.129450291259601[/C][C]8.43307314918361[/C][C]0.00729489519162625[/C][/ROW]
[ROW][C]76[/C][C]109.6[/C][C]114.161026501295[/C][C]0.134298243731241[/C][C]-4.56102650129502[/C][C]0.361962886688326[/C][/ROW]
[ROW][C]77[/C][C]112.2[/C][C]112.604386108122[/C][C]0.120964939881822[/C][C]-0.404386108121774[/C][C]-0.920615418437235[/C][/ROW]
[ROW][C]78[/C][C]119.6[/C][C]112.181108765687[/C][C]0.11651614200472[/C][C]7.41889123431271[/C][C]-0.296595234425069[/C][/ROW]
[ROW][C]79[/C][C]104.1[/C][C]113.958371906122[/C][C]0.129965622467148[/C][C]-9.85837190612178[/C][C]0.906606389332122[/C][/ROW]
[ROW][C]80[/C][C]105.3[/C][C]114.138195959418[/C][C]0.13034930991225[/C][C]-8.83819595941763[/C][C]0.0272664052496418[/C][/ROW]
[ROW][C]81[/C][C]115[/C][C]112.269419614238[/C][C]0.116190851594383[/C][C]2.7305803857619[/C][C]-1.09479043792397[/C][/ROW]
[ROW][C]82[/C][C]124.1[/C][C]113.538716199016[/C][C]0.123590138374985[/C][C]10.5612838009837[/C][C]0.632000765247875[/C][/ROW]
[ROW][C]83[/C][C]116.8[/C][C]113.75130202574[/C][C]0.124111422958527[/C][C]3.04869797426031[/C][C]0.048790116003608[/C][/ROW]
[ROW][C]84[/C][C]107.5[/C][C]112.757812861906[/C][C]0.117934958912487[/C][C]-5.25781286190578[/C][C]-0.61252779132921[/C][/ROW]
[ROW][C]85[/C][C]115.6[/C][C]114.187567345379[/C][C]0.12512873987581[/C][C]1.41243265462055[/C][C]0.718381811177091[/C][/ROW]
[ROW][C]86[/C][C]116.2[/C][C]117.032241776597[/C][C]0.140665206192519[/C][C]-0.832241776596874[/C][C]1.48744397952436[/C][/ROW]
[ROW][C]87[/C][C]116.3[/C][C]114.149766076153[/C][C]0.122141601178783[/C][C]2.15023392384664[/C][C]-1.65132379675596[/C][/ROW]
[ROW][C]88[/C][C]119[/C][C]116.750918604534[/C][C]0.138493295429606[/C][C]2.24908139546596[/C][C]1.35284093683125[/C][/ROW]
[ROW][C]89[/C][C]111.9[/C][C]115.732648044881[/C][C]0.130416568937675[/C][C]-3.83264804488106[/C][C]-0.631134446482959[/C][/ROW]
[ROW][C]90[/C][C]118.6[/C][C]114.119711361128[/C][C]0.117898793526824[/C][C]4.48028863887171[/C][C]-0.951706313954253[/C][/ROW]
[ROW][C]91[/C][C]106.9[/C][C]114.664902600848[/C][C]0.120950713725183[/C][C]-7.76490260084795[/C][C]0.233507565036805[/C][/ROW]
[ROW][C]92[/C][C]103.2[/C][C]113.501018431976[/C][C]0.112103796080564[/C][C]-10.3010184319762[/C][C]-0.702962717764913[/C][/ROW]
[ROW][C]93[/C][C]118.6[/C][C]114.457826932327[/C][C]0.117578641425988[/C][C]4.14217306767253[/C][C]0.462610278101363[/C][/ROW]
[ROW][C]94[/C][C]118.7[/C][C]112.295293398809[/C][C]0.103822839499088[/C][C]6.40470660119088[/C][C]-1.24950910738666[/C][/ROW]
[ROW][C]95[/C][C]102.8[/C][C]107.030547486234[/C][C]0.0735044595963799[/C][C]-4.23054748623386[/C][C]-2.94267042386132[/C][/ROW]
[ROW][C]96[/C][C]100.6[/C][C]105.991254620548[/C][C]0.0674854046597414[/C][C]-5.39125462054799[/C][C]-0.60985240104681[/C][/ROW]
[ROW][C]97[/C][C]94.9[/C][C]101.452037478405[/C][C]0.0427949452633875[/C][C]-6.55203747840549[/C][C]-2.52327019128589[/C][/ROW]
[ROW][C]98[/C][C]94.5[/C][C]97.6411036658358[/C][C]0.0216341741921853[/C][C]-3.14110366583582[/C][C]-2.10915295992929[/C][/ROW]
[ROW][C]99[/C][C]102.9[/C][C]98.4342101381903[/C][C]0.0260687157572324[/C][C]4.46578986180976[/C][C]0.421876497796053[/C][/ROW]
[ROW][C]100[/C][C]95.3[/C][C]96.1396135949516[/C][C]0.0120353347412972[/C][C]-0.839613594951578[/C][C]-1.26829203474018[/C][/ROW]
[ROW][C]101[/C][C]92.5[/C][C]95.3029015220238[/C][C]0.00668948303700552[/C][C]-2.80290152202383[/C][C]-0.463787779609454[/C][/ROW]
[ROW][C]102[/C][C]102.7[/C][C]96.2123628844734[/C][C]0.0124956493958672[/C][C]6.48763711552656[/C][C]0.493469157964951[/C][/ROW]
[ROW][C]103[/C][C]91.5[/C][C]97.2153817287346[/C][C]0.0188459165383239[/C][C]-5.71538172873458[/C][C]0.541794268442599[/C][/ROW]
[ROW][C]104[/C][C]89.5[/C][C]98.0962260914344[/C][C]0.0242284415681362[/C][C]-8.59622609143437[/C][C]0.471859895716036[/C][/ROW]
[ROW][C]105[/C][C]104.2[/C][C]97.7596543323489[/C][C]0.0220725523675258[/C][C]6.44034566765112[/C][C]-0.197638101411453[/C][/ROW]
[ROW][C]106[/C][C]105.2[/C][C]96.4213116364071[/C][C]0.0143571514042342[/C][C]8.77868836359291[/C][C]-0.745551806446163[/C][/ROW]
[ROW][C]107[/C][C]99[/C][C]97.7784306015476[/C][C]0.0216133549090135[/C][C]1.22156939845241[/C][C]0.73601819989275[/C][/ROW]
[ROW][C]108[/C][C]95.5[/C][C]97.7604017489756[/C][C]0.0214060003585525[/C][C]-2.26040174897555[/C][C]-0.0217273689041073[/C][/ROW]
[ROW][C]109[/C][C]90.5[/C][C]96.545315423633[/C][C]0.0149991037274387[/C][C]-6.04531542363301[/C][C]-0.677470386988509[/C][/ROW]
[ROW][C]110[/C][C]96.1[/C][C]97.2097222497158[/C][C]0.0184103905052445[/C][C]-1.10972224971584[/C][C]0.355626074200345[/C][/ROW]
[ROW][C]111[/C][C]113[/C][C]101.127000230831[/C][C]0.0395053563353804[/C][C]11.8729997691693[/C][C]2.13394577122698[/C][/ROW]
[ROW][C]112[/C][C]101.9[/C][C]102.57593415522[/C][C]0.0473981626672908[/C][C]-0.675934155220106[/C][C]0.771119958428032[/C][/ROW]
[ROW][C]113[/C][C]101.4[/C][C]103.847199131574[/C][C]0.054450543314066[/C][C]-2.44719913157401[/C][C]0.669525001261498[/C][/ROW]
[ROW][C]114[/C][C]113.6[/C][C]105.668748532017[/C][C]0.0647876265945888[/C][C]7.93125146798273[/C][C]0.966893942921447[/C][/ROW]
[ROW][C]115[/C][C]96.6[/C][C]104.904971177748[/C][C]0.0599513712253673[/C][C]-8.30497117774795[/C][C]-0.453553625944709[/C][/ROW]
[ROW][C]116[/C][C]97.8[/C][C]105.118332353001[/C][C]0.0608298282890074[/C][C]-7.31833235300054[/C][C]0.0840194374506019[/C][/ROW]
[ROW][C]117[/C][C]114.9[/C][C]106.282543511438[/C][C]0.0669481292867581[/C][C]8.61745648856189[/C][C]0.604587808434621[/C][/ROW]
[ROW][C]118[/C][C]112.5[/C][C]105.862851342518[/C][C]0.0643509072727006[/C][C]6.6371486574823[/C][C]-0.266741148533286[/C][/ROW]
[ROW][C]119[/C][C]108.4[/C][C]106.228672329749[/C][C]0.0659034402645493[/C][C]2.17132767025125[/C][C]0.165269877745043[/C][/ROW]
[ROW][C]120[/C][C]107[/C][C]107.482865677663[/C][C]0.071872003598929[/C][C]-0.482865677662638[/C][C]0.651408789763586[/C][/ROW]
[ROW][C]121[/C][C]103.5[/C][C]109.262084967575[/C][C]0.0803699953960795[/C][C]-5.76208496757534[/C][C]0.935748699062502[/C][/ROW]
[ROW][C]122[/C][C]107.5[/C][C]110.584498416857[/C][C]0.0865957836616631[/C][C]-3.08449841685709[/C][C]0.68050614768621[/C][/ROW]
[ROW][C]123[/C][C]122.3[/C][C]111.36923039469[/C][C]0.0901611945316595[/C][C]10.9307696053098[/C][C]0.382373210408552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149942&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	101.5	101.5	0	0	0
2	100.7	101.110914728874	-0.00798407021648019	-0.410914728873969	-0.190866113760831
3	110.6	105.801649268374	0.294948272708542	4.79835073162565	1.77793341107671
4	96.8	102.819705412202	0.103397965374441	-6.01970541220163	-1.5416659996985
5	100	100.994312024367	0.0254652812002814	-0.994312024367041	-1.02250675877947
6	104.8	102.022496207592	0.0514457379228577	2.77750379240826	0.549340851606076
7	86.8	96.2219196608434	-0.0556418670967111	-9.4219196608434	-3.22596596120342
8	92	92.9004685520394	-0.106360429329745	-0.900468552039409	-1.80068872754125
9	100.2	94.8999815840349	-0.0745876688248249	5.3000184159651	1.15983349891299
10	106.6	100.166896591191	0.00741559297661347	6.43310340880913	2.93856542931115
11	102.1	102.426798039419	0.0425499719507616	-0.326798039418552	1.23833291569953
12	93.7	99.5551425041882	-0.0030242499890409	-5.85514250418821	-1.6017280808444
13	97.6	98.3601572984398	0.0192207383707748	-0.760157298439834	-0.689941536140337
14	96.9	98.4103260176414	0.0190144529994933	-1.51032601764137	0.0176710012643789
15	105.6	98.422826971078	0.0189120087793836	7.17717302892199	-0.00338260617742581
16	102.8	102.149536815964	0.118315919068003	0.650463184036144	1.87823197323937
17	101.7	102.737143926952	0.131279290580172	-1.03714392695238	0.245195337284679
18	104.2	100.693093361817	0.0805000727157606	3.50690663818281	-1.17203087967141
19	92.7	100.312351943107	0.072033521915747	-7.61235194310654	-0.252391665613037
20	91.9	98.3653214681869	0.0423792472164244	-6.46532146818689	-1.11126900169209
21	106.5	100.326706189228	0.0661463849293835	6.17329381077155	1.05791294141102
22	112.3	103.116130439438	0.0947678279353965	9.18386956056156	1.50096287505103
23	102.8	103.006019323546	0.0931434813805423	-0.20601932354639	-0.112826285006804
24	96.5	102.526118382342	0.0907785496705155	-6.02611838234246	-0.315953859966049
25	101	102.366726110395	0.0906349717090661	-1.36672611039506	-0.138693072819252
26	98.9	102.071593033771	0.0894645828975912	-3.1715930337707	-0.212086602262207
27	105.1	101.264939777305	0.080708600039079	3.83506022269535	-0.480451269886664
28	103	101.331750616573	0.0804887508722171	1.66824938342685	-0.00733288449571652
29	99	100.198215925729	0.0578787074467842	-1.198215925729	-0.643589053485383
30	104.3	99.9362324541426	0.0520179219573324	4.36376754585745	-0.172067500134939
31	94.6	100.60527406106	0.0620245850144505	-6.00527406105998	0.336166638341445
32	90.4	100.08875957123	0.0541883193561983	-9.68875957122985	-0.317472545654792
33	108.9	101.609799688302	0.0702114783908292	7.29020031169785	0.80720541355292
34	111.4	102.123949118696	0.0739638458695379	9.27605088130399	0.244406860600834
35	100.8	101.673264021534	0.0707450079516713	-0.873264021533966	-0.288786892639873
36	102.5	104.100920452895	0.0809060269361568	-1.60092045289483	1.29745271441448
37	98.2	102.759316494522	0.0755082190508372	-4.55931649452203	-0.782096056914791
38	98.7	101.856388151057	0.0702886950493028	-3.15638815105681	-0.534481228499955
39	113.3	104.489595902644	0.0919110786984478	8.81040409735621	1.38492314633933
40	104.6	104.21308092027	0.0876155370666936	0.386919079730323	-0.197520279701741
41	99.3	102.695334620724	0.0655297969364819	-3.39533462072433	-0.860968621095262
42	111.8	104.352756434001	0.0882536923091506	7.44724356599899	0.859531697625339
43	97.3	104.396204448006	0.0876519977743917	-7.09620444800587	-0.0243870729635218
44	97.7	105.95971015044	0.104972891973451	-8.25971015044001	0.807957335990527
45	115.6	107.362823008904	0.117558384100905	8.2371769910958	0.712761046831337
46	111.9	105.968516927719	0.105951070611873	5.9314830722814	-0.830937616285717
47	107	106.799388231392	0.110293843259496	0.200611768608183	0.398474158575944
48	107.1	107.42972567292	0.112874399107033	-0.329725672920014	0.285714868423134
49	100.6	106.77106111679	0.10909180995271	-6.17106111679006	-0.423037384918288
50	99.2	105.476965550527	0.100803132649058	-6.27696555052726	-0.765970306194247
51	108.4	102.747330200611	0.0791123881178475	5.65266979938889	-1.53608731243452
52	103	101.933460907278	0.0705875159626745	1.06653909272196	-0.482569184515659
53	99.8	102.738519544733	0.0786188074351042	-2.93851954473314	0.396789374787888
54	115	105.009288153982	0.103759054620692	9.99071184601841	1.18824778731402
55	90.8	103.258328353177	0.0831495625340426	-12.4583283531769	-1.01014230562517
56	95.9	103.416653901326	0.0839066863203075	-7.51665390132604	0.041109944986303
57	114.4	104.301345306542	0.0908444208652733	10.0986546934585	0.439003281040356
58	108.2	103.942453573362	0.0875973552997235	4.25754642663777	-0.246832973818508
59	112.6	107.066983407285	0.105942183667801	5.53301659271506	1.66719885809041
60	109.1	108.240704600939	0.111677847093507	0.859295399061066	0.585860173333068
61	105	108.970473468295	0.114991171958746	-3.97047346829475	0.338561019956043
62	105	109.341212319097	0.116523828190554	-4.34121231909707	0.139677020287179
63	118.5	110.76496881612	0.125754338033006	7.73503118387984	0.711504428207517
64	103.7	108.338745331769	0.104768687086392	-4.63874533176943	-1.38558461298983
65	112.5	110.886747582812	0.127072276894256	1.61325241718814	1.32608982103777
66	116.6	109.472752010262	0.112374471509111	7.12724798973751	-0.837904169637812
67	96.6	109.152457768685	0.108317188469096	-12.5524577686854	-0.235916191864126
68	101.9	109.517806686835	0.110562227955183	-7.61780668683539	0.140528746782067
69	116.5	108.747326042364	0.103689012733759	7.75267395763564	-0.482619248414312
70	119.3	111.894645308775	0.124428700251512	7.40535469122542	1.6689489721079
71	115.4	112.216378186994	0.125612620421748	3.18362181300614	0.10822009631475
72	108.5	110.762431733474	0.116868235744461	-2.26243173347433	-0.866007892667615
73	111.5	112.407513817931	0.125286903503982	-0.90751381793149	0.836842674610217
74	108.8	113.224189127818	0.129362562925236	-4.42418912781763	0.377879384196783
75	121.8	113.366926850816	0.129450291259601	8.43307314918361	0.00729489519162625
76	109.6	114.161026501295	0.134298243731241	-4.56102650129502	0.361962886688326
77	112.2	112.604386108122	0.120964939881822	-0.404386108121774	-0.920615418437235
78	119.6	112.181108765687	0.11651614200472	7.41889123431271	-0.296595234425069
79	104.1	113.958371906122	0.129965622467148	-9.85837190612178	0.906606389332122
80	105.3	114.138195959418	0.13034930991225	-8.83819595941763	0.0272664052496418
81	115	112.269419614238	0.116190851594383	2.7305803857619	-1.09479043792397
82	124.1	113.538716199016	0.123590138374985	10.5612838009837	0.632000765247875
83	116.8	113.75130202574	0.124111422958527	3.04869797426031	0.048790116003608
84	107.5	112.757812861906	0.117934958912487	-5.25781286190578	-0.61252779132921
85	115.6	114.187567345379	0.12512873987581	1.41243265462055	0.718381811177091
86	116.2	117.032241776597	0.140665206192519	-0.832241776596874	1.48744397952436
87	116.3	114.149766076153	0.122141601178783	2.15023392384664	-1.65132379675596
88	119	116.750918604534	0.138493295429606	2.24908139546596	1.35284093683125
89	111.9	115.732648044881	0.130416568937675	-3.83264804488106	-0.631134446482959
90	118.6	114.119711361128	0.117898793526824	4.48028863887171	-0.951706313954253
91	106.9	114.664902600848	0.120950713725183	-7.76490260084795	0.233507565036805
92	103.2	113.501018431976	0.112103796080564	-10.3010184319762	-0.702962717764913
93	118.6	114.457826932327	0.117578641425988	4.14217306767253	0.462610278101363
94	118.7	112.295293398809	0.103822839499088	6.40470660119088	-1.24950910738666
95	102.8	107.030547486234	0.0735044595963799	-4.23054748623386	-2.94267042386132
96	100.6	105.991254620548	0.0674854046597414	-5.39125462054799	-0.60985240104681
97	94.9	101.452037478405	0.0427949452633875	-6.55203747840549	-2.52327019128589
98	94.5	97.6411036658358	0.0216341741921853	-3.14110366583582	-2.10915295992929
99	102.9	98.4342101381903	0.0260687157572324	4.46578986180976	0.421876497796053
100	95.3	96.1396135949516	0.0120353347412972	-0.839613594951578	-1.26829203474018
101	92.5	95.3029015220238	0.00668948303700552	-2.80290152202383	-0.463787779609454
102	102.7	96.2123628844734	0.0124956493958672	6.48763711552656	0.493469157964951
103	91.5	97.2153817287346	0.0188459165383239	-5.71538172873458	0.541794268442599
104	89.5	98.0962260914344	0.0242284415681362	-8.59622609143437	0.471859895716036
105	104.2	97.7596543323489	0.0220725523675258	6.44034566765112	-0.197638101411453
106	105.2	96.4213116364071	0.0143571514042342	8.77868836359291	-0.745551806446163
107	99	97.7784306015476	0.0216133549090135	1.22156939845241	0.73601819989275
108	95.5	97.7604017489756	0.0214060003585525	-2.26040174897555	-0.0217273689041073
109	90.5	96.545315423633	0.0149991037274387	-6.04531542363301	-0.677470386988509
110	96.1	97.2097222497158	0.0184103905052445	-1.10972224971584	0.355626074200345
111	113	101.127000230831	0.0395053563353804	11.8729997691693	2.13394577122698
112	101.9	102.57593415522	0.0473981626672908	-0.675934155220106	0.771119958428032
113	101.4	103.847199131574	0.054450543314066	-2.44719913157401	0.669525001261498
114	113.6	105.668748532017	0.0647876265945888	7.93125146798273	0.966893942921447
115	96.6	104.904971177748	0.0599513712253673	-8.30497117774795	-0.453553625944709
116	97.8	105.118332353001	0.0608298282890074	-7.31833235300054	0.0840194374506019
117	114.9	106.282543511438	0.0669481292867581	8.61745648856189	0.604587808434621
118	112.5	105.862851342518	0.0643509072727006	6.6371486574823	-0.266741148533286
119	108.4	106.228672329749	0.0659034402645493	2.17132767025125	0.165269877745043
120	107	107.482865677663	0.071872003598929	-0.482865677662638	0.651408789763586
121	103.5	109.262084967575	0.0803699953960795	-5.76208496757534	0.935748699062502
122	107.5	110.584498416857	0.0865957836616631	-3.08449841685709	0.68050614768621
123	122.3	111.36923039469	0.0901611945316595	10.9307696053098	0.382373210408552

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 = 12 ;

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