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rwasp_structuraltimeseries.wasp

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Structural Time Series Models

Date of computation

Fri, 30 Nov 2012 10:11:14 -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/2012/Nov/30/t1354288310x65819y6sswiohy.htm/, Retrieved Fri, 03 May 2024 20:26:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195093, Retrieved Fri, 03 May 2024 20:26:34 +0000

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Estimated Impact

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Decomposition by Loess] [Unemployment] [2010-11-30 13:30:23] [b98453cac15ba1066b407e146608df68]
- RMPD      [Structural Time Series Models] [] [2012-11-30 15:11:14] [195a7509fef65339447329cdcf8835cc] [Current]
- R  D        [Structural Time Series Models] [] [2012-11-30 17:59:30] [74be16979710d4c4e7c6647856088456] 

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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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195093&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195093&T=0

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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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	112.8	112.8	0	0	0
2	116.7	116.517222998974	0.567834594714074	0.182777001025732	0.565409390838798
3	119.4	119.231765741215	1.38057117208508	0.168234258784778	0.449989653489851
4	129.8	129.667546927876	5.15398787451447	0.132453072124165	1.84545415201493
5	131.9	131.760649294732	3.83869893732185	0.139350705268115	-0.618222697451815
6	129.8	129.653066187873	1.25748740411035	0.146933812127264	-1.19798656557481
7	131.6	131.453456953824	1.49397222226914	0.14654304617585	0.109316176821515
8	134.3	134.15394662628	2.02017240916277	0.146053373719683	0.242927760095655
9	136.7	136.554033537925	2.18594291709768	0.145966462075126	0.076499245707281
10	134.7	134.55349378301	0.358876189159077	0.146506216989863	-0.84304027188398
11	138.1	137.953714756069	1.68629516154975	0.146285243931395	0.612469067079526
12	132.4	132.253412322041	-1.53777619742481	0.146587677959371	-1.48756222230761
13	125	127.652597566725	-2.8339663446751	-2.6525975667247	-0.702772644611231
14	117.7	117.613890868718	-5.69158112658533	0.0861091312824908	-1.18297478689257
15	112	111.913867470041	-5.69528611708848	0.0861325299592146	-0.0016901095667935
16	106.3	106.213860099523	-5.69734906362555	0.0861399004772734	-0.000948392573978235
17	100.5	100.413769713474	-5.74219276785388	0.0862302865255695	-0.0206667241431879
18	95.6	95.5141875044392	-5.37448289366277	0.0858124955608021	0.169595814827971
19	89.5	89.4139847060613	-5.69119430135892	0.086015293938747	-0.146110489626483
20	87.7	87.6145976039771	-3.99266015296568	0.0854023960228708	0.783657362076313
21	88.2	88.1149963563439	-2.03161725172513	0.0850036436560621	0.90479440060958
22	88.7	88.6151229739679	-0.926574488919616	0.0848770260320904	0.509853432100263
23	91.4	91.315225183108	0.65641069458144	0.0847748168920425	0.730372157136665
24	95.7	95.6152830486152	2.24682185803587	0.0847169513848283	0.733799011834588
25	96.8	97.7496190816659	2.19841923133305	-0.949619081665916	-0.0241977539428367
26	93.8	93.7984754432179	-0.328763823923405	0.00152455678206713	-1.09858470442761
27	91	90.9940296049081	-1.41318130843316	0.00597039509185428	-0.496667869640587
28	86.8	86.7912081126492	-2.63166593360104	0.00879188735079182	-0.560883601240605
29	91.5	91.4953892081869	0.570286314377252	0.0046107918131171	1.47625167274855
30	89.3	89.2944990806568	-0.639136912831987	0.00550091934317543	-0.557883902879592
31	97.9	97.8961718580003	3.39392331423661	0.00382814199971486	1.86067310039407
32	95.7	95.6956011489162	0.952158525736878	0.00439885108375714	-1.12657828705229
33	86.9	86.8950404954603	-3.30463900771774	0.00495950453969375	-1.96402760062763
34	82	81.9949888122546	-4.00100827952587	0.00501118774537626	-0.321296820368189
35	83.2	83.1950837579192	-1.73078975390916	0.00491624208079016	1.0474545847544
36	85.7	85.6951272796625	0.115931721353522	0.00487272033751208	0.852058010489893
37	77.8	78.5943953640105	-3.00499484997968	-0.794395364010496	-1.51898039264716
38	79.4	79.2902330938294	-1.45914586738184	0.109766906170631	0.684633115776445
39	83.4	83.2974928792266	0.933110167260973	0.10250712077337	1.09776792426153
40	102.8	102.711318026123	9.00387383886214	0.0886819738771911	3.71733539541066
41	108.7	108.610009012303	7.64851046343682	0.0899909876973572	-0.625007523513729
42	120.3	120.210947991664	9.37353498484777	0.0890520083360022	0.79576979935185
43	121.9	121.809907118883	5.98028573725389	0.0900928811172826	-1.56552351985895
44	112.7	112.608761732321	-0.645926274023385	0.0912382676792284	-3.05721206528552
45	113.1	113.008806202529	-0.18938221093449	0.0911937974712242	0.210643540288397
46	115.7	115.608873032764	1.02817243330608	0.091126967236084	0.56176614297116
47	113.5	113.40882944959	-0.380911233063526	0.0911705504100079	-0.650136285302349
48	103.1	103.008753226313	-4.75420005751946	0.0912467736867718	-2.01778993714595
49	95.9	96.9992469465751	-5.29838100961228	-1.0992469465751	-0.261339832045585
50	88.5	88.4263476600077	-6.67901970980446	0.0736523399923543	-0.617476020986335
51	86.2	86.1309664585227	-4.76164005330731	0.0690335414773148	0.880845675426067
52	83.8	83.7323690394473	-3.72977522181329	0.0676309605527155	0.475439289511135
53	76.4	76.3311410388602	-5.33231511908649	0.0688589611398459	-0.739073455874701
54	76	75.9320709051413	-3.1791666399046	0.0679290948586814	0.99330311824934
55	75.7	75.6323767654644	-1.92238326790762	0.0676232345355793	0.579841409454633
56	71.5	71.4322404230724	-2.91656296316384	0.0677595769276244	-0.458697848803749
57	69.7	69.6322780873561	-2.42918657640342	0.0677219126438736	0.224869435888582
58	72.1	72.0323698820214	-0.32126570084123	0.067630117978556	0.972571554861737
59	72.6	72.5323786788138	0.037213287422581	0.0676213211862349	0.165398429096026
60	70.2	70.1323639681774	-1.02661972144979	0.0676360318226069	-0.490841493784291
61	69.4	70.0847977217866	-0.601593858156112	-0.684797721786567	0.202486740569827
62	68	67.9479365865702	-1.2528556796831	0.0520634134297711	-0.293028349964671
63	63.1	63.0447491448565	-2.84892899189315	0.0552508551434875	-0.733780075446004
64	59.4	59.3443302729733	-3.22072216289711	0.0556697270266678	-0.17134667003916
65	59.3	59.2451956000565	-1.85818626793987	0.0548043999434662	0.628433158050689
66	61.2	61.1457827824268	-0.217618958147732	0.054217217573248	0.756854079295651
67	59.8	59.7456786848441	-0.733736628787317	0.0543213151558563	-0.238122698223196
68	61.3	61.2457895026774	0.241287723643142	0.054210497322579	0.449860968659552
69	60.2	60.145752005718	-0.344180027577637	0.0542479942819853	-0.270127782815867
70	59.7	59.6457495510416	-0.412194818580174	0.0542504489583853	-0.0313812855734852
71	60.7	60.6457620871562	0.204222184327295	0.0542379128438227	0.284408333765613
72	59.8	59.7457565635579	-0.277765992221112	0.0542434364420591	-0.22238434071184

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 112.8 & 112.8 & 0 & 0 & 0 \tabularnewline
2 & 116.7 & 116.517222998974 & 0.567834594714074 & 0.182777001025732 & 0.565409390838798 \tabularnewline
3 & 119.4 & 119.231765741215 & 1.38057117208508 & 0.168234258784778 & 0.449989653489851 \tabularnewline
4 & 129.8 & 129.667546927876 & 5.15398787451447 & 0.132453072124165 & 1.84545415201493 \tabularnewline
5 & 131.9 & 131.760649294732 & 3.83869893732185 & 0.139350705268115 & -0.618222697451815 \tabularnewline
6 & 129.8 & 129.653066187873 & 1.25748740411035 & 0.146933812127264 & -1.19798656557481 \tabularnewline
7 & 131.6 & 131.453456953824 & 1.49397222226914 & 0.14654304617585 & 0.109316176821515 \tabularnewline
8 & 134.3 & 134.15394662628 & 2.02017240916277 & 0.146053373719683 & 0.242927760095655 \tabularnewline
9 & 136.7 & 136.554033537925 & 2.18594291709768 & 0.145966462075126 & 0.076499245707281 \tabularnewline
10 & 134.7 & 134.55349378301 & 0.358876189159077 & 0.146506216989863 & -0.84304027188398 \tabularnewline
11 & 138.1 & 137.953714756069 & 1.68629516154975 & 0.146285243931395 & 0.612469067079526 \tabularnewline
12 & 132.4 & 132.253412322041 & -1.53777619742481 & 0.146587677959371 & -1.48756222230761 \tabularnewline
13 & 125 & 127.652597566725 & -2.8339663446751 & -2.6525975667247 & -0.702772644611231 \tabularnewline
14 & 117.7 & 117.613890868718 & -5.69158112658533 & 0.0861091312824908 & -1.18297478689257 \tabularnewline
15 & 112 & 111.913867470041 & -5.69528611708848 & 0.0861325299592146 & -0.0016901095667935 \tabularnewline
16 & 106.3 & 106.213860099523 & -5.69734906362555 & 0.0861399004772734 & -0.000948392573978235 \tabularnewline
17 & 100.5 & 100.413769713474 & -5.74219276785388 & 0.0862302865255695 & -0.0206667241431879 \tabularnewline
18 & 95.6 & 95.5141875044392 & -5.37448289366277 & 0.0858124955608021 & 0.169595814827971 \tabularnewline
19 & 89.5 & 89.4139847060613 & -5.69119430135892 & 0.086015293938747 & -0.146110489626483 \tabularnewline
20 & 87.7 & 87.6145976039771 & -3.99266015296568 & 0.0854023960228708 & 0.783657362076313 \tabularnewline
21 & 88.2 & 88.1149963563439 & -2.03161725172513 & 0.0850036436560621 & 0.90479440060958 \tabularnewline
22 & 88.7 & 88.6151229739679 & -0.926574488919616 & 0.0848770260320904 & 0.509853432100263 \tabularnewline
23 & 91.4 & 91.315225183108 & 0.65641069458144 & 0.0847748168920425 & 0.730372157136665 \tabularnewline
24 & 95.7 & 95.6152830486152 & 2.24682185803587 & 0.0847169513848283 & 0.733799011834588 \tabularnewline
25 & 96.8 & 97.7496190816659 & 2.19841923133305 & -0.949619081665916 & -0.0241977539428367 \tabularnewline
26 & 93.8 & 93.7984754432179 & -0.328763823923405 & 0.00152455678206713 & -1.09858470442761 \tabularnewline
27 & 91 & 90.9940296049081 & -1.41318130843316 & 0.00597039509185428 & -0.496667869640587 \tabularnewline
28 & 86.8 & 86.7912081126492 & -2.63166593360104 & 0.00879188735079182 & -0.560883601240605 \tabularnewline
29 & 91.5 & 91.4953892081869 & 0.570286314377252 & 0.0046107918131171 & 1.47625167274855 \tabularnewline
30 & 89.3 & 89.2944990806568 & -0.639136912831987 & 0.00550091934317543 & -0.557883902879592 \tabularnewline
31 & 97.9 & 97.8961718580003 & 3.39392331423661 & 0.00382814199971486 & 1.86067310039407 \tabularnewline
32 & 95.7 & 95.6956011489162 & 0.952158525736878 & 0.00439885108375714 & -1.12657828705229 \tabularnewline
33 & 86.9 & 86.8950404954603 & -3.30463900771774 & 0.00495950453969375 & -1.96402760062763 \tabularnewline
34 & 82 & 81.9949888122546 & -4.00100827952587 & 0.00501118774537626 & -0.321296820368189 \tabularnewline
35 & 83.2 & 83.1950837579192 & -1.73078975390916 & 0.00491624208079016 & 1.0474545847544 \tabularnewline
36 & 85.7 & 85.6951272796625 & 0.115931721353522 & 0.00487272033751208 & 0.852058010489893 \tabularnewline
37 & 77.8 & 78.5943953640105 & -3.00499484997968 & -0.794395364010496 & -1.51898039264716 \tabularnewline
38 & 79.4 & 79.2902330938294 & -1.45914586738184 & 0.109766906170631 & 0.684633115776445 \tabularnewline
39 & 83.4 & 83.2974928792266 & 0.933110167260973 & 0.10250712077337 & 1.09776792426153 \tabularnewline
40 & 102.8 & 102.711318026123 & 9.00387383886214 & 0.0886819738771911 & 3.71733539541066 \tabularnewline
41 & 108.7 & 108.610009012303 & 7.64851046343682 & 0.0899909876973572 & -0.625007523513729 \tabularnewline
42 & 120.3 & 120.210947991664 & 9.37353498484777 & 0.0890520083360022 & 0.79576979935185 \tabularnewline
43 & 121.9 & 121.809907118883 & 5.98028573725389 & 0.0900928811172826 & -1.56552351985895 \tabularnewline
44 & 112.7 & 112.608761732321 & -0.645926274023385 & 0.0912382676792284 & -3.05721206528552 \tabularnewline
45 & 113.1 & 113.008806202529 & -0.18938221093449 & 0.0911937974712242 & 0.210643540288397 \tabularnewline
46 & 115.7 & 115.608873032764 & 1.02817243330608 & 0.091126967236084 & 0.56176614297116 \tabularnewline
47 & 113.5 & 113.40882944959 & -0.380911233063526 & 0.0911705504100079 & -0.650136285302349 \tabularnewline
48 & 103.1 & 103.008753226313 & -4.75420005751946 & 0.0912467736867718 & -2.01778993714595 \tabularnewline
49 & 95.9 & 96.9992469465751 & -5.29838100961228 & -1.0992469465751 & -0.261339832045585 \tabularnewline
50 & 88.5 & 88.4263476600077 & -6.67901970980446 & 0.0736523399923543 & -0.617476020986335 \tabularnewline
51 & 86.2 & 86.1309664585227 & -4.76164005330731 & 0.0690335414773148 & 0.880845675426067 \tabularnewline
52 & 83.8 & 83.7323690394473 & -3.72977522181329 & 0.0676309605527155 & 0.475439289511135 \tabularnewline
53 & 76.4 & 76.3311410388602 & -5.33231511908649 & 0.0688589611398459 & -0.739073455874701 \tabularnewline
54 & 76 & 75.9320709051413 & -3.1791666399046 & 0.0679290948586814 & 0.99330311824934 \tabularnewline
55 & 75.7 & 75.6323767654644 & -1.92238326790762 & 0.0676232345355793 & 0.579841409454633 \tabularnewline
56 & 71.5 & 71.4322404230724 & -2.91656296316384 & 0.0677595769276244 & -0.458697848803749 \tabularnewline
57 & 69.7 & 69.6322780873561 & -2.42918657640342 & 0.0677219126438736 & 0.224869435888582 \tabularnewline
58 & 72.1 & 72.0323698820214 & -0.32126570084123 & 0.067630117978556 & 0.972571554861737 \tabularnewline
59 & 72.6 & 72.5323786788138 & 0.037213287422581 & 0.0676213211862349 & 0.165398429096026 \tabularnewline
60 & 70.2 & 70.1323639681774 & -1.02661972144979 & 0.0676360318226069 & -0.490841493784291 \tabularnewline
61 & 69.4 & 70.0847977217866 & -0.601593858156112 & -0.684797721786567 & 0.202486740569827 \tabularnewline
62 & 68 & 67.9479365865702 & -1.2528556796831 & 0.0520634134297711 & -0.293028349964671 \tabularnewline
63 & 63.1 & 63.0447491448565 & -2.84892899189315 & 0.0552508551434875 & -0.733780075446004 \tabularnewline
64 & 59.4 & 59.3443302729733 & -3.22072216289711 & 0.0556697270266678 & -0.17134667003916 \tabularnewline
65 & 59.3 & 59.2451956000565 & -1.85818626793987 & 0.0548043999434662 & 0.628433158050689 \tabularnewline
66 & 61.2 & 61.1457827824268 & -0.217618958147732 & 0.054217217573248 & 0.756854079295651 \tabularnewline
67 & 59.8 & 59.7456786848441 & -0.733736628787317 & 0.0543213151558563 & -0.238122698223196 \tabularnewline
68 & 61.3 & 61.2457895026774 & 0.241287723643142 & 0.054210497322579 & 0.449860968659552 \tabularnewline
69 & 60.2 & 60.145752005718 & -0.344180027577637 & 0.0542479942819853 & -0.270127782815867 \tabularnewline
70 & 59.7 & 59.6457495510416 & -0.412194818580174 & 0.0542504489583853 & -0.0313812855734852 \tabularnewline
71 & 60.7 & 60.6457620871562 & 0.204222184327295 & 0.0542379128438227 & 0.284408333765613 \tabularnewline
72 & 59.8 & 59.7457565635579 & -0.277765992221112 & 0.0542434364420591 & -0.22238434071184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195093&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]112.8[/C][C]112.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]116.7[/C][C]116.517222998974[/C][C]0.567834594714074[/C][C]0.182777001025732[/C][C]0.565409390838798[/C][/ROW]
[ROW][C]3[/C][C]119.4[/C][C]119.231765741215[/C][C]1.38057117208508[/C][C]0.168234258784778[/C][C]0.449989653489851[/C][/ROW]
[ROW][C]4[/C][C]129.8[/C][C]129.667546927876[/C][C]5.15398787451447[/C][C]0.132453072124165[/C][C]1.84545415201493[/C][/ROW]
[ROW][C]5[/C][C]131.9[/C][C]131.760649294732[/C][C]3.83869893732185[/C][C]0.139350705268115[/C][C]-0.618222697451815[/C][/ROW]
[ROW][C]6[/C][C]129.8[/C][C]129.653066187873[/C][C]1.25748740411035[/C][C]0.146933812127264[/C][C]-1.19798656557481[/C][/ROW]
[ROW][C]7[/C][C]131.6[/C][C]131.453456953824[/C][C]1.49397222226914[/C][C]0.14654304617585[/C][C]0.109316176821515[/C][/ROW]
[ROW][C]8[/C][C]134.3[/C][C]134.15394662628[/C][C]2.02017240916277[/C][C]0.146053373719683[/C][C]0.242927760095655[/C][/ROW]
[ROW][C]9[/C][C]136.7[/C][C]136.554033537925[/C][C]2.18594291709768[/C][C]0.145966462075126[/C][C]0.076499245707281[/C][/ROW]
[ROW][C]10[/C][C]134.7[/C][C]134.55349378301[/C][C]0.358876189159077[/C][C]0.146506216989863[/C][C]-0.84304027188398[/C][/ROW]
[ROW][C]11[/C][C]138.1[/C][C]137.953714756069[/C][C]1.68629516154975[/C][C]0.146285243931395[/C][C]0.612469067079526[/C][/ROW]
[ROW][C]12[/C][C]132.4[/C][C]132.253412322041[/C][C]-1.53777619742481[/C][C]0.146587677959371[/C][C]-1.48756222230761[/C][/ROW]
[ROW][C]13[/C][C]125[/C][C]127.652597566725[/C][C]-2.8339663446751[/C][C]-2.6525975667247[/C][C]-0.702772644611231[/C][/ROW]
[ROW][C]14[/C][C]117.7[/C][C]117.613890868718[/C][C]-5.69158112658533[/C][C]0.0861091312824908[/C][C]-1.18297478689257[/C][/ROW]
[ROW][C]15[/C][C]112[/C][C]111.913867470041[/C][C]-5.69528611708848[/C][C]0.0861325299592146[/C][C]-0.0016901095667935[/C][/ROW]
[ROW][C]16[/C][C]106.3[/C][C]106.213860099523[/C][C]-5.69734906362555[/C][C]0.0861399004772734[/C][C]-0.000948392573978235[/C][/ROW]
[ROW][C]17[/C][C]100.5[/C][C]100.413769713474[/C][C]-5.74219276785388[/C][C]0.0862302865255695[/C][C]-0.0206667241431879[/C][/ROW]
[ROW][C]18[/C][C]95.6[/C][C]95.5141875044392[/C][C]-5.37448289366277[/C][C]0.0858124955608021[/C][C]0.169595814827971[/C][/ROW]
[ROW][C]19[/C][C]89.5[/C][C]89.4139847060613[/C][C]-5.69119430135892[/C][C]0.086015293938747[/C][C]-0.146110489626483[/C][/ROW]
[ROW][C]20[/C][C]87.7[/C][C]87.6145976039771[/C][C]-3.99266015296568[/C][C]0.0854023960228708[/C][C]0.783657362076313[/C][/ROW]
[ROW][C]21[/C][C]88.2[/C][C]88.1149963563439[/C][C]-2.03161725172513[/C][C]0.0850036436560621[/C][C]0.90479440060958[/C][/ROW]
[ROW][C]22[/C][C]88.7[/C][C]88.6151229739679[/C][C]-0.926574488919616[/C][C]0.0848770260320904[/C][C]0.509853432100263[/C][/ROW]
[ROW][C]23[/C][C]91.4[/C][C]91.315225183108[/C][C]0.65641069458144[/C][C]0.0847748168920425[/C][C]0.730372157136665[/C][/ROW]
[ROW][C]24[/C][C]95.7[/C][C]95.6152830486152[/C][C]2.24682185803587[/C][C]0.0847169513848283[/C][C]0.733799011834588[/C][/ROW]
[ROW][C]25[/C][C]96.8[/C][C]97.7496190816659[/C][C]2.19841923133305[/C][C]-0.949619081665916[/C][C]-0.0241977539428367[/C][/ROW]
[ROW][C]26[/C][C]93.8[/C][C]93.7984754432179[/C][C]-0.328763823923405[/C][C]0.00152455678206713[/C][C]-1.09858470442761[/C][/ROW]
[ROW][C]27[/C][C]91[/C][C]90.9940296049081[/C][C]-1.41318130843316[/C][C]0.00597039509185428[/C][C]-0.496667869640587[/C][/ROW]
[ROW][C]28[/C][C]86.8[/C][C]86.7912081126492[/C][C]-2.63166593360104[/C][C]0.00879188735079182[/C][C]-0.560883601240605[/C][/ROW]
[ROW][C]29[/C][C]91.5[/C][C]91.4953892081869[/C][C]0.570286314377252[/C][C]0.0046107918131171[/C][C]1.47625167274855[/C][/ROW]
[ROW][C]30[/C][C]89.3[/C][C]89.2944990806568[/C][C]-0.639136912831987[/C][C]0.00550091934317543[/C][C]-0.557883902879592[/C][/ROW]
[ROW][C]31[/C][C]97.9[/C][C]97.8961718580003[/C][C]3.39392331423661[/C][C]0.00382814199971486[/C][C]1.86067310039407[/C][/ROW]
[ROW][C]32[/C][C]95.7[/C][C]95.6956011489162[/C][C]0.952158525736878[/C][C]0.00439885108375714[/C][C]-1.12657828705229[/C][/ROW]
[ROW][C]33[/C][C]86.9[/C][C]86.8950404954603[/C][C]-3.30463900771774[/C][C]0.00495950453969375[/C][C]-1.96402760062763[/C][/ROW]
[ROW][C]34[/C][C]82[/C][C]81.9949888122546[/C][C]-4.00100827952587[/C][C]0.00501118774537626[/C][C]-0.321296820368189[/C][/ROW]
[ROW][C]35[/C][C]83.2[/C][C]83.1950837579192[/C][C]-1.73078975390916[/C][C]0.00491624208079016[/C][C]1.0474545847544[/C][/ROW]
[ROW][C]36[/C][C]85.7[/C][C]85.6951272796625[/C][C]0.115931721353522[/C][C]0.00487272033751208[/C][C]0.852058010489893[/C][/ROW]
[ROW][C]37[/C][C]77.8[/C][C]78.5943953640105[/C][C]-3.00499484997968[/C][C]-0.794395364010496[/C][C]-1.51898039264716[/C][/ROW]
[ROW][C]38[/C][C]79.4[/C][C]79.2902330938294[/C][C]-1.45914586738184[/C][C]0.109766906170631[/C][C]0.684633115776445[/C][/ROW]
[ROW][C]39[/C][C]83.4[/C][C]83.2974928792266[/C][C]0.933110167260973[/C][C]0.10250712077337[/C][C]1.09776792426153[/C][/ROW]
[ROW][C]40[/C][C]102.8[/C][C]102.711318026123[/C][C]9.00387383886214[/C][C]0.0886819738771911[/C][C]3.71733539541066[/C][/ROW]
[ROW][C]41[/C][C]108.7[/C][C]108.610009012303[/C][C]7.64851046343682[/C][C]0.0899909876973572[/C][C]-0.625007523513729[/C][/ROW]
[ROW][C]42[/C][C]120.3[/C][C]120.210947991664[/C][C]9.37353498484777[/C][C]0.0890520083360022[/C][C]0.79576979935185[/C][/ROW]
[ROW][C]43[/C][C]121.9[/C][C]121.809907118883[/C][C]5.98028573725389[/C][C]0.0900928811172826[/C][C]-1.56552351985895[/C][/ROW]
[ROW][C]44[/C][C]112.7[/C][C]112.608761732321[/C][C]-0.645926274023385[/C][C]0.0912382676792284[/C][C]-3.05721206528552[/C][/ROW]
[ROW][C]45[/C][C]113.1[/C][C]113.008806202529[/C][C]-0.18938221093449[/C][C]0.0911937974712242[/C][C]0.210643540288397[/C][/ROW]
[ROW][C]46[/C][C]115.7[/C][C]115.608873032764[/C][C]1.02817243330608[/C][C]0.091126967236084[/C][C]0.56176614297116[/C][/ROW]
[ROW][C]47[/C][C]113.5[/C][C]113.40882944959[/C][C]-0.380911233063526[/C][C]0.0911705504100079[/C][C]-0.650136285302349[/C][/ROW]
[ROW][C]48[/C][C]103.1[/C][C]103.008753226313[/C][C]-4.75420005751946[/C][C]0.0912467736867718[/C][C]-2.01778993714595[/C][/ROW]
[ROW][C]49[/C][C]95.9[/C][C]96.9992469465751[/C][C]-5.29838100961228[/C][C]-1.0992469465751[/C][C]-0.261339832045585[/C][/ROW]
[ROW][C]50[/C][C]88.5[/C][C]88.4263476600077[/C][C]-6.67901970980446[/C][C]0.0736523399923543[/C][C]-0.617476020986335[/C][/ROW]
[ROW][C]51[/C][C]86.2[/C][C]86.1309664585227[/C][C]-4.76164005330731[/C][C]0.0690335414773148[/C][C]0.880845675426067[/C][/ROW]
[ROW][C]52[/C][C]83.8[/C][C]83.7323690394473[/C][C]-3.72977522181329[/C][C]0.0676309605527155[/C][C]0.475439289511135[/C][/ROW]
[ROW][C]53[/C][C]76.4[/C][C]76.3311410388602[/C][C]-5.33231511908649[/C][C]0.0688589611398459[/C][C]-0.739073455874701[/C][/ROW]
[ROW][C]54[/C][C]76[/C][C]75.9320709051413[/C][C]-3.1791666399046[/C][C]0.0679290948586814[/C][C]0.99330311824934[/C][/ROW]
[ROW][C]55[/C][C]75.7[/C][C]75.6323767654644[/C][C]-1.92238326790762[/C][C]0.0676232345355793[/C][C]0.579841409454633[/C][/ROW]
[ROW][C]56[/C][C]71.5[/C][C]71.4322404230724[/C][C]-2.91656296316384[/C][C]0.0677595769276244[/C][C]-0.458697848803749[/C][/ROW]
[ROW][C]57[/C][C]69.7[/C][C]69.6322780873561[/C][C]-2.42918657640342[/C][C]0.0677219126438736[/C][C]0.224869435888582[/C][/ROW]
[ROW][C]58[/C][C]72.1[/C][C]72.0323698820214[/C][C]-0.32126570084123[/C][C]0.067630117978556[/C][C]0.972571554861737[/C][/ROW]
[ROW][C]59[/C][C]72.6[/C][C]72.5323786788138[/C][C]0.037213287422581[/C][C]0.0676213211862349[/C][C]0.165398429096026[/C][/ROW]
[ROW][C]60[/C][C]70.2[/C][C]70.1323639681774[/C][C]-1.02661972144979[/C][C]0.0676360318226069[/C][C]-0.490841493784291[/C][/ROW]
[ROW][C]61[/C][C]69.4[/C][C]70.0847977217866[/C][C]-0.601593858156112[/C][C]-0.684797721786567[/C][C]0.202486740569827[/C][/ROW]
[ROW][C]62[/C][C]68[/C][C]67.9479365865702[/C][C]-1.2528556796831[/C][C]0.0520634134297711[/C][C]-0.293028349964671[/C][/ROW]
[ROW][C]63[/C][C]63.1[/C][C]63.0447491448565[/C][C]-2.84892899189315[/C][C]0.0552508551434875[/C][C]-0.733780075446004[/C][/ROW]
[ROW][C]64[/C][C]59.4[/C][C]59.3443302729733[/C][C]-3.22072216289711[/C][C]0.0556697270266678[/C][C]-0.17134667003916[/C][/ROW]
[ROW][C]65[/C][C]59.3[/C][C]59.2451956000565[/C][C]-1.85818626793987[/C][C]0.0548043999434662[/C][C]0.628433158050689[/C][/ROW]
[ROW][C]66[/C][C]61.2[/C][C]61.1457827824268[/C][C]-0.217618958147732[/C][C]0.054217217573248[/C][C]0.756854079295651[/C][/ROW]
[ROW][C]67[/C][C]59.8[/C][C]59.7456786848441[/C][C]-0.733736628787317[/C][C]0.0543213151558563[/C][C]-0.238122698223196[/C][/ROW]
[ROW][C]68[/C][C]61.3[/C][C]61.2457895026774[/C][C]0.241287723643142[/C][C]0.054210497322579[/C][C]0.449860968659552[/C][/ROW]
[ROW][C]69[/C][C]60.2[/C][C]60.145752005718[/C][C]-0.344180027577637[/C][C]0.0542479942819853[/C][C]-0.270127782815867[/C][/ROW]
[ROW][C]70[/C][C]59.7[/C][C]59.6457495510416[/C][C]-0.412194818580174[/C][C]0.0542504489583853[/C][C]-0.0313812855734852[/C][/ROW]
[ROW][C]71[/C][C]60.7[/C][C]60.6457620871562[/C][C]0.204222184327295[/C][C]0.0542379128438227[/C][C]0.284408333765613[/C][/ROW]
[ROW][C]72[/C][C]59.8[/C][C]59.7457565635579[/C][C]-0.277765992221112[/C][C]0.0542434364420591[/C][C]-0.22238434071184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195093&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	112.8	112.8	0	0	0
2	116.7	116.517222998974	0.567834594714074	0.182777001025732	0.565409390838798
3	119.4	119.231765741215	1.38057117208508	0.168234258784778	0.449989653489851
4	129.8	129.667546927876	5.15398787451447	0.132453072124165	1.84545415201493
5	131.9	131.760649294732	3.83869893732185	0.139350705268115	-0.618222697451815
6	129.8	129.653066187873	1.25748740411035	0.146933812127264	-1.19798656557481
7	131.6	131.453456953824	1.49397222226914	0.14654304617585	0.109316176821515
8	134.3	134.15394662628	2.02017240916277	0.146053373719683	0.242927760095655
9	136.7	136.554033537925	2.18594291709768	0.145966462075126	0.076499245707281
10	134.7	134.55349378301	0.358876189159077	0.146506216989863	-0.84304027188398
11	138.1	137.953714756069	1.68629516154975	0.146285243931395	0.612469067079526
12	132.4	132.253412322041	-1.53777619742481	0.146587677959371	-1.48756222230761
13	125	127.652597566725	-2.8339663446751	-2.6525975667247	-0.702772644611231
14	117.7	117.613890868718	-5.69158112658533	0.0861091312824908	-1.18297478689257
15	112	111.913867470041	-5.69528611708848	0.0861325299592146	-0.0016901095667935
16	106.3	106.213860099523	-5.69734906362555	0.0861399004772734	-0.000948392573978235
17	100.5	100.413769713474	-5.74219276785388	0.0862302865255695	-0.0206667241431879
18	95.6	95.5141875044392	-5.37448289366277	0.0858124955608021	0.169595814827971
19	89.5	89.4139847060613	-5.69119430135892	0.086015293938747	-0.146110489626483
20	87.7	87.6145976039771	-3.99266015296568	0.0854023960228708	0.783657362076313
21	88.2	88.1149963563439	-2.03161725172513	0.0850036436560621	0.90479440060958
22	88.7	88.6151229739679	-0.926574488919616	0.0848770260320904	0.509853432100263
23	91.4	91.315225183108	0.65641069458144	0.0847748168920425	0.730372157136665
24	95.7	95.6152830486152	2.24682185803587	0.0847169513848283	0.733799011834588
25	96.8	97.7496190816659	2.19841923133305	-0.949619081665916	-0.0241977539428367
26	93.8	93.7984754432179	-0.328763823923405	0.00152455678206713	-1.09858470442761
27	91	90.9940296049081	-1.41318130843316	0.00597039509185428	-0.496667869640587
28	86.8	86.7912081126492	-2.63166593360104	0.00879188735079182	-0.560883601240605
29	91.5	91.4953892081869	0.570286314377252	0.0046107918131171	1.47625167274855
30	89.3	89.2944990806568	-0.639136912831987	0.00550091934317543	-0.557883902879592
31	97.9	97.8961718580003	3.39392331423661	0.00382814199971486	1.86067310039407
32	95.7	95.6956011489162	0.952158525736878	0.00439885108375714	-1.12657828705229
33	86.9	86.8950404954603	-3.30463900771774	0.00495950453969375	-1.96402760062763
34	82	81.9949888122546	-4.00100827952587	0.00501118774537626	-0.321296820368189
35	83.2	83.1950837579192	-1.73078975390916	0.00491624208079016	1.0474545847544
36	85.7	85.6951272796625	0.115931721353522	0.00487272033751208	0.852058010489893
37	77.8	78.5943953640105	-3.00499484997968	-0.794395364010496	-1.51898039264716
38	79.4	79.2902330938294	-1.45914586738184	0.109766906170631	0.684633115776445
39	83.4	83.2974928792266	0.933110167260973	0.10250712077337	1.09776792426153
40	102.8	102.711318026123	9.00387383886214	0.0886819738771911	3.71733539541066
41	108.7	108.610009012303	7.64851046343682	0.0899909876973572	-0.625007523513729
42	120.3	120.210947991664	9.37353498484777	0.0890520083360022	0.79576979935185
43	121.9	121.809907118883	5.98028573725389	0.0900928811172826	-1.56552351985895
44	112.7	112.608761732321	-0.645926274023385	0.0912382676792284	-3.05721206528552
45	113.1	113.008806202529	-0.18938221093449	0.0911937974712242	0.210643540288397
46	115.7	115.608873032764	1.02817243330608	0.091126967236084	0.56176614297116
47	113.5	113.40882944959	-0.380911233063526	0.0911705504100079	-0.650136285302349
48	103.1	103.008753226313	-4.75420005751946	0.0912467736867718	-2.01778993714595
49	95.9	96.9992469465751	-5.29838100961228	-1.0992469465751	-0.261339832045585
50	88.5	88.4263476600077	-6.67901970980446	0.0736523399923543	-0.617476020986335
51	86.2	86.1309664585227	-4.76164005330731	0.0690335414773148	0.880845675426067
52	83.8	83.7323690394473	-3.72977522181329	0.0676309605527155	0.475439289511135
53	76.4	76.3311410388602	-5.33231511908649	0.0688589611398459	-0.739073455874701
54	76	75.9320709051413	-3.1791666399046	0.0679290948586814	0.99330311824934
55	75.7	75.6323767654644	-1.92238326790762	0.0676232345355793	0.579841409454633
56	71.5	71.4322404230724	-2.91656296316384	0.0677595769276244	-0.458697848803749
57	69.7	69.6322780873561	-2.42918657640342	0.0677219126438736	0.224869435888582
58	72.1	72.0323698820214	-0.32126570084123	0.067630117978556	0.972571554861737
59	72.6	72.5323786788138	0.037213287422581	0.0676213211862349	0.165398429096026
60	70.2	70.1323639681774	-1.02661972144979	0.0676360318226069	-0.490841493784291
61	69.4	70.0847977217866	-0.601593858156112	-0.684797721786567	0.202486740569827
62	68	67.9479365865702	-1.2528556796831	0.0520634134297711	-0.293028349964671
63	63.1	63.0447491448565	-2.84892899189315	0.0552508551434875	-0.733780075446004
64	59.4	59.3443302729733	-3.22072216289711	0.0556697270266678	-0.17134667003916
65	59.3	59.2451956000565	-1.85818626793987	0.0548043999434662	0.628433158050689
66	61.2	61.1457827824268	-0.217618958147732	0.054217217573248	0.756854079295651
67	59.8	59.7456786848441	-0.733736628787317	0.0543213151558563	-0.238122698223196
68	61.3	61.2457895026774	0.241287723643142	0.054210497322579	0.449860968659552
69	60.2	60.145752005718	-0.344180027577637	0.0542479942819853	-0.270127782815867
70	59.7	59.6457495510416	-0.412194818580174	0.0542504489583853	-0.0313812855734852
71	60.7	60.6457620871562	0.204222184327295	0.0542379128438227	0.284408333765613
72	59.8	59.7457565635579	-0.277765992221112	0.0542434364420591	-0.22238434071184

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