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WS09 - Local level model, local trend model, and basic structural model

*The author of this computation has been verified*

R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)

Title produced by software: Structural Time Series Models

Date of computation: Wed, 02 Dec 2009 13:43:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz.htm/, Retrieved Wed, 02 Dec 2009 21:45:41 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

423.4 404.1 500 472.6 496.1 562 434.8 538.2 577.6 518.1 625.2 561.2 523.3 536.1 607.3 637.3 606.9 652.9 617.2 670.4 729.9 677.2 710 844.3 748.2 653.9 742.6 854.2 808.4 1819 1936.5 1966.1 2083.1 1620.1 1527.6 1795 1685.1 1851.8 2164.4 1981.8 1726.5 2144.6 1758.2 1672.9 1837.3 1596.1 1446 1898.4 1964.1 1755.9 2255.3 1881.2 2117.9 1656.5 1544.1 2098.9 2133.3 1963.5 1801.2 2365.4 1936.5 1667.6 1983.5 2058.6 2448.3 1858.1 1625.4 2130.6 2515.7 2230.2 2086.9 2235 2100.2 2288.6 2490 2573.7 2543.8 2004.7 2390 2338.4 2724.5 2292.5 2386 2477.9 2337 2605.1 2560.8 2839.3 2407.2 2085.2 2735.6 2798.7 3053.2 2405 2471.9 2727.3 2790.7 2385.4 3206.6 2705.6 3518.4 1954.9 2584.3 2535.8 2685.9 2866 2236.6 2934.9 2668.6 2371.2 3165.9 2887.2 3112.2 2671.2 2432.6 2812.3 3095.7 2862.9 2607.3 2862.5

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	423.4	423.4	0	0	0
2	404.1	414.681615828779	-0.79705651882702	-1.93728484637907	-0.0748849046629789
3	500	451.460369099	1.96301562745611	10.7048791179609	0.33105286135969
4	472.6	461.92035405361	2.42724040973775	1.19894904926220	0.080670994278407
5	496.1	476.585110875684	2.95340393080522	5.10842524021229	0.120787400133489
6	562	511.918583769467	4.12152958075158	10.8796997287959	0.326151303350756
7	434.8	483.36101361428	3.07995286631461	-8.38288153604376	-0.332851874718943
8	538.2	504.404515559841	3.60474448313365	11.5128158055671	0.184140383918859
9	577.6	534.879736224004	4.34198399441463	9.21028925041608	0.276498908524525
10	518.1	530.278681808333	4.10796450356718	-0.987949681849582	-0.0922457911814492
11	625.2	568.257220577168	4.96141112643288	14.4621526986920	0.349928097632418
12	561.2	567.938170942389	4.83253310576678	-0.104420004486369	-0.0546163700688248
13	523.3	572.105013476562	4.89491405168368	-47.8183911310501	-0.00919973127486513
14	536.1	562.187699228511	4.43310186613281	-10.9255770722826	-0.133816320615445
15	607.3	577.399406168213	4.79974553977373	18.6389051112383	0.100182128668110
16	637.3	603.672299247585	5.38706338991811	9.45223287896997	0.211532665589422
17	606.9	608.502827307186	5.37483467316522	-0.950844547061103	-0.00564945171623517
18	652.9	622.119088800349	5.52807326885415	20.9410222413410	0.084853066246064
19	617.2	627.547305804706	5.52641884647024	-10.2269552614216	-0.00103529745057395
20	670.4	643.566830445431	5.68743458374923	14.1238750253802	0.109187500165899
21	729.9	675.802698841356	6.07459358960958	21.8533397546293	0.276810524347979
22	677.2	683.520905304843	6.09772562141712	-8.32039906787182	0.0171578244000113
23	710	691.273591909463	6.12008661265377	16.7103911967106	0.0172911155801777
24	844.3	752.365548572271	6.67933282384765	24.6177126429685	0.57569474685432
25	748.2	777.59647839865	6.03121236921146	-53.9259589268945	0.219212382849823
26	653.9	741.138467698815	5.34676458649737	-39.9442839008349	-0.417958907922997
27	742.6	736.503594475234	5.1193925347843	16.9095226695473	-0.096937755290350
28	854.2	779.546856226033	5.87366316703624	31.9568568367488	0.380285134192497
29	808.4	797.389028923652	6.06923663547251	-2.84762212319504	0.122649098111375
30	1819	1170.15651069708	11.1366676903444	217.872836008404	3.80015891535140
31	1936.5	1488.28012587611	14.8987516905338	84.6909338240146	3.19929130714277
32	1966.1	1691.36922728271	17.0298511277811	51.0021300194606	1.96694818968353
33	2083.1	1849.50998201992	18.5486156662294	65.471507412887	1.47721516434563
34	1620.1	1788.4777369985	17.7261832801294	-73.436811757611	-0.833887993254807
35	1527.6	1694.65728535002	16.6717882644994	-33.7550595192486	-1.16984570448234
36	1795	1726.19201599965	16.7483788139583	50.9301593016458	0.156422452801543
37	1685.1	1760.34076960241	16.4555387359094	-97.1265453087756	0.194589179903709
38	1851.8	1824.19918622291	16.9218919230483	-26.5977918547481	0.481696763552767
39	2164.4	1960.53764821524	18.9332150880959	71.8644862312695	1.18763942944971
40	1981.8	1979.47479652846	18.9332779878966	2.32077025052791	3.98189781001649e-05
41	1726.5	1939.37886136656	18.1296235182491	-144.950031058440	-0.607563724682302
42	2144.6	1974.7923130348	18.3302201976358	149.664961888909	0.179625438413395
43	1758.2	1899.13047308939	17.3659908728787	-30.6418282790216	-0.981839150931345
44	1672.9	1816.22559675767	16.4204909906713	-25.2428046842766	-1.05024568558892
45	1837.3	1792.80645467560	16.0659004761360	91.5049021046926	-0.417898103098114
46	1596.1	1743.52800115373	15.5183945315555	-70.210851657177	-0.6860556357527
47	1446	1654.76417784715	14.7711028954023	-85.284521873523	-1.0958684107077
48	1898.4	1727.41590420138	14.9487957275431	102.020263968929	0.610623584245753
49	1964.1	1861.04976419486	13.9421765732852	-42.1591938061262	1.29270357376042
50	1755.9	1862.48411217444	13.8559090901685	-92.132150889158	-0.128962171458361
51	2255.3	1990.17034004615	15.3475786676892	137.512383421624	1.14950415400863
52	1881.2	1963.10006391371	14.7804943081271	-33.9229053299088	-0.432388162885295
53	2117.9	2080.50978582681	15.9961106998368	-80.4661267842994	1.05936803220661
54	1656.5	1880.20290960533	13.7773130051387	27.390221987977	-2.25165643708501
55	1544.1	1753.90771533616	12.5059259070236	-46.1741826399388	-1.46513487296703
56	2098.9	1877.47000313565	13.4266586630249	91.2347352244816	1.16468294381579
57	2133.3	1942.49910511026	13.8252903893520	130.180808765717	0.541963513517947
58	1963.5	1978.93098686500	13.9851713195094	-42.0292612880407	0.237644193091478
59	1801.2	1966.10319842372	13.8324159034571	-133.289056058794	-0.282124432613277
60	2365.4	2092.73407126232	14.0860404407878	138.958760602548	1.19117757119819
61	1936.5	2071.78207665818	14.2272948601356	-93.1080792983525	-0.376278806217526
62	1667.6	1978.78844622617	13.6464144891560	-186.733152716078	-1.11345639529800
63	1983.5	1927.78306376109	12.962650485947	128.942833260640	-0.659701973307434
64	2058.6	1995.57392398497	13.5883505236395	0.743690260151816	0.561960294236888
65	2448.3	2173.01149503698	15.3095151552976	87.1190956313598	1.69524300723591
66	1858.1	2058.68664583270	14.1068456028677	-50.3475590490785	-1.3510507818597
67	1625.4	1934.84652863461	12.9690761620916	-148.635292413847	-1.44417392948922
68	2130.6	1976.39287695622	13.1830798622253	120.777203758186	0.299952412488763
69	2515.7	2133.94521101020	14.1748973589787	212.509584883698	1.51756260181880
70	2230.2	2202.17826236837	14.5054764459158	-35.4542567700631	0.568748783384594
71	2086.9	2234.05589814963	14.5876076591898	-167.596093221383	0.182939477133200
72	2235	2189.90572881202	14.4708947643872	114.502439429009	-0.620417966237304
73	2100.2	2184.42537285255	14.5004052859691	-60.4498538718683	-0.212552185859943
74	2288.6	2292.50356683451	14.9332628256618	-112.757921127396	0.975540535709335
75	2490	2342.71872548968	15.2437089661143	107.024944595666	0.362650697387888
76	2573.7	2451.96924413409	16.1732639350564	14.4897244529040	0.967849557947195
77	2543.8	2452.76569912149	16.0285108241447	108.712075400525	-0.159421684123625
78	2004.7	2306.62130234491	14.6526230558671	-114.059869700991	-1.69184310816180
79	2390	2394.64187373071	15.2097974650261	-90.0876757891502	0.768604048349434
80	2338.4	2361.43475742451	14.8775509689728	33.544469182577	-0.508501667836641
81	2724.5	2426.80415528719	15.1907342646091	238.563235007658	0.531074532330278
82	2292.5	2404.33786085544	14.9876386803755	-67.6638149641772	-0.396423861622161
83	2386	2458.42793284984	15.1473524141049	-118.383274852990	0.411992538473963
84	2477.9	2438.09045135798	15.0775960910862	81.6509690256624	-0.374746211625817
85	2337	2443.87684561586	15.0771170248228	-95.874214394794	-0.0985211033689705
86	2605.1	2557.22525099611	15.4870396322428	-66.5662736083889	1.02681499152840
87	2560.8	2545.16301899572	15.2800292390497	47.2389521579837	-0.284660650886326
88	2839.3	2649.05489198203	16.0488255660766	88.7743203422224	0.915686935787295
89	2407.2	2523.57699703456	14.8464123661232	46.5665049617651	-1.47004283581418
90	2085.2	2415.59171377946	13.8878115060695	-188.083360113410	-1.28258112417302
91	2735.6	2557.63456336713	14.7900263003081	28.7696515393519	1.34329543921780
92	2798.7	2652.67717000838	15.2989649864161	52.2883829277495	0.843243234925903
93	3053.2	2722.64042473771	15.6085402854971	266.573236076617	0.575208881577013
94	2405	2651.85678697910	15.1902118076113	-145.567970819499	-0.909841148191891
95	2471.9	2631.60124309449	15.0606449165907	-118.074090159692	-0.373589867922924
96	2727.3	2645.29803489513	15.0578658894824	83.6075755735832	-0.0143987327864590
97	2790.7	2750.25840298078	15.1475446389026	-65.5897575590314	0.950619622651217
98	2385.4	2656.97056761019	14.7259312209612	-145.212663696169	-1.13470415528651
99	3206.6	2845.02599850767	15.8633057511006	161.963145975105	1.79791858199428
100	2705.6	2766.22739159178	15.1345934256816	48.1254107678746	-0.981206003165279
101	3518.4	3014.66607189713	16.9337009181384	234.697291023687	2.42745148945704
102	1954.9	2745.45148491047	14.8720388970241	-458.877676294272	-2.99044186614255
103	2584.3	2679.91275136416	14.3452339659046	-2.00502499422826	-0.843259468453997
104	2535.8	2615.69599597557	13.8822043049847	11.8428830372442	-0.82577610359993
105	2685.9	2538.2378708689	13.4055770850045	254.549053113237	-0.961436959811166
106	2866	2704.28898013606	14.0798540770138	-17.1945059219146	1.60804825770784
107	2236.6	2599.89671350018	13.6810622381244	-224.239518588987	-1.24891539579506
108	2934.9	2698.60906786369	13.8626526041147	136.310673994245	0.897397860258287
109	2668.6	2717.65110336349	13.8709089387702	-55.1434237360001	0.0546727393183424
110	2371.2	2673.05942045597	13.6549473201582	-233.705256149577	-0.6124209648126
111	3165.9	2790.35974383382	14.2601597808862	255.82761492746	1.07823695045743
112	2887.2	2839.57475916538	14.5013424591777	7.35649226674583	0.363242017332657
113	3112.2	2831.36679506593	14.3415894715205	307.061721915677	-0.236645570305387
114	2671.2	2934.6273847807	14.9346663846294	-366.557661306286	0.930013829035987
115	2432.6	2761.99644584600	13.7881684114683	-111.019332674058	-1.96785534708222
116	2812.3	2766.61741203591	13.7377415660165	56.3865451288016	-0.0963861001898183
117	3095.7	2813.79118085573	13.8997538714006	242.788194144845	0.3520256798499
118	2862.9	2837.32535856298	13.9391151715575	14.2855328265236	0.101514311857133
119	2607.3	2854.00993551540	13.9478119417654	-249.931027717017	0.0289453637617892
120	2862.5	2817.9611438155	13.8363005281297	103.267604395130	-0.527483258536329

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/1b5ly1259786589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/1b5ly1259786589.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/2i6471259786589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/2i6471259786589.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/3qcb21259786589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/3qcb21259786589.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/4tcgt1259786589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/4tcgt1259786589.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/57tla1259786589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259786700bp7p0e38nts7ltz/57tla1259786589.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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