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*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, 29 Dec 2010 14:42:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl.htm/, Retrieved Wed, 29 Dec 2010 15:40:06 +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/2010/Dec/29/t129363360024i2eodvjckcebl.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

1856 1834 2095 2164 2368 2072 2521 1823 1947 2226 1754 1786 2072 1846 2137 2466 2154 2289 2628 2074 2798 2194 2442 2565 2063 2069 2539 1898 2139 2408 2725 2201 2311 2548 2276 2351 2280 2057 2479 2379 2295 2456 2546 2844 2260 2981 2678 3440 2842 2450 2669 2570 2540 2318 2930 2947 2799 2695 2498 2260 2160 2058 2533 2150 2172 2155 3016 2333 2355 2825 2214 2360 2299 1746 2069 2267 1878 2266 2282 2085 2277 2251 1828 1954 1851 1570 1852 2187 1855 2218 2253 2028 2169 1997 2034 1791 1627 1631 2319 1707 1747 2397 2059 2251 2558 2406 2049 2074 1734

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	9 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	1856	1856	0	0	0
2	1834	1849.00401376043	-0.866462741645097	-2.24138791113759	-0.0855674077443585
3	2095	1933.00006849901	7.91207399924354	30.2739093958164	0.920814634266865
4	2164	2016.71277158759	14.2011147018338	25.0821306891067	0.845563690284613
5	2368	2140.53204876574	21.7948757506358	43.1166868924572	1.26237592739167
6	2072	2130.16637510345	19.8617121680156	-2.23569239351824	-0.380016029024471
7	2521	2261.36280714832	25.8561990768036	61.1387153721757	1.34112305919828
8	1823	2136.29664900874	18.3915213148299	-39.3565272526978	-1.84344776585951
9	1947	2077.48482602115	14.8150161536194	11.4390488237704	-0.952346721962866
10	2226	2126.37855059767	16.3153634926086	36.4100995634055	0.423300385229205
11	1754	2017.47077871442	11.0194791721335	-29.7247098481464	-1.56298140119547
12	1786	1944.12637724845	7.56517138428682	0.0591258798614192	-1.05657203296087
13	2072	1990.96328391624	4.2020392547632	-16.1605083059300	0.710194717180928
14	1846	1954.14102715993	2.44566442592975	-44.0540259228977	-0.453025048240505
15	2137	2009.04877432318	4.91468790750323	46.4590758796867	0.582652112027052
16	2466	2159.94999800892	11.1400832445387	64.464013730499	1.70827586330405
17	2154	2163.91736062963	10.8630840591197	2.46440825733971	-0.086840065289077
18	2289	2218.10365431485	12.4131555817080	-5.74891867167232	0.534950655984567
19	2628	2330.63375702498	15.8043479617601	117.697731107628	1.25039984990017
20	2074	2281.12892131806	13.6747461120318	-88.9364967324584	-0.821120371188022
21	2798	2439.38171610098	18.2685801572995	95.6644109911254	1.82484521325883
22	2194	2371.67665578113	15.5845803948641	-20.8502603530585	-1.08759196202597
23	2442	2402.09766035342	16.0403872045896	12.7851323731704	0.187946057405880
24	2565	2464.69633364254	17.3557492846899	14.7035553913065	0.591757011560477
25	2063	2402.01887979372	18.2222123787923	-177.687726262595	-1.16201889448117
26	2069	2326.58218760525	15.2844475949366	-99.0895446452328	-1.12782875331418
27	2539	2389.4105316299	17.0512586925777	71.9497540548032	0.559463970507761
28	1898	2234.43182245384	10.8830472682195	-47.9082378101042	-2.07243240584179
29	2139	2203.84386939866	9.4801405110519	6.41385312759767	-0.509604565413696
30	2408	2275.62278236465	11.4891012806336	23.7125971053252	0.774838753687826
31	2725	2381.13819449239	14.4199471795924	178.426969749659	1.17753880719335
32	2201	2382.62664898416	14.0258873333501	-158.761635421280	-0.162576001144295
33	2311	2336.75413416009	12.2271520125757	80.451777000753	-0.754663194328951
34	2548	2409.99349635531	14.0402137239295	29.6518349396965	0.769591630052417
35	2276	2384.49583283888	12.8854315314510	-38.1794947117766	-0.499106278086742
36	2351	2368.58196306914	12.1179081880454	33.8808509422194	-0.364557047304815
37	2280	2385.41613594782	12.1725533680226	-114.170130056734	0.063399443341562
38	2057	2327.88737573754	10.1592773979396	-150.951401315467	-0.861682006720261
39	2479	2336.65588903099	10.1128392468197	144.658733149978	-0.0167790817292452
40	2379	2366.84995375234	10.7818402290727	-21.6273864467535	0.244823544580364
41	2295	2360.04851760571	10.2138029055493	-35.0279408920613	-0.217067870507476
42	2456	2395.72408709213	11.0124437439252	16.3582790116231	0.316927589427486
43	2546	2395.63946382603	10.6719550042110	169.616043005943	-0.138780287798058
44	2844	2573.44512693157	15.7237965937197	-20.4222636467289	2.09555971322776
45	2260	2488.94555423471	12.7249435159341	-54.1387975858044	-1.25832639425816
46	2981	2620.80684516328	16.2577783919955	152.180914523204	1.49678019660481
47	2678	2665.76211759077	17.0933551838880	-37.9126994906149	0.360646363977283
48	3440	2893.89911708092	22.8360953038057	176.393358059848	2.65685016884167
49	2842	2938.73901089045	23.2999949757211	-135.972328396457	0.285488905055748
50	2450	2862.0751534925	20.4312235045217	-239.749285256507	-1.2464512490544
51	2669	2771.64253895017	16.9208290995776	83.7070981314688	-1.35544153240520
52	2570	2720.3095386397	14.7378155760905	-35.2273139203102	-0.83789219359093
53	2540	2684.96870346548	13.1592177338961	-59.7412705698716	-0.619746752675726
54	2318	2581.02329613585	9.53179944889732	-62.2918662517905	-1.45770808106484
55	2930	2645.2064582064	11.2006842931147	190.709487536901	0.682599401332796
56	2947	2742.34627320136	13.7979918751777	56.356485028651	1.07529534764335
57	2799	2804.96294559299	15.2620634339766	-90.308873023946	0.611351643824623
58	2695	2753.50671652080	13.2773246172922	56.8339747241062	-0.835723001540595
59	2498	2717.67540803193	11.8393042714856	-134.758462468735	-0.615019709736363
60	2260	2538.55208320895	6.48122319330301	51.9076942854881	-2.39408691438801
61	2160	2444.51040588726	3.91682343995129	-108.907279511997	-1.28132608902420
62	2058	2381.63558023611	1.97912774313349	-208.704077553093	-0.834914159066098
63	2533	2387.00112370285	2.08351292572281	140.274588778856	0.0417188277800402
64	2150	2321.43473370249	-0.0267652538521386	-57.1136880869589	-0.83422318567053
65	2172	2280.26567939317	-1.30257983175175	-38.3332987440948	-0.510021742405173
66	2155	2265.18459602348	-1.72562061020482	-86.6433597727155	-0.171533679977553
67	3016	2432.61357365038	3.42098343655144	293.449334128135	2.11114338629866
68	2333	2405.67438384447	2.50387041773582	-20.5469214096226	-0.37938121631614
69	2355	2409.24683041836	2.53595760672286	-56.082978349615	0.0133590522323261
70	2825	2504.14560714921	5.29069178689218	162.118830888265	1.15457646958223
71	2214	2448.36772685131	3.49086567228421	-129.449506415065	-0.762977960121812
72	2360	2395.47726831333	1.87037824929759	61.3876679160496	-0.7049564700646
73	2299	2388.72627942566	1.63180812406517	-74.8278683188769	-0.108872620591849
74	1746	2262.54061257741	-2.11810716165301	-297.123617546189	-1.5983244210972
75	2069	2146.88895379273	-5.57044025139316	114.635788765717	-1.40492822372487
76	2267	2180.76661497741	-4.3588718740703	19.4486496620494	0.487929812371759
77	1878	2105.32636872957	-6.53802464069114	-106.547545733590	-0.882260019418131
78	2266	2182.61927647234	-3.98197201754566	-59.6009294012494	1.04382230096728
79	2282	2127.31194626323	-5.5380709547135	242.443024553837	-0.640299167523958
80	2085	2116.23987097918	-5.70502810286925	-21.7661479162565	-0.0690976463676675
81	2277	2181.12587026067	-3.58487897577327	-25.0228625437212	0.881533975400648
82	2251	2149.51279579999	-4.42227990805325	149.480722780880	-0.349879948945289
83	1828	2082.95325012733	-6.26343536482708	-148.625383508770	-0.77513685000886
84	1954	2014.26556831331	-8.08688068608497	46.5299202000564	-0.779249442295863
85	1851	1962.56479013236	-9.34124191358312	-36.6467867227512	-0.547937700483472
86	1570	1913.91562199681	-10.5039318689200	-276.581646333038	-0.491356676252319
87	1852	1854.66245356543	-11.9761274038354	80.1482206233398	-0.604852620666575
88	2187	1926.65233894198	-9.42183871789272	118.004728584497	1.04071032819889
89	1855	1942.17187521455	-8.66317904363502	-129.549947334817	0.309851790029715
90	2218	2029.58521290353	-5.74918531485462	24.7085047366001	1.19648834672343
91	2253	2028.0418463014	-5.6220658167709	217.778033368776	0.0524556287423158
92	2028	2036.97742852879	-5.18352445364373	-33.8528586311110	0.181672706971415
93	2169	2074.26071609937	-3.90838650949032	22.1626334273218	0.529927760982713
94	1997	2001.17639728716	-5.9775820121492	113.995851451709	-0.862737707536558
95	2034	2036.48627363584	-4.74936232318035	-72.9593243639823	0.514560753171482
96	1791	1946.62550762319	-7.26110378739564	-10.3763785558530	-1.06144687649336
97	1627	1851.53088775974	-9.83665587436138	-74.179953205435	-1.10020246269001
98	1631	1852.12836095423	-9.52637354476888	-238.971095626550	0.130356243790705
99	2319	1966.08434302041	-5.81027694954828	142.966942318331	1.53452832693994
100	1707	1867.11689864009	-8.62772817697718	-2.04662736199526	-1.15625865151546
101	1747	1867.9135505837	-8.34255613176523	-136.927495684913	0.117157091627650
102	2397	2007.44664374147	-3.87464698898578	137.742093047112	1.84177777839206
103	2059	1969.18298054706	-4.91149101521205	148.466540089527	-0.428827980104091
104	2251	2056.99571563387	-2.12194795263664	35.7578073675337	1.15673309234974
105	2558	2192.07096253954	1.99615022918312	131.790756402553	1.71115493565311
106	2406	2233.56519952296	3.17856041062205	105.066899044309	0.492309840561236
107	2049	2197.84130388033	2.01809952195158	-82.5443521411148	-0.48457406901269
108	2074	2157.89347190802	0.771812322923348	-12.3806992989925	-0.523080327638101
109	1734	2060.01427650079	-2.15025908393324	-157.507899649222	-1.23347114126401

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/1av511293633729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/1av511293633729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/22m4m1293633729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/22m4m1293633729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/3dvlp1293633729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/3dvlp1293633729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/4dvlp1293633729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/4dvlp1293633729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/5642a1293633729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363360024i2eodvjckcebl/5642a1293633729.ps (open in new window)

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')

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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