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W8

*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: Thu, 16 Dec 2010 13:47:24 +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/16/t1292507134xa6lak2bk5y5xrk.htm/, Retrieved Thu, 16 Dec 2010 14:45:34 +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/16/t1292507134xa6lak2bk5y5xrk.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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	1856	1856	0	0	0
2	1834	1849.00677901170	-0.866277322744983	-2.24329946878328	-0.0855713141816245
3	2095	1932.98272858665	7.91315360135593	30.3037666386156	0.920773758514936
4	2164	2016.69035440675	14.2041073419567	25.1014935750664	0.845636642814966
5	2368	2140.49933996714	21.8000068151347	43.1513017068241	1.26244008784519
6	2072	2130.15911963160	19.8672794969790	-2.25688091100772	-0.379845280563682
7	2521	2261.33349198797	25.862680969871	61.1900955148915	1.34105053873475
8	1823	2136.32041325568	18.3974008317198	-39.423965567844	-1.84325536953674
9	1947	2077.51422861899	14.8195400449968	11.4327606166553	-0.952552636611803
10	2226	2126.38696308157	16.3193068923908	36.4383955337287	0.423076534649782
11	1754	2017.51072329800	11.0227401364538	-29.7753476532942	-1.56298930805744
12	1786	1944.16936521168	7.56725541500755	0.0449619722944906	-1.05681731523340
13	2072	1990.99009091908	4.20691014016583	-16.1671047233639	0.710048144374171
14	1846	1954.18839816044	2.45128100765119	-44.1090784671614	-0.45299504641554
15	2137	2009.06208467391	4.91904676918733	46.4979070242693	0.582329714445175
16	2466	2159.92599352002	11.1448985085202	64.5337828188391	1.70811593476162
17	2154	2163.90531180315	10.8680629798581	2.46546559649123	-0.0867712600011075
18	2289	2218.0988665271	12.4188735100711	-5.75741567923132	0.535093639741788
19	2628	2330.58527846132	15.809850826556	117.811508677249	1.25006117520687
20	2074	2281.13930355047	13.6810739621624	-89.0272948122377	-0.820636891225523
21	2798	2439.34959135606	18.2753137464588	95.7482196995303	1.82465241401208
22	2194	2371.67767874879	15.5910108578911	-20.8768197803889	-1.08751312069146
23	2442	2402.10081104947	16.0468710223893	12.7858510787277	0.187936077363493
24	2565	2464.69660752253	17.3624589556829	14.7072612847180	0.591781327679578
25	2063	2402.04145458738	18.2262497356037	-177.717587410971	-1.16202972002217
26	2069	2326.65277432987	15.2896804840721	-99.1994137369548	-1.12764028825202
27	2539	2389.44081057151	17.055214369634	71.9823248776717	0.559061662224207
28	1898	2234.48635564978	10.8855774559520	-47.9633952541951	-2.07263573808604
29	2139	2203.88817078151	9.4816737239956	6.39970239554116	-0.509872288447007
30	2408	2275.63837582326	11.4905110897147	23.736558254078	0.77463554178737
31	2725	2381.09227525354	14.4206572437398	178.562601230372	1.17701918071131
32	2201	2382.63913246473	14.0281865425366	-158.873148092259	-0.161888137601245
33	2311	2336.75775364768	12.2283479372056	80.4821492963715	-0.75498019042137
34	2548	2409.98220649803	14.0416909324939	29.6770280537185	0.769569425607615
35	2276	2384.50755821804	12.8870730139018	-38.2198331649597	-0.498952397018952
36	2351	2368.58902629516	12.1190646123319	33.8923124572294	-0.364724296551222
37	2280	2385.42280900641	12.1738123286146	-114.175031354706	0.0633912775576905
38	2057	2327.94259598895	10.1614584059506	-151.065283217200	-0.861337316732986
39	2479	2336.66805225396	10.1134980330295	144.722248268373	-0.0173292191185292
40	2379	2366.86214367166	10.7826949329479	-21.6430291312477	0.244871985749692
41	2295	2360.07316094591	10.2148201791189	-35.0685691830888	-0.216973648711578
42	2456	2395.73006322135	11.0131602683603	16.3805795171323	0.316754826213950
43	2546	2395.61138029551	10.6714660933779	169.707030922128	-0.139247368484586
44	2844	2573.39691129358	15.7247658343628	-20.3791710294614	2.09580207960602
45	2260	2488.94976368731	12.7262446978074	-54.2088309625798	-1.25797540059087
46	2981	2620.76101320660	16.2589540615583	152.287659701814	1.49648733015764
47	2678	2665.7356560585	17.095384275869	-37.925011731198	0.360960125513249
48	3440	2893.81661808253	22.839008243436	176.526110230800	2.65674965561724
49	2842	2938.68651894352	23.3039260859963	-135.973123208271	0.285899440905705
50	2450	2862.10826084632	20.436601228407	-239.893831489386	-1.24575796097112
51	2669	2771.68737159515	16.9254659812500	83.6828521885968	-1.35570838740394
52	2570	2720.36110431901	14.7418390907276	-35.2655862715918	-0.838064950177667
53	2540	2685.02859554352	13.1628254858881	-59.7967375329949	-0.61983686308221
54	2318	2581.09211173324	9.53422684537268	-62.3421865883817	-1.45797980804168
55	2930	2645.21584789585	11.2018569394381	190.793489767872	0.681986063803361
56	2947	2742.31365749409	13.7988532422547	56.4427221015941	1.07500750391916
57	2799	2804.95785169896	15.2642823010650	-90.3618215602581	0.611829607801072
58	2695	2753.51128142332	13.2790172231233	56.8329688057498	-0.83582675836851
59	2498	2717.7070331049	11.8411970288735	-134.821884037423	-0.614846815481384
60	2260	2538.59523166308	6.48111768344218	51.8947803347048	-2.39453214173193
61	2160	2444.55369558524	3.91505879898997	-108.927604101295	-1.28159821299290
62	2058	2381.70537075975	1.97750226012180	-208.804096629078	-0.834769491784797
63	2533	2387.04171876514	2.08106806611763	140.279646596819	0.0413896400698018
64	2150	2321.48386585283	-0.0295257670351129	-57.1638598374745	-0.83428850609375
65	2172	2280.31463812709	-1.30568991996116	-38.3765083462462	-0.510109454238787
66	2155	2265.23305283238	-1.7288004246389	-86.6928938143915	-0.171541391207341
67	3016	2432.57290923517	3.4170577072288	293.595461724956	2.11056718405261
68	2333	2405.63600829408	2.49979619006629	-20.5116395942459	-0.37939309740531
69	2355	2409.22103661744	2.53239547215348	-56.0860766746049	0.0135704865723837
70	2825	2504.08915999286	5.28732946332533	162.198722797145	1.15451019275586
71	2214	2448.34819454463	3.48802114676725	-129.483953671453	-0.762654530428371
72	2360	2395.47067015715	1.8673245581572	61.3812330177369	-0.704925769813531
73	2299	2388.72044565505	1.62873780590411	-74.8265596620747	-0.108848510766505
74	1746	2262.59654976619	-2.12063781186515	-297.256858216115	-1.59790282059093
75	2069	2146.95076894006	-5.57380209694953	114.591506381698	-1.40517554730947
76	2267	2180.80053256943	-4.36260147052931	19.4458187440966	0.487744441805661
77	1878	2105.38376152757	-6.54164654893659	-106.633113771674	-0.882131294759222
78	2266	2182.64700000811	-3.98550420144873	-59.6053000377485	1.04374403211719
79	2282	2127.30570945422	-5.54307626358428	242.514255916826	-0.640830163878807
80	2085	2116.22022759429	-5.71034662183146	-21.7307155127993	-0.0692189309974396
81	2277	2181.08825270887	-3.58981717229625	-24.9815040069481	0.881584589889836
82	2251	2149.46830874801	-4.42757764030574	149.535617282821	-0.34998674507118
83	1828	2082.93893196887	-6.26835944877092	-148.656071633200	-0.774877496247055
84	1954	2014.26624048412	-8.09194154849332	46.5110015635037	-0.779185214010929
85	1851	1962.56448749359	-9.34674068712734	-36.6427525560592	-0.548010317868758
86	1570	1913.9503117304	-10.5086568322436	-276.675434166961	-0.490968361799109
87	1852	1854.71095453821	-11.9807770009269	80.0816850315142	-0.604772216961945
88	2187	1926.65477727655	-9.42691385557034	118.050040346391	1.04044934941535
89	1855	1942.19192299707	-8.66730999875547	-129.614987252938	0.310207423429667
90	2218	2029.56573811184	-5.75339034670993	24.7637722803418	1.19633064528540
91	2253	2028.00783311825	-5.62653891135796	217.828615351986	0.0523391431891837
92	2028	2036.93750489552	-5.18788624879428	-33.8142100926095	0.181697849112385
93	2169	2074.20116509741	-3.91275450822712	22.2373944543963	0.529862829729522
94	1997	2001.13464696845	-5.98202638660238	114.01739906272	-0.862665377193845
95	2034	2036.44230017994	-4.75329285654099	-72.9296810737832	0.514710364202021
96	1791	1946.62220650160	-7.26467637208701	-10.4273775533224	-1.06114206637846
97	1627	1851.54785805209	-9.8405711001353	-74.2157290592173	-1.10015617688115
98	1631	1852.15693140741	-9.52971464220552	-239.028905045737	0.130581166644055
99	2319	1966.09050293135	-5.81293480165451	142.959579161602	1.53466733064561
100	1707	1867.14913930592	-8.63045763261929	-2.10266222141391	-1.15618207381797
101	1747	1867.95037643218	-8.34496784084239	-136.979209580839	0.117275995325598
102	2397	2007.41238061928	-3.87760144756737	137.855247428456	1.84135890111606
103	2059	1969.15952661878	-4.91439060864137	148.475365143973	-0.428757976994958
104	2251	2056.93713581241	-2.12483963010166	35.8474937121204	1.15660545882873
105	2558	2191.96649525593	1.99342062243652	131.933261120510	1.71102448419760
106	2406	2233.47975971899	3.1769030338036	105.105067274238	0.492697820953331
107	2049	2197.78441379926	2.01692405691674	-82.5289336980783	-0.4843128082832
108	2074	2157.87650933914	0.771393894626389	-12.4229404343499	-0.522692009093206
109	1734	2060.04507720472	-2.15036893325859	-157.596006541382	-1.23315430640682

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/1t3271292507239.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/1t3271292507239.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/2t3271292507239.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/2t3271292507239.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/3muks1292507239.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/3muks1292507239.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/4fl1v1292507239.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/4fl1v1292507239.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/5fl1v1292507239.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292507134xa6lak2bk5y5xrk/5fl1v1292507239.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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