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Paper

*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: Tue, 28 Dec 2010 20:59:26 +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/28/t1293569840ttma8u0oeow7szz.htm/, Retrieved Tue, 28 Dec 2010 21:57:22 +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/28/t1293569840ttma8u0oeow7szz.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 «

235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 214126 206903 204442 220375 214320 212588 205816 202196 195722 198563 229139 229527 211868 203555 195770

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	235243	235243	0	0	0
2	230354	232283.475300317	-3118.98546718632	-1929.47530031745	-0.787770786139232
3	227184	226737.043058758	-4667.55045327995	446.956941242212	-0.314224091923093
4	221678	221561.922420082	-5005.54543250559	116.077579917826	-0.071999339595215
5	217142	216898.935455963	-4777.82355696093	243.064544037223	0.0449541604538859
6	219452	217433.461776764	-1312.92777950473	2018.53822323614	0.688572060871794
7	256446	245673.039130419	18012.034389361	10772.9608695808	3.85734568502129
8	265845	267933.871596819	20797.4692310085	-2088.87159681906	0.554935040690873
9	248624	260257.126115788	2125.53403808093	-11633.1261157883	-3.71935122915677
10	241114	244536.289229718	-9574.88059089592	-3422.28922971804	-2.33087005318605
11	229245	229277.411038897	-13300.5565978056	-32.411038896804	-0.742179145405557
12	231805	226913.205900511	-6132.7909741586	4891.79409948901	1.42785852085247
13	219277	220596.426578587	-6252.94520354418	-1319.4265785873	-0.0240284551797335
14	219313	218258.291322507	-3684.64827810473	1054.70867749254	0.520038923266318
15	212610	211882.273225669	-5403.86472967043	727.726774330758	-0.33946396850086
16	214771	210534.651651769	-2851.4499552408	4236.34834823129	0.515689148976804
17	211142	211986.062548644	-109.067057220854	-844.062548643847	0.550216572046135
18	211457	219667.008839153	4826.62660617173	-8210.00883915304	0.97900546599519
19	240048	230625.936858628	8692.09125520746	9422.0631413718	0.769657809871539
20	240636	235259.81343547	6129.7580031356	5376.18656452976	-0.510881514528709
21	230580	236834.342967043	3249.43051961296	-6254.34296704321	-0.573777676921273
22	208795	218436.564653128	-10440.6554181222	-9641.56465312842	-2.72716790482247
23	197922	202030.328090383	-14211.3805973328	-4108.32809038303	-0.751187175939356
24	194596	188821.104848968	-13578.7013261792	5774.89515103165	0.126098282857188
25	194581	190553.625863171	-3909.59532475463	4027.37413682891	1.932342386762
26	185686	184778.249522188	-5089.45660868973	907.750477812478	-0.2354425777624
27	178106	178163.860071679	-6046.06533564857	-57.8600716789767	-0.189976400953351
28	172608	170360.121716464	-7142.2339836255	2247.87828353585	-0.219140218164648
29	167302	169410.018440859	-3261.32092299261	-2108.01844085947	0.776881772309404
30	168053	176474.537922729	3213.05582589735	-8421.53792272916	1.28832533634249
31	202300	189940.055174568	9617.96389374864	12359.9448254316	1.27393816818813
32	202388	196887.834023677	7950.65690762981	5500.16597632308	-0.332184095681747
33	182516	186807.23545374	-3321.57149718465	-4291.23545373993	-2.24587418391417
34	173476	180162.302467512	-5400.04613149327	-6686.30246751232	-0.414047163981782
35	166444	172531.68125591	-6794.52712687721	-6087.68125591043	-0.277821536677563
36	171297	169600.330112866	-4380.24512249172	1696.66988713449	0.481335141427902
37	169701	164873.355591314	-4597.10585510348	4827.64440868621	-0.0432704221247869
38	164182	160991.666746623	-4149.74274399488	3190.33325337734	0.089111366597111
39	161914	159351.935854454	-2586.57808734296	2562.06414554566	0.310929178690287
40	159612	159043.357433323	-1171.65522107888	568.642566677129	0.282279828668302
41	151001	158348.976122202	-874.530947359976	-7347.97612220182	0.0593581284609816
42	158114	167694.406679814	5495.7522704793	-9580.40667981372	1.26920530017726
43	186530	173559.380065215	5725.48084138091	12970.6199347845	0.0457091639308827
44	187069	175926.92139224	3638.62808639775	11142.0786077599	-0.415535207167158
45	174330	177636.098766244	2439.16335767283	-3306.09876624417	-0.238959092548035
46	169362	176635.221022719	299.840975595553	-7273.22102271888	-0.426228488063223
47	166827	174832.720507105	-1007.54407215932	-8005.72050710466	-0.260527834256694
48	178037	175280.961486966	-102.060899705734	2756.0385130343	0.180519749166594
49	186413	179870.875495755	2817.97272918215	6542.12450424504	0.582122455906605
50	189226	185671.883585803	4673.28904961722	3554.11641419733	0.36942268709986
51	191563	189675.874907847	4258.05910248038	1887.12509215314	-0.082643755255516
52	188906	190335.818221649	2028.99532284567	-1429.81822164902	-0.444422383109327
53	186005	195991.271897971	4278.53217885679	-9986.271897971	0.448956904681937
54	195309	204153.79650601	6690.55331169134	-8844.79650601042	0.48074346176637
55	223532	210076.941439276	6214.3869188622	13455.0585607243	-0.0947850942146274
56	226899	215171.058723992	5520.11811844759	11727.9412760083	-0.138217594040503
57	214126	217029.405839082	3251.52539822038	-2903.40583908191	-0.451886535516855
58	206903	214883.799169536	-92.7381171694744	-7980.79916953632	-0.666379595495791
59	204442	213310.665913817	-1010.2650646007	-8868.6659138167	-0.182874987463589
60	220375	217561.595167895	2251.93151830071	2813.40483210534	0.650301218751216
61	214320	212156.014582494	-2497.6580778006	2163.98541750632	-0.946444689196778
62	212588	208105.379468978	-3460.18209530756	4482.62053102215	-0.191637979443586
63	205816	203063.437639888	-4438.83384747022	2752.56236011208	-0.194837158824675
64	202196	203404.570810108	-1484.02833993371	-1208.57081010757	0.588965764473686
65	195722	206204.151765535	1166.2399327503	-10482.1517655351	0.528666137790662
66	198563	207629.746865737	1326.85416587885	-9066.74686573736	0.0320147999893518
67	229139	213566.288803157	4180.36989740567	15572.711196843	0.568183536881156
68	229527	216885.804770334	3648.06076624843	12641.1952296657	-0.105972790114439
69	211868	214846.136836091	133.325135065316	-2978.13683609107	-0.700038566080598
70	203555	212339.306904918	-1498.14441994838	-8784.30690491777	-0.325106632455227
71	195770	207585.790379837	-3510.52938433171	-11815.7903798365	-0.401137466304889

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/17azr1293569961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/17azr1293569961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/2zjgc1293569961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/2zjgc1293569961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/3stgf1293569961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/3stgf1293569961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/4stgf1293569961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/4stgf1293569961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/5k2fi1293569961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293569840ttma8u0oeow7szz/5k2fi1293569961.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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