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Paper Statistiek

*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: Sun, 26 Dec 2010 13:26:19 +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/26/t1293369912j6u4vhwo7v2qrow.htm/, Retrieved Sun, 26 Dec 2010 14:25:18 +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/26/t1293369912j6u4vhwo7v2qrow.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:

Structural Time Series Model bouwgrondprijzen: gemiddelde prijs(€/m²)

Dataseries X:

» Textbox « » Textfile « » CSV «

26 26 27 28 27 29 27 30 27 30 32 30 32 33 34 32 34 37 37 36 34 38 41 41 44 42 45 45 49 54 52 53 51 55 60 60 63 60 64 65 75 70 72 69 75 74 74 75 79 79 85 78 84 85 85 82 91 90 98 98

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	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	26	26	0	0	0
2	26	26	0	0	0
3	27	26.4885072084148	0.122153739677173	0.133847377390101	0.311760858102279
4	28	27.1342139787824	0.233118255632730	0.228731262357845	0.457902952748373
5	27	27.4402760855130	0.247518422173008	-0.618866072381305	0.107913249961221
6	29	28.1643885357689	0.334228863262016	0.269053415973408	0.406258176803948
7	27	27.8313691417159	0.214297196219431	0.123585017988838	-0.655240729634882
8	30	28.6681305761669	0.328271129587664	0.354050270433736	0.654334776357932
9	27	28.5763173732614	0.243146165322458	-0.869867284285748	-0.473927224296203
10	30	29.1337628643354	0.300739691199911	0.394864646113366	0.319730795081523
11	32	30.3282469900917	0.466701966869033	0.289088784018708	0.931954047212896
12	30	30.3661382898020	0.385580915727939	0.304392170664299	-0.449556493624059
13	32	31.5406982829708	0.540959024058378	-0.714938743274434	0.816190965739956
14	33	32.3308094633352	0.588054633367041	0.289099752490549	0.257863805577972
15	34	33.2162676644242	0.644462705894904	0.327045364309705	0.309688840936
16	32	33.1134458187647	0.501792772087465	0.0333059243567654	-0.776046584144826
17	34	34.0086541322497	0.577398247942449	-0.587107902519284	0.403193677854578
18	37	35.3867461481501	0.730093234935232	0.403051953665283	0.826298883541811
19	37	36.3167226811369	0.768221517323864	0.380058105126853	0.207164683675655
20	36	36.7045391454117	0.695527650284469	-0.126966174439744	-0.393774339235075
21	34	36.4234347165548	0.509339793078035	-0.978061075206743	-1.00499506364408
22	38	37.1447861304711	0.549826259669821	0.537151858628066	0.218276514321450
23	41	38.7261110735168	0.74673973519033	0.722374875997814	1.06586906159781
24	41	40.0518354376283	0.857323486112755	0.0750967143855673	0.598406534170209
25	44	42.4186841606676	1.14480758721019	-0.660442307976261	1.55667131929052
26	42	42.9089626793242	1.01986487631535	0.0690265686603976	-0.673473901677294
27	45	44.0900904776949	1.05063606975600	0.668566234223496	0.166393315635449
28	45	45.1442502396122	1.05130865599812	-0.149538279409317	0.00363809002217009
29	49	47.4067455162186	1.28205241149257	-0.206433208400234	1.24926726787648
30	54	50.6390895035875	1.65414855663668	0.45309209387698	2.00708179380598
31	52	52.0253791247045	1.60306217424042	0.374314600472984	-0.276200244826131
32	53	53.5330227905509	1.58485786323550	-0.39031443816904	-0.09844269171555
33	51	53.8143590714567	1.33646061649704	-0.878126048922161	-1.34402971906003
34	55	54.8722493068712	1.28333145550776	0.542527073932561	-0.286763584541826
35	60	57.3719448989305	1.51524769952023	0.816382397045657	1.25381252112246
36	60	59.3928467966224	1.61168624892955	-0.147279632574143	0.521405111518667
37	63	62.0592722838602	1.81269199830320	-0.62536393993839	1.08713776852673
38	60	62.3855666027673	1.52927158133358	-0.174545167455207	-1.53043624920666
39	64	63.6492334928828	1.47863917634907	0.745869923915414	-0.273719345577482
40	65	65.165464310073	1.48580700944209	-0.221455218277328	0.0387484148476624
41	75	69.7927881872859	2.08450332368169	0.543903161609824	3.23723313595437
42	70	71.3544356757763	1.98482310068779	-0.57724741234765	-0.538416359528932
43	72	72.6263342718263	1.84893195130445	0.433275091617407	-0.734581920792908
44	69	72.7263417447026	1.51550798876610	-1.12452229870255	-1.8022892935136
45	75	74.2201769798673	1.51137772029396	0.811988644194288	-0.0223295466831262
46	74	75.2492008126526	1.41942939210537	-0.53259991774425	-0.496746980013409
47	74	75.438794573858	1.18502539125921	0.388011908750471	-1.26703945153618
48	75	76.3956127336959	1.14152382947651	-1.05640065860976	-0.235130011074764
49	79	77.7158755895938	1.17558665520892	1.01888073381216	0.184136170260871
50	79	79.0564953622532	1.20704340379994	-0.301577650627588	0.169965300409228
51	85	81.8250751240503	1.50465491248330	0.85634639476333	1.60863211013474
52	78	81.8535565917786	1.22328535447966	-1.66062761274873	-1.52077448559197
53	84	83.0300736449797	1.21437262197530	1.03932328103317	-0.0481769764152994
54	85	84.6872447910746	1.29876892201547	-0.344634135817353	0.456044350314516
55	85	85.2537376281421	1.15920973097611	0.833250254835934	-0.754314366045447
56	82	85.4024491947146	0.966612554835191	-1.90191954722115	-1.04094507427672
57	91	87.6412293047514	1.20905137196067	1.47118710338695	1.31041865321177
58	90	89.3725785632114	1.30859585444345	-0.147833561319080	0.537930415956737
59	98	92.9981016668497	1.75015242124173	1.56330669799700	2.38655217471476
60	98	96.759455553512	2.13346407384452	-1.74511328831461	2.07168501175944

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/1o4di1293369976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/1o4di1293369976.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/2zdul1293369976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/2zdul1293369976.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/3zdul1293369976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/3zdul1293369976.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/4a5co1293369976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/4a5co1293369976.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/5a5co1293369976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293369912j6u4vhwo7v2qrow/5a5co1293369976.ps (open in new window)

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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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