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WS 9 Structural Time Series Models

*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: Fri, 11 Dec 2009 02:15:19 -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/11/t1260522985afz46utfg0pac49.htm/, Retrieved Fri, 11 Dec 2009 10:16:32 +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/11/t1260522985afz46utfg0pac49.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 «

108.8 128.4 121.1 119.5 128.7 108.7 105.5 119.8 111.3 110.6 120.1 97.5 107.7 127.3 117.2 119.8 116.2 111 112.4 130.6 109.1 118.8 123.9 101.6 112.8 128 129.6 125.8 119.5 115.7 113.6 129.7 112 116.8 127 112.1 114.2 121.1 131.6 125 120.4 117.7 117.5 120.6 127.5 112.3 124.5 115.2 104.7 130.9 129.2 113.5 125.6 107.6 107 121.6 110.7 106.3 118.6 104.6

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	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	108.8	108.8	0	0	0
2	128.4	117.211178824977	0.0955901788615555	11.1621324864549	2.91042415177307
3	121.1	122.613264855301	0.446742285937217	-1.52256234981527	1.27584387391735
4	119.5	122.431703860164	0.406649382648722	-2.930319386644	-0.185107233242648
5	128.7	124.764250613934	0.497015352915069	3.93057569746883	0.652755825876451
6	108.7	119.428351127576	0.314427530908749	-10.7114641479625	-2.07062832614314
7	105.5	112.653097314982	0.158465266813489	-7.13211396268631	-2.54476718975896
8	119.8	113.272513592459	0.166728626641419	6.52611465285805	0.165735949731735
9	111.3	112.714782371213	0.154572223289337	-1.41262609499108	-0.260287107656059
10	110.6	111.748506668731	0.135748087886444	-1.14517522864395	-0.402205332917689
11	120.1	114.573986933762	0.181536760427425	5.51802900451686	0.964273439457565
12	97.5	109.028899021416	0.0835286660817276	-11.5119123385102	-2.0520579284585
13	107.7	109.240441174363	0.0814538545698723	-1.54083215298086	0.0481474759572477
14	127.3	112.883122377830	0.0563866848473752	14.4060152093126	1.33082013482536
15	117.2	116.072519444230	0.102230166072411	1.11889391659614	1.06917712514347
16	119.8	119.324010609306	0.187196507095847	0.467877081809701	1.03683012395512
17	116.2	115.674037188333	0.0745110154165837	0.536029683628525	-1.29438045188072
18	111	115.574677276458	0.0699802926197199	-4.57420278283701	-0.0605916767018478
19	112.4	117.109818336192	0.101020040807521	-4.71392707402822	0.520614000319272
20	130.6	119.838396630885	0.145851848573793	10.7541340574783	0.941596109887867
21	109.1	117.049147788465	0.104399564248782	-7.94075484394322	-1.05487103715998
22	118.8	117.384714760774	0.107105186005922	1.41462263841072	0.0831074481886406
23	123.9	116.702083292557	0.100113754826242	7.20018335269996	-0.283758824517858
24	101.6	115.770178702340	0.0948073598168744	-14.1672090196103	-0.371235482538938
25	112.8	116.264128864976	0.0955408813941065	-3.46528295746135	0.144212800865412
26	128	116.353704645913	0.0955183354462984	11.6463124649919	-0.00213923242881425
27	129.6	121.157916226389	0.141919892906098	8.4289501631333	1.65005392130372
28	125.8	123.179547598457	0.171693622580222	2.61534580260706	0.647216238041346
29	119.5	122.418539385858	0.153851167444917	-2.91601813294827	-0.321529571579393
30	115.7	122.04467911483	0.143587038697963	-6.34323500915275	-0.18429730523603
31	113.6	120.956797871764	0.121735521118530	-7.3533732526361	-0.435876159858604
32	129.7	119.320045443285	0.095126642234908	10.3849044215012	-0.627821539904236
33	112	119.060522017402	0.090751907826279	-7.05951671069976	-0.127128210242285
34	116.8	117.403341748749	0.073897953118858	-0.598369862280964	-0.627323265370247
35	127	117.705397266486	0.0755404095248206	9.29395263756678	0.081901534534699
36	112.1	121.183596956774	0.0937628455099252	-9.09330120256582	1.22155101136178
37	114.2	121.428367478884	0.0944847538632363	-7.228797640353	0.0541352741272421
38	121.1	118.441690238415	0.0758275816920888	2.66702805978261	-1.09800231279720
39	131.6	119.721982898053	0.086426225824066	11.8746512798573	0.424949908180246
40	125	120.709332820443	0.0970814467288747	4.28817962287632	0.315284817311608
41	120.4	121.577892686559	0.107883688253814	-1.18001318676815	0.269681696819412
42	117.7	122.182599199998	0.115228465688199	-4.48397018877281	0.174596772256568
43	117.5	122.806348985447	0.122463256085422	-5.30776394003054	0.180059857507474
44	120.6	118.262812441455	0.063069213877425	2.35027621565872	-1.66241181166642
45	127.5	122.782815826510	0.111044300330536	4.70460993294604	1.5937213351406
46	112.3	120.835435412983	0.0930351472144077	-8.52960853904714	-0.737249490652575
47	124.5	119.020112265090	0.0796031427388439	5.48529884885469	-0.683842587799757
48	115.2	120.253435367258	0.086480383281025	-5.05670762579813	0.413279777203966
49	104.7	117.111097793344	0.0678060931119178	-12.4019559863291	-1.15448580876976
50	130.9	120.786351986143	0.0915284173140489	10.1034808306257	1.28474215063655
51	129.2	120.815891532127	0.0910275097288677	8.38428200121722	-0.0219596379699571
52	113.5	116.836763587804	0.0512256512208885	-3.32544059702542	-1.43578630759011
53	125.6	119.499574773266	0.080276617835844	6.09318075612538	0.920351497895281
54	107.6	117.293503928411	0.0534024354007198	-9.68715266390997	-0.80765911880492
55	107	114.308935341325	0.0182361598947053	-7.30045970956358	-1.07760892098400
56	121.6	116.101632811877	0.0372622940776565	5.49339190400291	0.631925100307959
57	110.7	112.309193499492	0.00102101549997884	-1.59841154879415	-1.36763415269111
58	106.3	111.895588926665	-0.00234246877659599	-5.59441842845491	-0.148292487865067
59	118.6	112.319305377174	0.000625324413290365	6.27949013779561	0.152464752920625
60	104.6	111.098500861179	-0.00702497886673446	-6.49504731022547	-0.436941679997534

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/1nrsj1260522912.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/1nrsj1260522912.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/2y4xo1260522912.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/2y4xo1260522912.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/32vqk1260522912.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/32vqk1260522912.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/4epwk1260522912.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/4epwk1260522912.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/550wt1260522912.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260522985afz46utfg0pac49/550wt1260522912.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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