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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: Tue, 07 Dec 2010 09:56:13 +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/07/t1291715692blrs0kzyf92vw5o.htm/, Retrieved Tue, 07 Dec 2010 10:54:52 +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/07/t1291715692blrs0kzyf92vw5o.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 «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	46	46	0	0	0
2	62	48.0597721845123	0.438809647807576	3.54588131669584	1.57354753017656
3	66	52.6075402792847	1.21254641887133	3.23398221008467	1.69784159753678
4	59	55.196897804194	1.42576222524469	0.757802304723039	0.518056104064447
5	58	56.7474657807925	1.44205635486036	0.974649914617405	0.0471245700968842
6	61	58.5123192353288	1.47843238398802	1.74015611823267	0.125792982206389
7	41	55.5229329157744	1.03572082198720	-3.65481966413236	-1.81350760115556
8	27	49.6182155640278	0.422091070104714	-4.86177924259477	-2.93940161834491
9	58	50.8872940012819	0.489705041541521	4.83917127273958	0.373688244996032
10	70	55.0707456051864	0.758568568079706	4.56725852046717	1.69258734286791
11	49	54.7479114478633	0.686198814276719	-2.59132078952599	-0.512856998388462
12	59	55.8619648560587	0.712711230136431	1.84410451993083	0.209260503745663
13	44	56.2102932789977	0.724336651337164	-10.1672209657321	-0.330330369268821
14	36	52.9978655845587	0.550595808963865	-5.21233157658326	-1.99983014108562
15	72	55.9513481574925	0.679545079453177	9.7601272797712	1.09667763768074
16	45	54.8177833072999	0.58393566045628	-4.97509991511472	-0.845724481363
17	56	55.2100671607486	0.57440008249081	1.32727511458341	-0.0933827996623771
18	54	54.844192057275	0.530571469084065	1.9163361892134	-0.477263984019083
19	53	54.9588864543482	0.51238082511351	-0.689924797490876	-0.218436954150590
20	35	52.9973496699936	0.410448802847295	-10.2063903347090	-1.33642346160890
21	61	53.7916442489172	0.425406155891318	5.96765487376864	0.212218423268656
22	52	53.167550891779	0.386629854743144	2.30019097290813	-0.591716224831296
23	47	52.8558009355291	0.36232564533282	-3.4990023275797	-0.401116083199345
24	51	52.3907511456306	0.337225517451316	1.50411936837785	-0.489986388477468
25	52	53.1331519391485	0.339054207920607	-2.82688702533649	0.286110773472820
26	63	55.8107031764728	0.392831392870773	-1.04624331380961	1.41538539512040
27	74	57.6332490985803	0.436800349321582	11.7324351466442	0.807281734840497
28	45	57.0703406621145	0.404417354131301	-8.87141218919692	-0.559501095878015
29	51	56.0681686025309	0.359638497420152	-0.510231058219521	-0.796994854466369
30	64	56.9495348335839	0.375604084600534	5.32792319320188	0.300736105834529
31	36	54.1030393876645	0.281393320613122	-7.2681865324244	-1.88836276403969
32	30	51.8779910994564	0.211399010945687	-13.3115959268030	-1.49061077732025
33	55	51.0991219646514	0.184976775222993	7.33378245168349	-0.596482511333149
34	64	52.4738256890102	0.215185757443916	7.34699369109719	0.725080347463454
35	39	51.3760692641207	0.184192139087732	-7.69268005990597	-0.810889291688109
36	40	49.7130745531784	0.147642570274642	-2.9387304010156	-1.16850670005281
37	63	51.8405964223862	0.167191446733645	3.38177882730635	1.3376441979419
38	45	51.5779860201348	0.160131530081514	-4.99493046061466	-0.274098748821633
39	59	50.895108502376	0.142190360730116	11.0615153520207	-0.515707765343614
40	55	52.5346372207714	0.176807223093539	-2.70325631829123	0.90460011278997
41	40	51.1462397448066	0.140270282058093	-5.73373085676533	-0.948006943457502
42	64	51.6259562999033	0.148031833012400	11.1900650557176	0.207289558900143
43	27	49.0650355969983	0.0881076514158906	-12.5172993555984	-1.67021700097748
44	28	47.58222884341	0.0546667273702632	-13.9882077766203	-0.977654965159655
45	45	46.0953522544883	0.0232256090199660	4.44812177250886	-0.967850638149091
46	57	46.1237958841759	0.0233265332720753	10.8572520970193	0.00330500071976019
47	45	46.8224365275428	0.0353458485571801	-4.30527936745036	0.432263225001445
48	69	50.4697307328244	0.0897151812255462	4.99454079739819	2.35094343313774
49	60	51.7856112804661	0.102837887569286	3.48101976194119	0.820339889895021
50	56	53.2653076605075	0.121261940597883	-2.43386972899106	0.898329857720658
51	58	52.89516576079	0.113245087746417	6.89674204132185	-0.312747898662718
52	50	52.7090692759089	0.107906503517759	-1.63188193443569	-0.188475617741982
53	51	53.213240835909	0.115155321105339	-3.63669026764013	0.249291393763048
54	53	51.4209294827991	0.0805087726444711	8.45857807320653	-1.20484683301625
55	37	50.71522883305	0.0665610586463731	-10.8615549477149	-0.499572656763515
56	22	48.5097972250097	0.0275639274452978	-18.2044626383856	-1.45305366354837
57	55	48.5333845576781	0.0274984448370330	6.48125901181083	-0.00256000560218153
58	70	50.1573161653137	0.0523744088965303	13.9175367652720	1.03485707997136
59	62	53.0477739825201	0.0930402180971634	-1.68144798393238	1.85489353670178
60	58	53.7658116416095	0.100827122248203	1.86244623340146	0.413073638120074
61	39	51.8077017429776	0.0795282592978184	-4.88575862293053	-1.37785229209219
62	49	51.4544558027878	0.0745312288340987	-0.811612224101413	-0.286117634131379
63	58	51.3138679537037	0.0716640859417043	7.48854516362709	-0.140089812690450
64	47	50.9147085318999	0.0648480367139138	-2.17594801076229	-0.304099694632655
65	42	49.9005241499484	0.0487102047337609	-3.92637963360346	-0.695636940269711
66	62	50.0847680013577	0.0507407846279815	11.4151670815977	0.0875473461718351
67	39	49.867890016197	0.0467970781302325	-9.87647960925	-0.173532429737553
68	40	51.0594151431041	0.0631894214363188	-15.3217537401326	0.745742192752294
69	72	53.4561576308915	0.0953074992742823	9.80596740754347	1.52788565374017
70	70	54.5697932795816	0.108582624677618	11.5934161465255	0.670388347514449
71	54	54.9852558253818	0.112283011449092	-2.14985901041551	0.203296282712907
72	65	55.928543696999	0.121253337694937	5.89095897658286	0.554615216213689

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/1zezp1291715768.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/1zezp1291715768.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/2a6ys1291715768.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/2a6ys1291715768.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/32xfv1291715768.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/32xfv1291715768.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/42xfv1291715768.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/42xfv1291715768.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/52xfv1291715768.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715692blrs0kzyf92vw5o/52xfv1291715768.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 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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