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Paper: Structural Time Series Analysis -AEX

*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 01:36:48 +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/t129350014487jcj056k1nyaxf.htm/, Retrieved Tue, 28 Dec 2010 02:35:50 +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/t129350014487jcj056k1nyaxf.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 «

508643 527568 520008 498484 523917 553522 558901 548933 567013 551085 588245 605010 631572 639180 653847 657073 626291 625616 633352 672820 691369 702595 692241 718722 732297 721798 766192 788456 806132 813944 788025 765985 702684 730159 678942 672527 594783 594575 576299 530770 524491 456590 428448 444937 372206 317272 297604 288561 289287 258923 255493 277992 295474 291680 318736 338463 351963 347240 347081 383486

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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	508643	508643	0	0	0
2	527568	522879.737907261	2235.54280668410	880.570267395239	0.679303067014587
3	520008	520796.001371167	996.795015088428	765.275075422108	-0.243427050519995
4	498484	503560.94062598	-5295.81893424825	732.968754851264	-0.947006177484237
5	523917	517414.232542759	1636.66492039466	794.986576711566	0.953082098762873
6	553522	545188.497627135	11212.4883283357	700.294307405367	1.28471769597676
7	558901	557855.492210381	11747.1124366646	622.584009950372	0.0713250413239441
8	548933	553110.123013028	5677.75448637661	616.737770967309	-0.808827985701807
9	567013	564625.046532452	7827.16489197715	690.68250092035	0.286389305936121
10	551085	555423.975052409	1554.77422647304	613.855402129362	-0.83572580679396
11	588245	580623.740896998	10266.1205282576	742.55171450639	1.16069288393369
12	605010	601310.493982289	14105.7163429042	667.652022724942	0.511585887166022
13	631572	628239.793306811	18596.4610658461	-210.306644224539	0.729299621435798
14	639180	640578.322376321	16435.4087605407	-129.931498527007	-0.250167206246470
15	653847	654652.20860595	15577.1458193328	-126.925143892356	-0.115418825504425
16	657073	660253.152926578	11899.5042631907	-287.83803785221	-0.489106217650624
17	626291	636772.459353388	-1141.36001055664	-254.148786458373	-1.73060835486476
18	625616	627864.302269351	-4000.86459090566	-1.34669412313031	-0.380141688125085
19	633352	631216.058422033	-1294.70203283899	5.98699305746485	0.360240919284134
20	672820	663172.170389181	10944.7546932926	7.16150964955054	1.63027772212875
21	691369	687487.855032411	15867.4625681848	2.59764550632268	0.655838226061422
22	702595	702948.885151191	15717.8059228557	-235.961903076208	-0.0199396744163479
23	692241	698303.169753426	8218.82534935807	-153.130575179061	-0.99915478906515
24	718722	716007.343795401	11711.7910413418	-37.7375766397637	0.465400457032939
25	732297	729951.723231772	12514.0324432613	1713.06535706441	0.118683922536796
26	721798	726110.589812661	6740.59227656606	-516.813170496904	-0.70603027917733
27	766192	758782.000471856	16199.5968023204	-41.4585978402295	1.26811487042180
28	788456	785645.893548372	20127.4105096696	-274.910403398728	0.522730032274457
29	806132	806421.226659312	20366.0359282316	-476.285587331538	0.0317093666897173
30	813944	817089.971611704	16797.3256909277	-344.820344599108	-0.474776398854136
31	788025	798809.772413497	3891.14654477199	-643.309830327182	-1.71856979833561
32	765985	774530.683132659	-6474.38151495653	-396.491162230097	-1.38081451977589
33	702684	717758.709195631	-24984.2587289551	-519.882835634134	-2.46609516221689
34	730159	721709.675032519	-14334.8077222910	74.8731042570749	1.41890446246529
35	678942	685814.728003832	-22270.4212982397	-632.260199730614	-1.05733375108728
36	672527	670590.065285948	-19677.3728513075	-102.201661374764	0.345497027198647
37	594783	610567.894496334	-34293.0198164359	-4281.86959513517	-2.08982269214111
38	594575	590641.630655958	-29166.994563884	389.560034521141	0.642464534745484
39	576299	572304.346249627	-25210.7169378212	886.045810830544	0.529598517436605
40	530770	534077.4971425	-30001.3836008155	449.299166231358	-0.637781472220461
41	524491	519411.797332152	-24357.0622374916	659.803988673835	0.750521747724276
42	456590	464867.87315356	-35460.9133840915	424.736430042922	-1.47777298827776
43	428448	428260.566477481	-35882.5311876229	518.152288689237	-0.0561502261798934
44	444937	432125.601786134	-21263.4400747238	1339.68856889385	1.94753762706702
45	372206	381139.297982589	-32196.5266642407	-352.814968523353	-1.45665169505806
46	317272	323629.368723455	-41508.3908607915	951.078195664782	-1.24069340101103
47	297604	293847.217310637	-37194.5227785536	370.985690818326	0.574776418881518
48	288561	280459.431575179	-28438.0400007376	1228.97765628388	1.16671956217339
49	289287	282962.702731473	-17185.4437558441	-2519.95964073206	1.58048912720570
50	258923	260483.862645361	-19085.9787334948	-209.332049499595	-0.241580024153711
51	255493	251752.16391006	-15300.9673259458	773.497115857667	0.506220109776332
52	277992	268540.725016916	-3497.46645586085	209.955251914043	1.57174074866072
53	295474	288103.855204534	4985.10703724913	737.668639060526	1.12834901281228
54	291680	292048.098689574	4602.41929475903	-68.6415006026201	-0.050941238873255
55	318736	313933.496953407	10955.8986525835	-172.574555918405	0.84621538156101
56	338463	334477.111006579	14480.6480726626	1224.96805028303	0.469576478158825
57	351963	351678.884376289	15481.1004640056	-499.624623694192	0.133294815364596
58	347240	351511.962933636	9727.55428130257	235.448915146358	-0.766592517058976
59	347081	350508.571419431	5781.78484233479	-336.366757860426	-0.525731564377954
60	383486	376720.500209268	13292.0990938283	881.8245512265	1.0006922242197

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/1g6le1293500202.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/1g6le1293500202.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/2rfkz1293500202.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/2rfkz1293500202.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/32o2k1293500202.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/32o2k1293500202.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/42o2k1293500202.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/42o2k1293500202.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/5cf141293500202.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129350014487jcj056k1nyaxf/5cf141293500202.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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