Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2009 » Dec » 03 »

*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: Thu, 03 Dec 2009 13:11:45 -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/03/t1259871174uu1144d3bfixbcn.htm/, Retrieved Thu, 03 Dec 2009 21:13:00 +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/03/t1259871174uu1144d3bfixbcn.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 «

1915 1843 1761 2858 3968 5061 4661 4269 3857 3568 3274 2987 1683 1381 1071 2772 4485 6181 5479 4782 4067 3489 2903 2330 1736 1483 1242 2334 3423 4523 3986 3462 2908 2575 2237 1904 1610 1251 941 2450 3946 5409 4741 4069 3539 3189 2960 2704 1697 1598 1456 2316 3083 4158 3469 2892 2578 2233 1947 2049

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	1915	1915	0	0	0
2	1843	1843.99431779336	-71.0878572278306	-0.994317793362496	-0.118782434738233
3	1761	1760.73098327906	-82.7960266163255	0.269016720944476	-0.0197979134286433
4	2858	2822.07852254198	1008.51469586646	35.9214774580235	1.80930312201797
5	3968	3973.66531697558	1145.05557395077	-5.66531697558136	0.226651816858512
6	5061	5064.75001076945	1093.53921250168	-3.75001076945432	-0.0855081585733372
7	4661	4707.95024201491	-290.809005748789	-46.9502420149081	-2.29777874671134
8	4269	4262.81579709793	-438.111537284517	6.18420290207231	-0.244496699778275
9	3857	3855.57711371601	-408.643564979029	1.42288628398723	0.048911732379963
10	3568	3565.2986173083	-295.664705840661	2.70138269170044	0.187525346612445
11	3274	3275.62819664525	-289.943191544671	-1.62819664525496	0.00949672318951281
12	2987	2987.82371629392	-287.901802766272	-0.823716293917027	0.00338835195504231
13	1683	1713.56712235695	-1229.09328966190	-30.5671223569538	-1.56288797789183
14	1381	1310.58847923549	-440.188256731552	70.4115207645126	1.31544286775096
15	1071	1115.78963292764	-211.956642260241	-44.7896329276447	0.382814720271252
16	2772	2656.37727082158	1417.3902456518	115.622729178416	2.70100818871470
17	4485	4522.43573291238	1834.19199689547	-37.435732912378	0.69191532764831
18	6181	6141.50930492809	1634.28478253756	39.4906950719122	-0.331810694409317
19	5479	5624.42982228918	-364.968921181233	-145.429822289177	-3.3184186995403
20	4782	4775.8528407719	-814.37349558736	6.14715922809708	-0.745933775605698
21	4067	4056.26948079706	-726.287659350374	10.7305192029450	0.14620723998589
22	3489	3478.66689042194	-588.11838202883	10.3331095780554	0.229337083254824
23	2903	2933.57001990285	-548.139156145035	-30.5700199028507	0.0663586288894683
24	2330	2275.39758623601	-650.388123301669	54.6024137639919	-0.169715967477611
25	1736	1789.52878030154	-497.551705537405	-53.5287803015409	0.253817080946218
26	1483	1358.69512767047	-435.517824043713	124.304872329533	0.103160040904261
27	1242	1360.81582933842	-34.3595457358069	-118.815829338419	0.669222722740359
28	2334	2212.03858623321	779.028281892274	121.961413766788	1.34931369578257
29	3423	3503.31693450372	1248.84227706923	-80.316934503724	0.779813126068055
30	4523	4377.37502345757	904.978553551751	145.624976542429	-0.570766233674772
31	3986	4155.86452813121	-128.625373867469	-169.864528131208	-1.71560135414889
32	3462	3477.50155379676	-633.02257755839	-15.5015537967614	-0.837212454578822
33	2908	2895.71191154208	-586.015721732472	12.2880884579188	0.0780232446176738
34	2575	2556.15594892908	-359.884048543337	18.8440510709248	0.375339447186656
35	2237	2254.92944466363	-306.063859348415	-17.9294446636345	0.0893324696921452
36	1904	1868.31048068351	-379.969738312634	35.6895193164873	-0.122671607646575
37	1610	1643.48892647039	-237.656303453972	-33.4889264703898	0.236367686330915
38	1251	1137.84448956637	-483.583488938503	113.155510433633	-0.408410331825218
39	941	1081.90698047364	-94.1583891589908	-140.906980473639	0.648005992213137
40	2450	2312.19681880834	1114.45402849545	137.80318119166	2.00602416300433
41	3946	4015.43203056638	1651.00213730320	-69.4320305663794	0.890443149671629
42	5409	5226.22705213235	1249.74236455958	182.772947867653	-0.66605263897509
43	4741	4952.31071987489	-139.244484583548	-211.310719874888	-2.30546717433684
44	4069	4111.01882682801	-779.231723660451	-42.0188268280059	-1.06226887344331
45	3539	3523.76325955734	-604.228826453218	15.2367404426565	0.290474512133344
46	3189	3158.66780754494	-386.235918611633	30.3321924550622	0.361830642206055
47	2960	2961.76516842858	-213.639583286423	-1.76516842858439	0.286481270971357
48	2704	2701.5272080579	-256.113326812728	2.47279194210022	-0.0705004546891371
49	1697	1728.62859318626	-909.41822328979	-31.6285931862648	-1.08506379466651
50	1598	1424.10866382671	-358.094960988995	173.89133617329	0.915106245886558
51	1456	1651.48212534320	173.136180758787	-195.482125343203	0.882959536644735
52	2316	2235.67392653673	546.746313620669	80.326073463267	0.620274005397241
53	3083	3160.34386444056	889.878033750948	-77.3438644405608	0.56940580779805
54	4158	3880.08849755857	735.391157317516	277.911502441432	-0.256435030215154
55	3469	3665.69139932732	-127.163398260822	-196.691399327316	-1.43168605919819
56	2892	2968.73774976568	-644.62138869767	-76.7377497656808	-0.858890513139222
57	2578	2556.69797954254	-433.403927005304	21.3020204574605	0.350584462021206
58	2233	2221.43373046111	-344.278386126272	11.5662695388940	0.147933212853412
59	1947	1964.37640494239	-265.069358169029	-17.3764049423858	0.1314735334007
60	2049	1945.14683438854	-41.8454611812789	103.853165611457	0.370530377263508

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/15xbu1259871102.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/15xbu1259871102.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/2xopp1259871102.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/2xopp1259871102.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/36zgp1259871102.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/36zgp1259871102.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/4ryr01259871102.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/4ryr01259871102.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/5d76l1259871102.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871174uu1144d3bfixbcn/5d76l1259871102.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by