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structural Time series analysis - Goudkoers

*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, 21 Dec 2010 20:38:33 +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/21/t12929637857xh9x9qyvoeikax.htm/, Retrieved Tue, 21 Dec 2010 21:36:32 +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/2010/Dec/21/t12929637857xh9x9qyvoeikax.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 «

10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320 24977 25204

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	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	10570	10570	0	0	0
2	10297	10311.4309338616	-14.3300168867088	-14.4309338616498	-0.227169279244938
3	10635	10645.4340167542	-11.5503640960789	-10.4340167541600	0.50969214536157
4	10872	10882.9297069481	-9.2485891206808	-10.9297069481005	0.364039375874384
5	10296	10313.5339426804	-15.4524785552112	-17.5339426803725	-0.818027307141764
6	10383	10394.8579236197	-14.2153091466331	-11.8579236197353	0.141200919554811
7	10431	10444.0648802964	-13.2992334631293	-13.0648802963941	0.0924525028809954
8	10574	10585.9057150308	-10.8085959503998	-11.9057150307783	0.225953065707245
9	10653	10665.1256981962	-9.22316568886463	-12.1256981961662	0.131009033519912
10	10805	10816.0338840354	-6.163100360503	-11.0338840353938	0.232827326833022
11	10872	10883.4040078868	-4.65198392042856	-11.4040078868024	0.106828923057185
12	10625	10638.8389634111	-9.91323577423113	-13.8389634111157	-0.348271837000529
13	10407	10383.9444843815	-5.96314347383333	23.0555156185204	-0.426990202390501
14	10463	10464.5467515216	-2.36986939545989	-1.54675152156581	0.106999428836634
15	10556	10554.9953835900	-0.07204887525933	1.00461641002221	0.134326064001681
16	10646	10640.9481593565	2.11063089589868	5.05184064354902	0.124391474525599
17	10702	10705.3663934412	3.76786453069574	-3.36639344124839	0.0900414212268233
18	11353	11343.3973073762	21.3249666445042	9.60269262379925	0.916030841199593
19	11346	11347.8142531303	20.8397106088232	-1.81425313026019	-0.024405364334406
20	11451	11448.1920040349	23.1988087749107	2.80799596514595	0.114744600080064
21	11964	11957.5334910195	38.0568707178104	6.46650898049286	0.700968772022597
22	12574	12566.9535094530	56.004354639465	7.04649054696238	0.823450370086635
23	13031	13024.3755319093	68.9426034235542	6.62446809065676	0.578282842290358
24	13812	13802.3644828845	92.2153203084025	9.63551711549519	1.02080642946155
25	14544	14461.0568846203	104.000923947969	82.943115379704	0.893221118276242
26	14931	14933.0239420776	119.560091975791	-2.02394207764874	0.48365443433101
27	14886	14892.2272791964	113.930974313189	-6.22727919639597	-0.230615695272288
28	16005	15983.7698087912	148.320561302916	21.2301912087567	1.40503050421761
29	17064	17065.8742390782	181.728681083697	-1.87423907817380	1.34170138404619
30	15168	15199.0330663883	107.400774340224	-31.0330663883255	-2.94264870076677
31	16050	16031.8443997713	134.056409441670	18.1556002286714	1.04172979031148
32	15839	15851.3175930065	122.361800688473	-12.3175930064887	-0.451646175900321
33	15137	15151.3172988842	91.4634489481066	-14.3172988841658	-1.18038819083854
34	14954	14954.3242140103	80.51865767997	-0.324214010258316	-0.413951768417101
35	15648	15641.1614438442	103.747423261370	6.83855615580507	0.869986214746308
36	15305	15316.5652745589	87.281418367961	-11.5652745589256	-0.614268355669947
37	15579	15532.780591473	91.6110170812512	46.2194085269958	0.196265736264609
38	16348	16328.1311469939	121.777570982425	19.8688530060636	0.949776244589926
39	15928	15954.4988768729	102.123000806226	-26.4988768729438	-0.710424099532503
40	16171	16164.8033425708	106.400209023995	6.19665742920384	0.155042051538028
41	15937	15906.8291013364	91.9020391740626	30.1708986636254	-0.522184443462542
42	15713	15755.0777472611	82.1573459744097	-42.0777472610955	-0.349143939918781
43	15594	15574.1843511912	71.5890491215501	19.8156488087597	-0.376898463657610
44	15683	15676.3924925048	72.8243243052353	6.60750749523735	0.0438665386065906
45	16438	16425.9249525618	100.229260990312	12.0750474382233	0.969397465199311
46	17032	17032.4770064146	120.807157673750	-0.477006414629217	0.725261131089244
47	17696	17668.3593634435	141.818910654865	27.6406365564653	0.73780275508995
48	17745	17757.4228852631	139.668970186307	-12.4228852630807	-0.0755240816961078
49	19394	19274.8688851192	192.860438113673	119.131114880780	2.06047619153955
50	20148	20115.825097015	220.623974754775	32.1749029849973	0.887884438663069
51	20108	20157.2353552000	213.205110021669	-49.235355199975	-0.256678521933197
52	18584	18621.1449944282	141.066501733468	-37.1449944282249	-2.50403529013489
53	18441	18410.7790711907	126.539326937438	30.2209288093089	-0.50307585419112
54	18391	18433.8517844117	122.254054256802	-42.8517844117177	-0.148110090241096
55	19178	19146.8309120854	146.759967990344	31.1690879146102	0.845574925628327
56	18079	18122.9570799997	98.1246066901327	-43.957079999665	-1.67560153872566
57	18483	18471.6869124512	108.550523309930	11.3130875487923	0.35869412614005
58	19644	19637.9152741721	152.611175702081	6.08472582785404	1.51384177085314
59	19195	19188.5675517928	127.498138337056	6.43244820716244	-0.861627992384058
60	19650	19679.5089195119	142.632334524159	-29.5089195119331	0.519914012929075
61	20830	20692.3644997046	178.003795999333	137.635500295441	1.28769784418317
62	23595	23511.8785745799	290.650795853435	83.1214254200916	3.65402350043202
63	22937	22978.6376106425	256.055656643196	-41.6376106425308	-1.17932711058717
64	21814	21866.0010399569	198.750238369558	-52.0010399568686	-1.95822450308203
65	21928	21876.5489588988	190.863655686686	51.4510411011698	-0.269277849997684
66	21777	21835.8791519986	181.153951520203	-58.8791519985783	-0.331283718039010
67	21383	21328.7075398016	152.270959464545	54.2924601983522	-0.984860485440262
68	21467	21495.0157323517	152.860291318174	-28.0157323516505	0.0200842474512446
69	22052	22048.9095535015	169.705329477211	3.09044649850417	0.573784967583753
70	22680	22638.2738545643	187.341708948314	41.7261454357485	0.600441647326592
71	24320	24266.3283297039	247.923102417157	53.671670296134	2.06149034020675
72	24977	25011.1175690590	268.781202872275	-34.1175690589637	0.710549527544314
73	25204	25292.4391434107	269.301659881545	-88.4391434106936	0.0184252213719177

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/1ez0e1292963909.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/1ez0e1292963909.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/27q0h1292963909.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/27q0h1292963909.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/37q0h1292963909.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/37q0h1292963909.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/40hhk1292963909.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/40hhk1292963909.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/50hhk1292963909.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929637857xh9x9qyvoeikax/50hhk1292963909.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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