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Paper: analyse (min18) STSM

*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 19:24:09 +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/t1293564119pxf8077ispsvx7c.htm/, Retrieved Tue, 28 Dec 2010 20:22:01 +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/t1293564119pxf8077ispsvx7c.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 «

3065 2997 2901 2815 2709 2711 3509 3369 3596 3448 3160 2934 2534 2266 2088 1932 1784 1851 2700 2580 2829 2298 2045 1824 1872 1801 1735 1639 1521 1758 2603 2540 3103 2801 2590 2324 2424 2288 2163 2082 1937 2155 2874 2836 3439 3278 3129 2959 3060 2898 2783 2632 2465 2689 3321 3359 4108 3407 3241 3013 3067 2965 2823 2718 2567 2658 3436 3375 3931 3371 3038

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	3065	3065	0	0	0
2	2997	3008.52132984141	-57.4308461652338	-11.5213298414105	-0.394571923099675
3	2901	2904.48245445651	-92.0410946133205	-3.482454456509	-0.233214850986717
4	2815	2811.98042638843	-92.4006291181543	3.01957361156934	-0.00228395106446355
5	2709	2710.84711376416	-99.0688472962668	-1.84711376416367	-0.0417410036872391
6	2711	2692.90041666764	-37.1127176303377	18.099583332359	0.390063775627983
7	3509	3360.9252125022	502.450445333022	148.074787497804	3.39282560013221
8	3369	3494.63203290656	220.254613650929	-125.63203290656	-1.77441480569011
9	3596	3598.04039785579	130.84742838385	-2.04039785578978	-0.562189657734893
10	3448	3492.23032542799	-50.2163857782155	-44.2303254279921	-1.13851232294309
11	3160	3198.12608032255	-236.811707873242	-38.1260803225456	-1.17329512656562
12	2934	2926.23880999051	-263.648105074292	7.76119000949463	-0.168744903466494
13	2534	2555.07420020928	-345.745313209625	-21.0742002092838	-0.517493978489517
14	2266	2254.63042018064	-311.042583490159	11.3695798193634	0.221450641719808
15	2088	2062.4048966199	-223.780385860205	25.5951033800988	0.548037194003999
16	1932	1885.12811360623	-189.436273627021	46.8718863937721	0.218798237261057
17	1784	1768.46397035217	-135.680422298517	15.5360296478293	0.337110549454524
18	1851	1949.36764264171	96.8386750230845	-98.3676426417081	1.4611662625695
19	2700	2410.25787418582	364.557413231091	289.742125814179	1.68429329247413
20	2580	2728.76396020645	330.663129715337	-148.763960206453	-0.213119576721193
21	2829	2842.21808779584	170.784291962522	-13.2180877958423	-1.00528997780698
22	2298	2422.9319125651	-263.520639190831	-124.931912565101	-2.73097136959565
23	2045	2071.68499435855	-328.076333395277	-26.6849943585501	-0.405921443073218
24	1824	1770.94605818772	-307.975294787013	53.0539418122791	0.126419177550124
25	1872	1813.71522837652	-50.0951096309418	58.2847716234812	1.62591288219237
26	1801	1812.27350932658	-14.2792011961628	-11.2735093265821	0.225515918419823
27	1735	1715.18250347072	-74.5217355450237	19.8174965292804	-0.378270078091017
28	1639	1588.69493438335	-112.319134459529	50.3050656166522	-0.239052361931656
29	1521	1559.68504954285	-51.5234587913615	-38.685049542846	0.382337989611295
30	1758	1890.44934070841	226.430773552593	-132.449340708406	1.74536624628129
31	2603	2312.76244695178	368.780125196721	290.237553048224	0.89534009133089
32	2540	2668.94970562274	359.619627478365	-128.949705622737	-0.0576076578612994
33	3103	2972.93319801753	319.135257613662	130.066801982469	-0.254552555312155
34	2801	2960.85093454054	78.1318580864534	-159.850934540542	-1.51549629249334
35	2590	2685.13473316619	-179.230373665122	-95.1347331661929	-1.61825202014122
36	2324	2385.92658635877	-266.434699894323	-61.9265863587737	-0.548616955098713
37	2424	2327.87996012428	-114.874431275599	96.1200398757212	0.954707986502277
38	2288	2257.33172597887	-82.6487653773345	30.6682740211252	0.202594005573066
39	2163	2112.02825671909	-127.946941679866	50.9717432809054	-0.284613928451145
40	2082	2020.28549144245	-101.782658861419	61.7145085575511	0.164995401597328
41	1937	2046.81273470064	-8.81664598509114	-109.812734700645	0.585039709485024
42	2155	2295.95177730898	177.766692944792	-140.951777308984	1.17196428997283
43	2874	2589.36348269849	261.323175068105	284.636517301509	0.525344853228414
44	2836	2958.82413658518	339.505870376773	-122.824136585179	0.491677046270253
45	3439	3246.73503793894	302.186193739311	192.264962061064	-0.23465905208662
46	3278	3374.02365686944	175.682184238808	-96.0236568694404	-0.795461686634786
47	3129	3252.48431823018	-39.2108882243069	-123.484318230177	-1.35127280967065
48	2959	3100.15180750171	-120.974293569908	-141.151807501715	-0.514423801137036
49	3060	2972.14054452987	-126.063645289801	87.8594554701331	-0.0320345741624389
50	2898	2836.12378596156	-133.256515505258	61.8762140384404	-0.0452095736285125
51	2783	2714.89932819909	-124.589293626072	68.1006718009058	0.0544746343218403
52	2632	2588.12644875065	-126.1617794179	43.8735512493452	-0.00990411744538079
53	2465	2604.05022701716	-23.6573808605812	-139.050227017159	0.645074161407301
54	2689	2816.61139198726	146.643517767402	-127.611391987259	1.07011712518994
55	3321	3066.03864354455	220.667824554741	254.961356455445	0.465318489748285
56	3359	3453.71793609093	340.978920306346	-94.7179360909344	0.756556254003159
57	4108	3868.98620739569	394.518085458683	239.013792604314	0.336652662732684
58	3407	3582.58900433025	-96.2147637535746	-175.589004330245	-3.08569895407298
59	3241	3349.92228909767	-194.527004960755	-108.922289097669	-0.618238700894315
60	3013	3156.33281984418	-193.851538820364	-143.33281984418	0.00424951123704307
61	3067	2970.52202683791	-188.055922648614	96.4779731620921	0.0364631942862495
62	2965	2868.42829301131	-126.144961359825	96.5717069886926	0.389131298758314
63	2823	2733.38062645764	-132.543382696662	89.619373542362	-0.0402215478615863
64	2718	2676.60491289207	-78.0989277341145	41.3950871079259	0.342707534470107
65	2567	2733.29299074601	18.878087622085	-166.29299074601	0.610223872428589
66	2658	2814.47117922924	63.6936816447249	-156.471179229237	0.281689107048199
67	3436	3195.8435886772	292.023865959307	240.156411322798	1.43521013520164
68	3375	3513.49534691749	310.443191405403	-138.495346917489	0.115816452023226
69	3931	3562.46723760569	122.461057320644	368.532762394312	-1.1820397174037
70	3371	3535.72795516838	15.1900677394097	-164.727955168382	-0.674528766231616
71	3038	3219.50169645456	-223.055421458684	-181.501696454564	-1.49829686584636

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/1o0mz1293564245.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/1o0mz1293564245.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/2o0mz1293564245.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/2o0mz1293564245.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/3zrm21293564245.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/3zrm21293564245.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/4ailn1293564245.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/4ailn1293564245.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/5ailn1293564245.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564119pxf8077ispsvx7c/5ailn1293564245.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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