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Ad hoc forecasting 3

*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 10:25:49 -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/t12598612074ypicxg40w153t0.htm/, Retrieved Thu, 03 Dec 2009 18:26:54 +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/t12598612074ypicxg40w153t0.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:

Uitleg in Word document

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

96.96 93.11 95.62 98.30 96.38 100.82 99.06 94.03 102.07 99.31 98.64 101.82 99.14 97.63 100.06 101.32 101.49 105.43 105.09 99.48 108.53 104.34 106.10 107.35 103.00 104.50 105.17 104.84 106.18 108.86 107.77 102.74 112.63 106.26 108.86 111.38 106.85 107.86 107.94 111.38 111.29 113.72 111.88 109.87 113.72 111.71 114.81 112.05 111.54 110.87 110.87 115.48 111.63 116.24 113.56 106.01 110.45 107.77 108.61 108.19

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	96.96	96.96	0	0	0
2	93.11	95.6913669472083	-0.000980021030655114	-2.58136694720834	-2.35439870022924
3	95.62	94.8736856730539	-0.0715190141505774	0.746314326946155	-0.843449423446045
4	98.3	96.0153359193982	0.0527649789900341	2.28466408060181	1.43549603843488
5	96.38	96.4476031709953	0.0940450311107307	-0.0676031709953206	0.514396721777169
6	100.82	98.1678597559032	0.279267966329127	2.65214024409679	2.268052813189
7	99.06	99.1186219677098	0.359601884479845	-0.0586219677097961	0.92162536853751
8	94.03	97.5960660972948	0.123310476354771	-3.56606609729481	-2.53072956565060
9	102.07	98.7649967933306	0.260186107983493	3.30500320666941	1.38499001785332
10	99.31	99.3972848247982	0.310521604107985	-0.0872848247981668	0.487976288400459
11	98.64	99.3643322430727	0.262934354531628	-0.724332243072709	-0.447416127904472
12	101.82	100.325431595931	0.361272711389759	1.49456840406851	0.905238791566546
13	99.14	100.093522870962	0.281118249826728	-0.953522870961724	-0.779133950577501
14	97.63	100.219687154677	0.259560722137456	-2.58968715467741	-0.207945451559612
15	100.06	100.444224940864	0.254555729207507	-0.384224940864347	-0.0442832205175691
16	101.32	100.330001561904	0.20176345901015	0.989998438095807	-0.449635778160728
17	101.49	101.218571975241	0.29967880362698	0.271428024759083	0.849420626623094
18	105.43	102.125116286416	0.386183344090064	3.30488371358431	0.767563496073078
19	105.09	103.313721279377	0.500789107144326	1.77627872062316	1.02198740401359
20	99.48	103.992085306402	0.526174494803314	-4.51208530640155	0.225129444599609
21	108.53	104.895925117743	0.58012542141154	3.63407488225701	0.475465674998847
22	104.34	105.139437528049	0.5321214313157	-0.799437528048958	-0.421640736441573
23	106.1	106.108922448752	0.594354402416231	-0.00892244875197856	0.546819405868286
24	107.35	106.314304742479	0.53912319587131	1.03569525752134	-0.48782863608616
25	103	105.609643495873	0.362575165195605	-2.60964349587308	-1.57388148443057
26	104.5	106.07637391379	0.377400403085289	-1.57637391378990	0.132346390257091
27	105.17	106.176510699194	0.337866657635272	-1.00651069919392	-0.348798959420721
28	104.84	105.707077938782	0.222975899857415	-0.867077938782345	-1.00339196360372
29	106.18	105.984984318016	0.230770090503347	0.195015681983815	0.0682097205664772
30	108.86	106.218746854509	0.231194268701244	2.64125314549062	0.00374328243966299
31	107.77	106.369141368573	0.219728657043503	1.4008586314268	-0.101655097675369
32	102.74	106.898607067006	0.263739395634661	-4.15860706700593	0.389490496459233
33	112.63	107.884621765110	0.366387079300419	4.74537823489034	0.903999092855174
34	106.26	107.979904909540	0.327900003699129	-1.71990490954012	-0.337764564139119
35	108.86	108.211499608656	0.314249277317939	0.648500391343989	-0.119835732872230
36	111.38	108.884283310002	0.365019863815243	2.49571668999779	0.447353213592940
37	106.85	109.362924486883	0.381113107618596	-2.51292448688286	0.142362655773949
38	107.86	109.480796057433	0.343789774283389	-1.62079605743325	-0.330251126803274
39	107.94	109.230671964586	0.259540914608190	-1.29067196458562	-0.74260390625776
40	111.38	110.410000407980	0.389919242876660	0.969999592020206	1.14486603829128
41	111.29	111.14879061502	0.439307416397044	0.141209384980030	0.433707369910372
42	113.72	111.517672330211	0.429344261551867	2.20232766978863	-0.0877675937289686
43	111.88	111.516254580638	0.368385500242395	0.363745419362447	-0.538398849073008
44	109.87	112.733466042757	0.48858785721744	-2.8634660427575	1.06139970862604
45	113.72	111.753764270742	0.280610168210390	1.96623572925750	-1.83217261052912
46	111.71	112.228765533310	0.308132937919581	-0.518765533310143	0.241957837634612
47	114.81	113.290479838713	0.414747753730156	1.51952016128710	0.93719175067661
48	112.05	112.287721550502	0.214298740856166	-0.237721550501600	-1.76509080836131
49	111.54	112.670748901700	0.238160946616792	-1.13074890170043	0.210503334246384
50	110.87	112.797086023392	0.222339535949491	-1.92708602339242	-0.139596124003331
51	110.87	112.937618709707	0.210762397569870	-2.06761870970746	-0.101994701269503
52	115.48	113.719114534012	0.291510083438655	1.76088546598836	0.710247001111174
53	111.63	113.143943927448	0.168957211384853	-1.51394392744759	-1.07776134551946
54	116.24	113.316524732870	0.169469429378559	2.92347526713025	0.00450996867662962
55	113.56	113.429743525224	0.161517490526188	0.130256474775515	-0.0701014886635743
56	106.01	111.482499538652	-0.136677084923912	-5.47249953865152	-2.62906421090012
57	110.45	109.846096888250	-0.348782322526111	0.603903111750462	-1.86826176844829
58	107.77	108.736963978813	-0.456301468765184	-0.966963978812583	-0.946090585318997
59	108.61	107.368862237890	-0.585193834466015	1.24113776211045	-1.13397580907822
60	108.19	107.270653538738	-0.516369492753632	0.919346461261617	0.605936834763827

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/1xoj71259861147.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/1xoj71259861147.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/2kgkz1259861147.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/2kgkz1259861147.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/3gp6u1259861147.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/3gp6u1259861147.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/4o6kq1259861147.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/4o6kq1259861147.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/5km221259861147.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598612074ypicxg40w153t0/5km221259861147.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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