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Ad hoc forecasting

*The author of this computation has been verified*

R Software Module: /rwasp_decomposeloess.wasp (opens new window with default values)

Title produced by software: Decomposition by Loess

Date of computation: Fri, 04 Dec 2009 09:14:42 -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/04/t1259943327ct5ai9sv3strzat.htm/, Retrieved Fri, 04 Dec 2009 17:15:33 +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/04/t1259943327ct5ai9sv3strzat.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:

Techniek 2: Seizoenale decompositie met de Loess techniek

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441

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

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	462	465.119535673915	-2.84771620094581	461.728180527031	3.11953567391498
2	455	455.50241226746	-7.33624724325024	461.833834975791	0.502412267459704
3	461	461.400372312312	-1.33986173686214	461.93948942455	0.400372312311902
4	461	457.402548498711	2.51908870978463	462.078362791504	-3.59745150128873
5	463	462.204727546749	1.57803629479271	462.217236158458	-0.795272453250732
6	462	463.765846889886	-2.14860256031235	462.382755670427	1.76584688988561
7	456	453.526961505097	-4.07523668749243	462.548275182395	-2.47303849490294
8	455	456.134942213054	-8.8890104071117	462.754068194058	1.13494221305353
9	456	456.942925907069	-7.90278711278955	462.959861205721	0.942925907068513
10	472	468.158441249063	12.5147555768886	463.326803174049	-3.84155875093739
11	472	466.573957835248	13.7322970223757	463.693745142377	-5.42604216475235
12	471	473.749639181854	4.19528406141069	464.055076756736	2.74963918185381
13	465	468.431307829851	-2.84771620094581	464.416408371094	3.43130782985139
14	459	460.491530285341	-7.33624724325024	464.844716957909	1.49153028534124
15	465	466.066836192139	-1.33986173686214	465.273025544724	1.06683619213862
16	468	467.908861922388	2.51908870978463	465.572049367827	-0.0911380776120154
17	467	466.550890514276	1.57803629479271	465.871073190931	-0.449109485723966
18	463	462.510300264967	-2.14860256031235	465.638302295346	-0.489699735033412
19	460	458.669705287732	-4.07523668749243	465.40553139976	-1.33029471226774
20	462	468.611896383448	-8.8890104071117	464.277114023664	6.61189638344774
21	461	466.754090465222	-7.90278711278955	463.148696647568	5.7540904652218
22	476	478.377542599855	12.5147555768886	461.107701823256	2.37754259985536
23	476	479.20099597868	13.7322970223757	459.066706998944	3.20099597867994
24	471	481.731180725917	4.19528406141069	456.073535212672	10.7311807259168
25	453	455.767352774545	-2.84771620094581	453.080363426401	2.7673527745452
26	443	444.092132355823	-7.33624724325024	449.244114887427	1.09213235582337
27	442	439.931995388409	-1.33986173686214	445.407866348453	-2.06800461159099
28	444	444.201402449635	2.51908870978463	441.279508840581	0.201402449634827
29	438	437.270812372499	1.57803629479271	437.151151332708	-0.729187627500664
30	427	422.832601529747	-2.14860256031235	433.316001030565	-4.16739847025269
31	424	422.59438595907	-4.07523668749243	429.480850728422	-1.40561404092966
32	416	414.609457183064	-8.8890104071117	426.279553224047	-1.39054281693558
33	406	396.824531393117	-7.90278711278955	423.078255719672	-9.17546860688287
34	431	429.050053172899	12.5147555768886	420.435191250213	-1.94994682710114
35	434	436.475576196872	13.7322970223757	417.792126780753	2.4755761968716
36	418	416.326574187241	4.19528406141069	415.478141751348	-1.67342581275864
37	412	413.683559479003	-2.84771620094581	413.164156721943	1.68355947900255
38	404	404.240695200922	-7.33624724325024	411.095552042329	0.240695200921721
39	409	410.312914374148	-1.33986173686214	409.026947362714	1.31291437414836
40	412	414.232521310526	2.51908870978463	407.24838997969	2.23252131052556
41	406	404.952131108541	1.57803629479271	405.469832596666	-1.04786889145856
42	398	394.125615458115	-2.14860256031235	404.022987102198	-3.87438454188549
43	397	395.499095079763	-4.07523668749243	402.57614160773	-1.50090492023742
44	385	376.960996158121	-8.8890104071117	401.928014248991	-8.03900384187915
45	390	386.622900222538	-7.90278711278955	401.279886890252	-3.37709977746226
46	413	411.532763231929	12.5147555768886	401.952481191182	-1.46723676807079
47	413	409.642627485512	13.7322970223757	402.625075492113	-3.35737251448825
48	401	392.993456451483	4.19528406141069	404.811259487106	-8.0065435485169
49	397	389.850272718846	-2.84771620094581	406.9974434821	-7.14972728115418
50	397	391.055419104716	-7.33624724325024	410.280828138534	-5.94458089528405
51	409	405.775648941894	-1.33986173686214	413.564212794969	-3.22435105810649
52	419	418.055388127585	2.51908870978463	417.425523162631	-0.944611872415464
53	424	425.135130174914	1.57803629479271	421.286833530293	1.13513017491425
54	428	433.163749025242	-2.14860256031235	424.984853535071	5.16374902524154
55	430	435.392363147644	-4.07523668749243	428.682873539849	5.39236314764389
56	424	424.500036076354	-8.8890104071117	432.388974330758	0.500036076353979
57	433	437.807711991123	-7.90278711278955	436.095075121667	4.80771199112257
58	456	459.703659001588	12.5147555768886	439.781585421523	3.70365900158828
59	459	460.799607256245	13.7322970223757	443.468095721379	1.79960725624494
60	446	440.732436060453	4.19528406141069	447.072279878136	-5.26756393954668
61	441	434.171252166053	-2.84771620094581	450.676464034893	-6.82874783394692

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/1vqr11259943280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/1vqr11259943280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/213qf1259943280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/213qf1259943280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/38kj11259943280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/38kj11259943280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/44zo01259943280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943327ct5ai9sv3strzat/44zo01259943280.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #seasonal period

if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window

par3 <- as.numeric(par3) #s.degree

if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window

par5 <- as.numeric(par5)#t.degree

if (par6 != '') par6 <- as.numeric(par6)#l.window

par7 <- as.numeric(par7)#l.degree

if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust

nx <- length(x)

x <- ts(x,frequency=par1)

if (par6 != '') {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)

} else {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)

}

m$time.series

m$win

m$deg

m$jump

m$inner

m$outer

bitmap(file='test1.png')

plot(m,main=main)

dev.off()

mylagmax <- nx/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')

acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Component',header=TRUE)

a<-table.element(a,'Window',header=TRUE)

a<-table.element(a,'Degree',header=TRUE)

a<-table.element(a,'Jump',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,m$win['s'])

a<-table.element(a,m$deg['s'])

a<-table.element(a,m$jump['s'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,m$win['t'])

a<-table.element(a,m$deg['t'])

a<-table.element(a,m$jump['t'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Low-pass',header=TRUE)

a<-table.element(a,m$win['l'])

a<-table.element(a,m$deg['l'])

a<-table.element(a,m$jump['l'])

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Seasonal Decomposition by Loess - Time Series Components',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,'Fitted',header=TRUE)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,'Remainder',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,x[i]+m$time.series[i,'remainder'])

a<-table.element(a,m$time.series[i,'seasonal'])

a<-table.element(a,m$time.series[i,'trend'])

a<-table.element(a,m$time.series[i,'remainder'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.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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