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WS 9 Estimation of Box-Jenkins ARIMA models

*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 08:02:19 -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/t1259939050oe8ak21ak499d9v.htm/, Retrieved Fri, 04 Dec 2009 16:04:16 +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/t1259939050oe8ak21ak499d9v.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:

WS 9 Estimation of Box-Jenkins ARIMA models

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

14,5 14,3 15,3 14,4 13,7 14,2 13,5 11,9 14,6 15,6 14,1 14,9 14,2 14,6 17,2 15,4 14,3 17,5 14,5 14,4 16,6 16,7 16,6 16,9 15,7 16,4 18,4 16,9 16,5 18,3 15,1 15,7 18,1 16,8 18,9 19 18,1 17,8 21,5 17,1 18,7 19 16,4 16,9 18,6 19,3 19,4 17,6 18,6 18,1 20,4 18,1 19,6 19,9 19,2 17,8 19,2 22 21,1 19,5 22,2 20,9 22,2 23,5 21,5 24,3 22,8 20,3 23,7 23,3 19,6 18 17,3 16,8 18,2 16,5 16 18,4

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	781	0	79
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	14.5	15.0944532290277	-0.321335927618347	14.2268826985906	0.594453229027726
2	14.3	14.9650721971997	-0.59085823509362	14.2257860378939	0.665072197199716
3	15.3	14.9499760662701	1.42533455653270	14.2246893771972	-0.350023933729888
4	14.4	14.7456178657239	-0.183679804806304	14.2380619390824	0.345617865723927
5	13.7	13.5555433650574	-0.406977866024921	14.2514345009676	-0.144456634942642
6	14.2	12.8760850067394	1.24921530405955	14.2746996892011	-1.32391499326060
7	13.5	13.6548576916501	-0.952822569084688	14.2979648774345	0.154857691650145
8	11.9	11.1995927387024	-1.72620934364556	14.3266166049432	-0.700407261297611
9	14.6	14.2943291927125	0.550402474835696	14.3552683324518	-0.305670807287495
10	15.6	15.7427654562491	1.00827513293133	14.4489594108195	0.142765456249149
11	14.1	13.3412002132200	0.316149297592766	14.5426504891873	-0.758799786780017
12	14.9	15.4668485678870	-0.367492995063122	14.7006444271762	0.56684856788697
13	14.2	13.8626975624533	-0.321335927618347	14.8586383651651	-0.337302437546709
14	14.6	14.7685528763388	-0.59085823509362	15.0223053587548	0.168552876338834
15	17.2	17.7886930911228	1.42533455653270	15.1859723523445	0.588693091122785
16	15.4	15.6421099855524	-0.183679804806304	15.3415698192539	0.242109985552359
17	14.3	13.5098105798616	-0.406977866024921	15.4971672861634	-0.79018942013845
18	17.5	18.1087233572831	1.24921530405955	15.6420613386574	0.608723357283052
19	14.5	14.1658671779333	-0.952822569084688	15.7869553911514	-0.334132822066735
20	14.4	14.6030839049608	-1.72620934364556	15.9231254386847	0.203083904960845
21	16.6	16.5903020389463	0.550402474835696	16.059295486218	-0.0096979610536998
22	16.7	16.2015447212874	1.00827513293133	16.1901801457813	-0.498455278712596
23	16.6	16.5627858970627	0.316149297592766	16.3210648053445	-0.0372141029372948
24	16.9	17.7352648692324	-0.367492995063122	16.4322281258307	0.835264869232414
25	15.7	15.1779444813015	-0.321335927618347	16.5433914463169	-0.52205551869854
26	16.4	16.7591426981985	-0.59085823509362	16.6317155368951	0.359142698198532
27	18.4	18.6546258159940	1.42533455653270	16.7200396274733	0.254625815994018
28	16.9	17.1676488388048	-0.183679804806304	16.8160309660015	0.267648838804806
29	16.5	16.4949555614952	-0.406977866024921	16.9120223045297	-0.00504443850478609
30	18.3	18.3010436952202	1.24921530405955	17.0497410007203	0.00104369522018999
31	15.1	13.9653628721739	-0.952822569084688	17.1874596969108	-1.13463712782612
32	15.7	15.7671766129765	-1.72620934364556	17.3590327306691	0.0671766129764677
33	18.1	18.1189917607369	0.550402474835696	17.5306057644274	0.0189917607369345
34	16.8	14.8988060824935	1.00827513293133	17.6929187845751	-1.90119391750646
35	18.9	19.6286188976843	0.316149297592766	17.8552318047229	0.728618897684328
36	19	20.3830520511956	-0.367492995063122	17.9844409438675	1.38305205119560
37	18.1	18.4076858446062	-0.321335927618347	18.1136500830121	0.307685844606208
38	17.8	17.9863847916615	-0.59085823509362	18.2044734434321	0.186384791661542
39	21.5	23.2793686396153	1.42533455653270	18.295296803852	1.77936863961529
40	17.1	16.0441556039335	-0.183679804806304	18.3395242008728	-1.05584439606645
41	18.7	19.4232262681314	-0.406977866024921	18.3837515978935	0.723226268131413
42	19	18.3724464907157	1.24921530405955	18.3783382052247	-0.62755350928428
43	16.4	15.3798977565287	-0.952822569084688	18.3729248125559	-1.02010224347126
44	16.9	17.1531573324591	-1.72620934364556	18.3730520111865	0.253157332459082
45	18.6	18.2764183153473	0.550402474835696	18.373179209817	-0.323581684652702
46	19.3	19.1692937740355	1.00827513293133	18.4224310930331	-0.130706225964452
47	19.4	20.012167726158	0.316149297592766	18.4716829762493	0.612167726157981
48	17.6	16.9893391266856	-0.367492995063122	18.5781538683775	-0.610660873314352
49	18.6	18.8367111671126	-0.321335927618347	18.6846247605057	0.236711167112645
50	18.1	17.9848713841974	-0.59085823509362	18.8059868508962	-0.115128615802622
51	20.4	20.4473165021805	1.42533455653270	18.9273489412868	0.047316502180518
52	18.1	17.3147424746840	-0.183679804806304	19.0689373301223	-0.785257525315984
53	19.6	20.3964521470671	-0.406977866024921	19.2105257189578	0.796452147067129
54	19.9	19.1468725545415	1.24921530405955	19.4039121413989	-0.753127445458471
55	19.2	19.7555240052446	-0.952822569084688	19.5972985638400	0.555524005244646
56	17.8	17.4878858871229	-1.72620934364556	19.8383234565226	-0.312114112877069
57	19.2	17.7702491759591	0.550402474835696	20.0793483492052	-1.42975082404092
58	22	22.6328269250382	1.00827513293133	20.3588979420305	0.632826925038188
59	21.1	21.2454031675515	0.316149297592766	20.6384475348558	0.145403167551478
60	19.5	18.4246517007967	-0.367492995063122	20.9428412942664	-1.07534829920328
61	22.2	23.4741008739413	-0.321335927618347	21.2472350536770	1.27410087394130
62	20.9	20.861797160875	-0.59085823509362	21.5290610742186	-0.038202839125006
63	22.2	21.1637783487071	1.42533455653270	21.8108870947602	-1.03622165129291
64	23.5	25.2461859749217	-0.183679804806304	21.9374938298846	1.74618597492174
65	21.5	21.342877301016	-0.406977866024921	22.0641005650089	-0.157122698984004
66	24.3	25.4267933095586	1.24921530405955	21.9239913863819	1.12679330955856
67	22.8	24.7689403613298	-0.952822569084688	21.7838822077548	1.96894036132984
68	20.3	20.9179896223853	-1.72620934364556	21.4082197212603	0.617989622385252
69	23.7	25.8170402903985	0.550402474835696	21.0325572347658	2.11704029039854
70	23.3	25.1388839369123	1.00827513293133	20.4528409301564	1.83888393691229
71	19.6	19.0107260768602	0.316149297592766	19.8731246255470	-0.589273923139785
72	18	17.0625475421009	-0.367492995063122	19.3049454529623	-0.937452457899145
73	17.3	16.1845696472408	-0.321335927618347	18.7367662803775	-1.11543035275917
74	16.8	16.0475862668205	-0.59085823509362	18.1432719682731	-0.752413733179505
75	18.2	17.4248877872986	1.42533455653270	17.5497776561687	-0.775112212701433
76	16.5	16.240476640808	-0.183679804806304	16.9432031639983	-0.259523359192006
77	16	16.0703491941970	-0.406977866024921	16.3366286718279	0.0703491941970356
78	18.4	19.8200096647170	1.24921530405955	15.7307750312235	1.42000966471696

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/1o9wx1259938937.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/1o9wx1259938937.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/2x1dp1259938937.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/2x1dp1259938937.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/300k41259938937.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/300k41259938937.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/4bv221259938937.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939050oe8ak21ak499d9v/4bv221259938937.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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