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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 16 Dec 2009 06:56:33 -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/16/t1260971845ue9xs5b88etwoed.htm/, Retrieved Wed, 16 Dec 2009 14:57:27 +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/16/t1260971845ue9xs5b88etwoed.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

1,61 1,58 1,69 1,78 1,76 1,83 1,8 1,57 1,45 1,4 1,55 1,58 1,58 1,59 1,8 1,99 2,06 2,06 2,08 2 1,85 1,77 1,7 1,66 1,67 1,73 1,91 2,02 2,07 2,15 2,1 1,68 1,68 1,65 1,72 1,73 1,76 1,84 1,99 2,05 2,12 2,13 2,08 1,88 1,81 1,81 1,88 1,87 1,87 1,9 2,01 2,05 2,16 2,18 2,15 2,12 2,04 2,04 2,06 1,93 1,86 1,94 2,35 2,46 2,59 2,66 2,41 2,18 2,13 2,11 2,12 2,16 2,07 2,2 2,29 2,32 2,37 2,38 2,38 2,28 2,22 2,25 2,3 2,3 2,23 2,27 2,3 2,32 2,41 2,43 2,45 2,47 2,46 2,5 2,46 2,43 2,37 2,45 2,53 2,56 2,62 2,67 2,62 2,6 2,53 2,49 2,48 2,44

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.933217	9.6983	0
2	0.82377	8.5609	0
3	0.714697	7.4273	0
4	0.622201	6.4661	0
5	0.55326	5.7496	0
6	0.521678	5.4214	0
7	0.518508	5.3885	0
8	0.534969	5.5596	0
9	0.559619	5.8157	0
10	0.58797	6.1104	0
11	0.615977	6.4014	0
12	0.6143	6.384	0
13	0.559821	5.8178	0
14	0.476753	4.9546	1e-06
15	0.397255	4.1284	3.6e-05
16	0.335631	3.488	0.000353
17	0.288483	2.998	0.001686
18	0.266083	2.7652	0.003346
19	0.265864	2.7629	0.003368
20	0.28639	2.9763	0.001801
21	0.316387	3.288	0.000681
22	0.359662	3.7377	0.000149
23	0.398479	4.1411	3.4e-05
24	0.403962	4.1981	2.8e-05
25	0.361702	3.7589	0.000139
26	0.299967	3.1173	0.001169
27	0.240724	2.5017	0.00693
28	0.187636	1.95	0.026886
29	0.139758	1.4524	0.074644
30	0.107911	1.1214	0.132292
31	0.092006	0.9562	0.170564
32	0.089828	0.9335	0.176317
33	0.108616	1.1288	0.130747
34	0.14077	1.4629	0.073197
35	0.181489	1.8861	0.030985
36	0.192185	1.9972	0.024157
37	0.154	1.6004	0.056214
38	0.098204	1.0206	0.15487
39	0.041039	0.4265	0.335301
40	-0.013116	-0.1363	0.445917
41	-0.0524	-0.5446	0.293592
42	-0.084711	-0.8803	0.190315
43	-0.104241	-1.0833	0.140544
44	-0.113373	-1.1782	0.120652
45	-0.113283	-1.1773	0.120837
46	-0.10124	-1.0521	0.147548
47	-0.078548	-0.8163	0.208063
48	-0.07757	-0.8061	0.21097

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.933217	9.6983	0
2	-0.365003	-3.7932	0.000123
3	0.053346	0.5544	0.290228
4	0.042541	0.4421	0.329649
5	0.071073	0.7386	0.230871
6	0.191988	1.9952	0.02427
7	0.075688	0.7866	0.216628
8	0.110818	1.1517	0.126003
9	0.072164	0.75	0.227458
10	0.10566	1.098	0.137313
11	0.108801	1.1307	0.130344
12	-0.162105	-1.6846	0.047472
13	-0.258705	-2.6885	0.004157
14	-0.035992	-0.374	0.354554
15	0.053227	0.5531	0.290653
16	0.037281	0.3874	0.349599
17	-0.098869	-1.0275	0.153246
18	0.012137	0.1261	0.44993
19	0.010772	0.1119	0.455537
20	0.114138	1.1862	0.119082
21	0.058443	0.6074	0.272443
22	0.131918	1.3709	0.086619
23	-0.016103	-0.1673	0.433706
24	-0.109788	-1.141	0.128207
25	-0.093913	-0.976	0.165631
26	0.079645	0.8277	0.204833
27	0.013125	0.1364	0.445879
28	-0.100998	-1.0496	0.148122
29	-0.135078	-1.4038	0.081627
30	-0.030062	-0.3124	0.377664
31	-0.026668	-0.2771	0.3911
32	0.001203	0.0125	0.495025
33	0.1011	1.0507	0.14788
34	-0.049058	-0.5098	0.305606
35	0.119797	1.245	0.107919
36	-0.108332	-1.1258	0.131369
37	-0.0985	-1.0236	0.154146
38	0.088485	0.9196	0.179925
39	-0.059455	-0.6179	0.268979
40	-0.015129	-0.1572	0.43768
41	0.057756	0.6002	0.274809
42	-0.205912	-2.1399	0.017307
43	0.030382	0.3157	0.376403
44	-0.098416	-1.0228	0.15435
45	-0.059363	-0.6169	0.269294
46	-0.009388	-0.0976	0.461229
47	0.011947	0.1242	0.450709
48	-0.04886	-0.5078	0.306325

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260971845ue9xs5b88etwoed/12vvf1260971791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260971845ue9xs5b88etwoed/12vvf1260971791.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260971845ue9xs5b88etwoed/2fy6i1260971791.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260971845ue9xs5b88etwoed/2fy6i1260971791.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

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

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

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

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

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

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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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