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ACF-48 lags

*The author of this computation has been verified*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 21 Dec 2010 19:52:07 +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/21/t12929610081zldbaonu00cg6g.htm/, Retrieved Tue, 21 Dec 2010 20:50:10 +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/21/t12929610081zldbaonu00cg6g.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 «

8.1 9.9 11.5 23.4 25.4 27.9 26.1 18.8 14.1 11.5 15.8 12.4 4.5 -2.2 -4.2 -9.4 -14.5 -17.9 -15.1 -15.2 -15.7 -18 -18.1 -13.5 -9.9 -4.8 -1.7 -0.1 2.2 10.2 7.6 10.8 3.8 11 10.8 20.1 14.9 13 10.9 9.6 4 -1.1 -7.7 -8.9 -8 -7.1 -5.3 -2.5 -2.4 -2.9 -4.8 -7.2 1.7 2.2 13.4 12.3 13.7 4.4 -2.5

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	0.918415	7.0545	0
2	0.807254	6.2006	0
3	0.649171	4.9864	3e-06
4	0.512327	3.9353	0.000111
5	0.362863	2.7872	0.003571
6	0.212592	1.6329	0.053903
7	0.055837	0.4289	0.334782
8	-0.097922	-0.7521	0.227476
9	-0.24951	-1.9165	0.030073
10	-0.386274	-2.967	0.002169
11	-0.50757	-3.8987	0.000125
12	-0.592977	-4.5547	1.3e-05
13	-0.628616	-4.8285	5e-06
14	-0.622069	-4.7782	6e-06
15	-0.57851	-4.4436	2e-05
16	-0.527219	-4.0496	7.6e-05
17	-0.447738	-3.4391	0.000538
18	-0.358787	-2.7559	0.003887
19	-0.245076	-1.8825	0.032354
20	-0.150699	-1.1575	0.125858
21	-0.05048	-0.3877	0.349801
22	0.024477	0.188	0.425756
23	0.127023	0.9757	0.166604
24	0.211295	1.623	0.054962
25	0.284095	2.1822	0.016545
26	0.315048	2.4199	0.009311
27	0.320388	2.4609	0.008401
28	0.31882	2.4489	0.00866
29	0.300765	2.3102	0.012196
30	0.268994	2.0662	0.021605
31	0.211823	1.627	0.054529
32	0.149501	1.1483	0.127732
33	0.087494	0.6721	0.252086
34	0.029985	0.2303	0.409319
35	-0.030852	-0.237	0.406749
36	-0.092839	-0.7131	0.239293
37	-0.15334	-1.1778	0.121798
38	-0.194812	-1.4964	0.069943
39	-0.216284	-1.6613	0.050978
40	-0.207374	-1.5929	0.058267
41	-0.178402	-1.3703	0.087887
42	-0.142131	-1.0917	0.139696
43	-0.108536	-0.8337	0.203911
44	-0.077053	-0.5919	0.278103
45	-0.058538	-0.4496	0.327309
46	-0.041861	-0.3215	0.374469
47	-0.023534	-0.1808	0.428585
48	0.010356	0.0795	0.468435

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.918415	7.0545	0
2	-0.23149	-1.7781	0.040269
3	-0.345945	-2.6573	0.00506
4	0.144391	1.1091	0.135946
5	-0.162494	-1.2481	0.108455
6	-0.217728	-1.6724	0.04987
7	-0.076574	-0.5882	0.279328
8	-0.129652	-0.9959	0.161689
9	-0.188249	-1.446	0.076739
10	-0.091299	-0.7013	0.242941
11	-0.11817	-0.9077	0.18387
12	-0.023307	-0.179	0.429266
13	0.137018	1.0525	0.14844
14	0.001292	0.0099	0.496056
15	0.017104	0.1314	0.447963
16	-0.081174	-0.6235	0.267678
17	0.081966	0.6296	0.265696
18	-0.001066	-0.0082	0.496747
19	0.012315	0.0946	0.46248
20	-0.202494	-1.5554	0.062601
21	0.00206	0.0158	0.493715
22	-0.113694	-0.8733	0.193019
23	0.188901	1.451	0.076041
24	-0.01506	-0.1157	0.454149
25	-0.122298	-0.9394	0.17568
26	-0.022172	-0.1703	0.432675
27	-0.034267	-0.2632	0.396653
28	0.123431	0.9481	0.173475
29	-0.063557	-0.4882	0.313613
30	-0.066321	-0.5094	0.306179
31	-0.086135	-0.6616	0.255396
32	0.005689	0.0437	0.482645
33	0.008575	0.0659	0.473852
34	-0.03695	-0.2838	0.38877
35	0.002398	0.0184	0.492684
36	-0.070748	-0.5434	0.294441
37	0.0024	0.0184	0.492677
38	-0.052782	-0.4054	0.343314
39	0.113743	0.8737	0.192918
40	0.119621	0.9188	0.180964
41	0.151464	1.1634	0.124673
42	-0.176106	-1.3527	0.090657
43	-0.122427	-0.9404	0.175429
44	-0.033745	-0.2592	0.398191
45	-0.056844	-0.4366	0.331987
46	0.005035	0.0387	0.484639
47	-0.085299	-0.6552	0.257444
48	0.014279	0.1097	0.456518

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929610081zldbaonu00cg6g/1ucl71292961125.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929610081zldbaonu00cg6g/1ucl71292961125.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929610081zldbaonu00cg6g/2ucl71292961125.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929610081zldbaonu00cg6g/2ucl71292961125.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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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