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*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: Thu, 03 Dec 2009 09:01:18 -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/t1259856154arkbg4jmazb1qp0.htm/, Retrieved Thu, 03 Dec 2009 17:02:36 +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/t1259856154arkbg4jmazb1qp0.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8 8.1 8

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.406605	3.1495	0.001275
2	-0.176074	-1.3639	0.088852
3	-0.522452	-4.0469	7.5e-05
4	-0.400424	-3.1017	0.001466
5	0.064889	0.5026	0.308534
6	0.420436	3.2567	0.000928
7	0.301447	2.335	0.011453
8	-0.068114	-0.5276	0.299857
9	-0.284633	-2.2048	0.015658
10	-0.270928	-2.0986	0.020035
11	0.015091	0.1169	0.453667
12	0.304305	2.3571	0.010849
13	0.129725	1.0048	0.159504
14	0.026141	0.2025	0.42011
15	-0.029837	-0.2311	0.409005
16	-0.107248	-0.8307	0.204707
17	-0.090195	-0.6986	0.243736
18	-0.017473	-0.1353	0.446395
19	0.011996	0.0929	0.463137
20	0.033712	0.2611	0.397442
21	0.087886	0.6808	0.24932
22	0.007538	0.0584	0.476815
23	-0.063458	-0.4915	0.312417
24	-0.051094	-0.3958	0.34684
25	-0.15156	-1.174	0.122521
26	0.004548	0.0352	0.486006
27	0.123459	0.9563	0.171377
28	0.111171	0.8611	0.196299
29	0.033966	0.2631	0.396688
30	-0.061838	-0.479	0.316841
31	-0.114365	-0.8859	0.189614
32	-0.146746	-1.1367	0.130094
33	-0.052385	-0.4058	0.343175
34	0.030975	0.2399	0.4056
35	0.097437	0.7547	0.226677
36	0.085072	0.659	0.25622
37	-0.066401	-0.5143	0.304452
38	-0.087937	-0.6812	0.249196
39	-0.089457	-0.6929	0.245512
40	0.038907	0.3014	0.382086
41	0.11472	0.8886	0.188879
42	0.155009	1.2007	0.117294
43	0.034526	0.2674	0.395023
44	-0.109166	-0.8456	0.200568
45	-0.161847	-1.2537	0.107414
46	-0.040077	-0.3104	0.378652
47	0.072728	0.5633	0.287649
48	0.125356	0.971	0.167722

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.406605	3.1495	0.001275
2	-0.409025	-3.1683	0.001206
3	-0.367271	-2.8449	0.003035
4	-0.108475	-0.8402	0.202055
5	0.152617	1.1822	0.120902
6	0.145067	1.1237	0.132811
7	-0.110387	-0.8551	0.197961
8	-0.109296	-0.8466	0.200291
9	0.067138	0.52	0.302473
10	-0.0334	-0.2587	0.39837
11	0.02606	0.2019	0.420355
12	0.111813	0.8661	0.194943
13	-0.248094	-1.9217	0.029697
14	0.22284	1.7261	0.044737
15	0.225278	1.745	0.043053
16	-0.156043	-1.2087	0.11576
17	-0.161825	-1.2535	0.107445
18	0.03267	0.2531	0.400542
19	0.111377	0.8627	0.195862
20	-0.041756	-0.3234	0.373743
21	-0.059255	-0.459	0.32395
22	-0.038905	-0.3014	0.382092
23	-0.00613	-0.0475	0.481143
24	0.101089	0.783	0.218344
25	-0.175382	-1.3585	0.089696
26	-0.057121	-0.4425	0.329876
27	0.01447	0.1121	0.455565
28	0.13035	1.0097	0.15835
29	0.032275	0.25	0.401721
30	-0.158039	-1.2242	0.112838
31	0.007032	0.0545	0.478372
32	-0.07839	-0.6072	0.273003
33	-0.079219	-0.6136	0.270891
34	0.025219	0.1953	0.422892
35	-0.061257	-0.4745	0.318434
36	-0.079618	-0.6167	0.269876
37	0.029915	0.2317	0.408772
38	0.050708	0.3928	0.347935
39	-0.093973	-0.7279	0.234749
40	0.102847	0.7966	0.214398
41	-0.010709	-0.083	0.467084
42	0.043961	0.3405	0.367326
43	-0.011513	-0.0892	0.464618
44	0.083194	0.6444	0.260879
45	-0.066636	-0.5162	0.303821
46	0.05902	0.4572	0.3246
47	-0.008811	-0.0682	0.472908
48	-0.009676	-0.0749	0.470253

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259856154arkbg4jmazb1qp0/1qoj41259856076.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259856154arkbg4jmazb1qp0/1qoj41259856076.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259856154arkbg4jmazb1qp0/29itc1259856076.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259856154arkbg4jmazb1qp0/29itc1259856076.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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