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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: Sun, 27 Dec 2009 03:33:35 -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/27/t1261910068ackpm89bvyglwl2.htm/, Retrieved Sun, 27 Dec 2009 11:34:30 +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/27/t1261910068ackpm89bvyglwl2.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 «

28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485

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	0.385435	3.2248	0.000958
2	0.175431	1.4678	0.073324
3	-0.020436	-0.171	0.432366
4	-0.195835	-1.6385	0.052905
5	-0.278864	-2.3331	0.01126
6	-0.501629	-4.1969	3.9e-05
7	-0.279419	-2.3378	0.011131
8	-0.205261	-1.7173	0.045169
9	-0.084584	-0.7077	0.240745
10	0.064703	0.5413	0.294993
11	0.230933	1.9321	0.028696
12	0.719208	6.0173	0
13	0.244645	2.0468	0.022215
14	0.107124	0.8963	0.186592
15	-0.040225	-0.3365	0.368734
16	-0.17941	-1.5011	0.068919
17	-0.244922	-2.0492	0.022098
18	-0.448956	-3.7562	0.000177
19	-0.262152	-2.1933	0.015804
20	-0.206493	-1.7276	0.044231
21	-0.101366	-0.8481	0.199639
22	0.055267	0.4624	0.322616
23	0.225911	1.8901	0.031442
24	0.600415	5.0234	2e-06
25	0.274961	2.3005	0.012202
26	0.139081	1.1636	0.124261
27	0.013456	0.1126	0.455343
28	-0.117223	-0.9808	0.165045
29	-0.171687	-1.4364	0.077666
30	-0.326869	-2.7348	0.003951
31	-0.190977	-1.5978	0.057293
32	-0.172029	-1.4393	0.077261
33	-0.10167	-0.8506	0.198937
34	0.024494	0.2049	0.419111
35	0.12406	1.038	0.151431
36	0.375807	3.1442	0.001222
37	0.180054	1.5064	0.068227
38	0.078502	0.6568	0.256733
39	0.011063	0.0926	0.46326
40	-0.086738	-0.7257	0.235221
41	-0.121069	-1.0129	0.15729
42	-0.192105	-1.6073	0.056249
43	-0.09679	-0.8098	0.210398
44	-0.098175	-0.8214	0.207105
45	-0.038071	-0.3185	0.375519
46	0.047118	0.3942	0.347308
47	0.099271	0.8306	0.204524
48	0.240875	2.0153	0.023857
49	0.146035	1.2218	0.112938
50	0.083155	0.6957	0.244453
51	0.044945	0.376	0.354013
52	-0.026918	-0.2252	0.411235
53	-0.045939	-0.3843	0.350942
54	-0.07608	-0.6365	0.263252
55	-0.068578	-0.5738	0.283982
56	-0.086306	-0.7221	0.236323
57	-0.054939	-0.4597	0.323594
58	-0.009399	-0.0786	0.468774
59	0.022437	0.1877	0.42582
60	0.073157	0.6121	0.271236

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.385435	3.2248	0.000958
2	0.031559	0.264	0.396261
3	-0.115312	-0.9648	0.168991
4	-0.186797	-1.5629	0.061298
5	-0.157512	-1.3178	0.095927
6	-0.394672	-3.3021	0.000757
7	0.011896	0.0995	0.4605
8	-0.122138	-1.0219	0.155179
9	-0.096596	-0.8082	0.210863
10	-0.049604	-0.415	0.339699
11	0.095553	0.7995	0.213365
12	0.613516	5.133	1e-06
13	-0.425899	-3.5633	0.000332
14	-0.09631	-0.8058	0.211548
15	-0.041966	-0.3511	0.363278
16	0.010328	0.0864	0.465692
17	-0.053445	-0.4472	0.328073
18	-0.054061	-0.4523	0.326225
19	-0.13376	-1.1191	0.133457
20	-0.085023	-0.7114	0.239613
21	-0.005101	-0.0427	0.48304
22	0.058163	0.4866	0.314022
23	0.059289	0.496	0.310709
24	-0.080853	-0.6765	0.250487
25	0.117804	0.9856	0.163857
26	-0.100676	-0.8423	0.20124
27	0.02356	0.1971	0.422155
28	-0.010562	-0.0884	0.464919
29	0.058449	0.489	0.313177
30	0.074666	0.6247	0.267099
31	-0.000622	-0.0052	0.497932
32	-0.046888	-0.3923	0.348016
33	-0.011033	-0.0923	0.463359
34	-0.008626	-0.0722	0.471336
35	-0.157231	-1.3155	0.09632
36	-0.103254	-0.8639	0.195301
37	-0.030232	-0.2529	0.400527
38	0.005923	0.0496	0.48031
39	-0.013268	-0.111	0.455963
40	-0.008471	-0.0709	0.471849
41	-0.045866	-0.3837	0.351167
42	0.105296	0.881	0.190675
43	0.065234	0.5458	0.293474
44	0.034387	0.2877	0.387211
45	0.055284	0.4625	0.322565
46	-0.043724	-0.3658	0.357802
47	0.028085	0.235	0.407456
48	-0.049475	-0.4139	0.340094
49	0.085185	0.7127	0.239199
50	0.053113	0.4444	0.329071
51	0.036814	0.308	0.379496
52	0.033701	0.282	0.389401
53	0.061802	0.5171	0.303367
54	-0.011803	-0.0988	0.460808
55	-0.077655	-0.6497	0.259003
56	0.0453	0.379	0.352915
57	-0.036752	-0.3075	0.379691
58	0.019677	0.1646	0.434854
59	0.014868	0.1244	0.450679
60	-0.001336	-0.0112	0.495557

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910068ackpm89bvyglwl2/1uf8o1261910013.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910068ackpm89bvyglwl2/1uf8o1261910013.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910068ackpm89bvyglwl2/24ht21261910013.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910068ackpm89bvyglwl2/24ht21261910013.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; 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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