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(partial) autocorrelation function

*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: Sat, 12 Dec 2009 03:03:05 -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/12/t1260612259htrdy2j6w3hqcyv.htm/, Retrieved Sat, 12 Dec 2009 11:04:21 +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/12/t1260612259htrdy2j6w3hqcyv.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 «

10,9 10 9,2 9,2 9,5 9,6 9,5 9,1 8,9 9 10,1 10,3 10,2 9,6 9,2 9,3 9,4 9,4 9,2 9 9 9 9,8 10 9,8 9,3 9 9 9,1 9,1 9,1 9,2 8,8 8,3 8,4 8,1 7,7 7,9 7,9 8 7,9 7,6 7,1 6,8 6,5 6,9 8,2 8,7 8,3 7,9 7,5 7,8 8,3 8,4 8,2 7,7 7,2 7,3 8,1 8,5

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.414377	3.1829	0.001164
2	-0.249016	-1.9127	0.03032
3	-0.510345	-3.92	0.000117
4	-0.344392	-2.6453	0.005222
5	0.092968	0.7141	0.23899
6	0.388229	2.982	0.002079
7	0.246584	1.894	0.031562
8	-0.125756	-0.966	0.169005
9	-0.336133	-2.5819	0.006165
10	-0.249552	-1.9168	0.030052
11	0.058101	0.4463	0.328514
12	0.376795	2.8942	0.00266
13	0.104458	0.8024	0.212784
14	-0.109888	-0.8441	0.201021
15	-0.102212	-0.7851	0.217766
16	-0.060246	-0.4628	0.322621
17	0.056907	0.4371	0.331813
18	0.093003	0.7144	0.238908
19	0.0112	0.086	0.465868
20	-0.14207	-1.0913	0.139797
21	-0.191835	-1.4735	0.072965
22	-0.088925	-0.683	0.248625
23	0.108083	0.8302	0.204885
24	0.234309	1.7998	0.038506
25	0.012991	0.0998	0.460425
26	-0.159559	-1.2256	0.112611
27	-0.100647	-0.7731	0.221279
28	-0.036632	-0.2814	0.389705
29	0.097616	0.7498	0.228176
30	0.157479	1.2096	0.115625
31	0.08705	0.6686	0.253165
32	-0.155949	-1.1979	0.117879
33	-0.242673	-1.864	0.033649
34	-0.066879	-0.5137	0.304688
35	0.16839	1.2934	0.100453
36	0.292647	2.2479	0.014168
37	0.118679	0.9116	0.182846
38	-0.131675	-1.0114	0.157974
39	-0.162743	-1.2501	0.108108
40	-0.043439	-0.3337	0.369909
41	0.167996	1.2904	0.100972
42	0.242469	1.8624	0.033761
43	0.077207	0.593	0.27771
44	-0.226218	-1.7376	0.043749
45	-0.322848	-2.4798	0.008009
46	-0.117017	-0.8988	0.186201
47	0.113482	0.8717	0.19346
48	0.209787	1.6114	0.056215
49	0.087422	0.6715	0.252262
50	-0.089715	-0.6891	0.246726
51	-0.11608	-0.8916	0.188108
52	-0.035769	-0.2747	0.392234
53	0.059735	0.4588	0.324021
54	0.108006	0.8296	0.205052
55	0.046467	0.3569	0.361213
56	-0.072946	-0.5603	0.288694
57	-0.104014	-0.7989	0.213763
58	-0.037263	-0.2862	0.387854
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.414377	3.1829	0.001164
2	-0.507943	-3.9016	0.000124
3	-0.234736	-1.803	0.038245
4	-0.136108	-1.0455	0.150037
5	0.108282	0.8317	0.204457
6	0.096096	0.7381	0.23168
7	-0.07692	-0.5908	0.278444
8	-0.114486	-0.8794	0.19138
9	-0.058426	-0.4488	0.327619
10	-0.057642	-0.4428	0.32978
11	0.028024	0.2153	0.415154
12	0.182302	1.4003	0.083332
13	-0.397019	-3.0496	0.001715
14	0.269919	2.0733	0.021261
15	0.102017	0.7836	0.218203
16	-0.07569	-0.5814	0.281599
17	0.019435	0.1493	0.440919
18	-0.0981	-0.7535	0.227066
19	0.066819	0.5132	0.304848
20	-0.145226	-1.1155	0.13458
21	-0.145012	-1.1139	0.134928
22	-0.034675	-0.2663	0.395451
23	0.088188	0.6774	0.250405
24	-0.06941	-0.5331	0.297967
25	-0.024856	-0.1909	0.424621
26	-0.11087	-0.8516	0.198937
27	0.072162	0.5543	0.290739
28	-0.017887	-0.1374	0.445595
29	-0.045945	-0.3529	0.362708
30	0.032551	0.25	0.401718
31	-0.015547	-0.1194	0.452674
32	-0.175763	-1.3501	0.091077
33	0.040803	0.3134	0.377536
34	0.069521	0.534	0.297675
35	-0.012847	-0.0987	0.460863
36	0.132229	1.0157	0.156967
37	0.00685	0.0526	0.479108
38	0.000894	0.0069	0.497271
39	0.060502	0.4647	0.321919
40	0.140654	1.0804	0.142183
41	0.099128	0.7614	0.224721
42	0.017108	0.1314	0.447948
43	-0.121782	-0.9354	0.176692
44	0.069947	0.5373	0.296551
45	-0.052735	-0.4051	0.343448
46	-0.123036	-0.9451	0.174242
47	-0.037034	-0.2845	0.388526
48	-0.09259	-0.7112	0.239881
49	0.052974	0.4069	0.342777
50	0.021568	0.1657	0.434492
51	-0.065402	-0.5024	0.30864
52	0.02785	0.2139	0.415675
53	-0.06117	-0.4699	0.320096
54	-0.03243	-0.2491	0.402076
55	0.086766	0.6665	0.253857
56	-0.030757	-0.2362	0.40703
57	0.002739	0.021	0.491644
58	-0.023439	-0.18	0.428869
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260612259htrdy2j6w3hqcyv/11ocf1260612183.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260612259htrdy2j6w3hqcyv/11ocf1260612183.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260612259htrdy2j6w3hqcyv/22d5z1260612183.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260612259htrdy2j6w3hqcyv/22d5z1260612183.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

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 (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='lags',ylab='ACF')

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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