Home » date » 2010 » Dec » 12 »

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: Sun, 12 Dec 2010 20:17:05 +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/12/t1292184924338cinfla355xvo.htm/, Retrieved Sun, 12 Dec 2010 21:15:26 +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/12/t1292184924338cinfla355xvo.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 «

1038.00 934.00 988.00 870.00 854.00 834.00 872.00 954.00 870.00 1238.00 1082.00 1053.00 934.00 787.00 1081.00 908.00 995.00 825.00 822.00 856.00 887.00 1094.00 990.00 936.00 1097.00 918.00 926.00 907.00 899.00 971.00 1087.00 1000.00 1071.00 1190.00 1116.00 1070.00 1314.00 1068.00 1185.00 1215.00 1145.00 1251.00 1363.00 1368.00 1535.00 1853.00 1866.00 2023.00 1373.00 1968.00 1424.00 1160.00 1243.00 1375.00 1539.00 1773.00 1906.00 2076.00 2004.00

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	0.798186	6.131	0
2	0.707585	5.4351	1e-06
3	0.575185	4.4181	2.2e-05
4	0.452405	3.475	0.000482
5	0.394333	3.0289	0.001819
6	0.362068	2.7811	0.003631
7	0.396707	3.0472	0.001726
8	0.450289	3.4587	0.000507
9	0.467778	3.5931	0.000334
10	0.438293	3.3666	0.000672
11	0.452527	3.4759	0.000481
12	0.365556	2.8079	0.003375
13	0.286618	2.2016	0.01581
14	0.183975	1.4131	0.081434
15	0.120314	0.9241	0.179587
16	0.064845	0.4981	0.310137
17	0.017523	0.1346	0.446693
18	-0.031523	-0.2421	0.404758
19	-0.038174	-0.2932	0.385191
20	-0.056316	-0.4326	0.33345
21	-0.067313	-0.517	0.303531
22	-0.060247	-0.4628	0.322618
23	-0.089111	-0.6845	0.248179
24	-0.103329	-0.7937	0.215281
25	-0.115716	-0.8888	0.188851
26	-0.174151	-1.3377	0.093067
27	-0.213529	-1.6401	0.053148
28	-0.233921	-1.7968	0.038745
29	-0.267667	-2.056	0.022108
30	-0.274436	-2.108	0.019645
31	-0.25243	-1.939	0.028647
32	-0.251264	-1.93	0.02921
33	-0.217041	-1.6671	0.050395
34	-0.22351	-1.7168	0.045629
35	-0.211297	-1.623	0.05496
36	-0.224793	-1.7267	0.04473
37	-0.245477	-1.8855	0.032141
38	-0.265679	-2.0407	0.022881
39	-0.292639	-2.2478	0.01417
40	-0.273867	-2.1036	0.019843
41	-0.298504	-2.2929	0.012719
42	-0.28442	-2.1847	0.016449
43	-0.269696	-2.0716	0.021343
44	-0.248965	-1.9123	0.030346
45	-0.223917	-1.7199	0.045343
46	-0.169857	-1.3047	0.098531
47	-0.127025	-0.9757	0.166599
48	-0.121293	-0.9317	0.177652

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.798186	6.131	0
2	0.194225	1.4919	0.07053
3	-0.100032	-0.7684	0.222668
4	-0.092027	-0.7069	0.241214
5	0.109172	0.8386	0.202548
6	0.116423	0.8943	0.187408
7	0.197973	1.5207	0.066844
8	0.163755	1.2578	0.106706
9	-0.012479	-0.0959	0.46198
10	-0.139282	-1.0698	0.144523
11	0.145495	1.1176	0.134141
12	-0.109966	-0.8447	0.200854
13	-0.114273	-0.8777	0.19182
14	-0.141974	-1.0905	0.139959
15	-0.004884	-0.0375	0.485102
16	-0.088491	-0.6797	0.249674
17	-0.085943	-0.6601	0.255865
18	-0.163375	-1.2549	0.10723
19	-0.030864	-0.2371	0.40671
20	-0.04671	-0.3588	0.360519
21	0.057367	0.4406	0.330541
22	0.040368	0.3101	0.378798
23	-0.047055	-0.3614	0.359533
24	-0.020368	-0.1565	0.438105
25	0.146244	1.1233	0.132925
26	-0.077119	-0.5924	0.277937
27	-0.048213	-0.3703	0.356231
28	0.044679	0.3432	0.366339
29	0.016979	0.1304	0.448339
30	-0.057653	-0.4428	0.329751
31	0.101153	0.777	0.22014
32	-0.083607	-0.6422	0.261616
33	-0.026107	-0.2005	0.420876
34	-0.052091	-0.4001	0.345256
35	0.090159	0.6925	0.245663
36	-0.138274	-1.0621	0.146258
37	-0.034987	-0.2687	0.394535
38	-0.034704	-0.2666	0.395366
39	-0.049255	-0.3783	0.353271
40	0.023765	0.1825	0.427891
41	-0.089657	-0.6887	0.246866
42	-0.079114	-0.6077	0.272864
43	0.030528	0.2345	0.407707
44	-0.010806	-0.083	0.467066
45	0.082155	0.631	0.265225
46	0.10714	0.823	0.206924
47	0.080071	0.615	0.270449
48	-0.086357	-0.6633	0.254855

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292184924338cinfla355xvo/12ci51292185023.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292184924338cinfla355xvo/12ci51292185023.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292184924338cinfla355xvo/22ci51292185023.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292184924338cinfla355xvo/22ci51292185023.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by