Home » date » 2010 » Dec » 29 »

Paper

*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: Wed, 29 Dec 2010 13:52:33 +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/29/t1293630624hyrenr0iic8xh9q.htm/, Retrieved Wed, 29 Dec 2010 14:50:24 +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/29/t1293630624hyrenr0iic8xh9q.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 «

26548 26752 26967 27034 27056 27476 28497 29085 28720 29067 29249 29672 29761 30066 30315 30571 30757 30742 31310 31381 31470 31226 31081 31061 31114 30828 30418 30195 29877 29192 29876 29409 28458 28340 28164 28438 28053 27599 27226 27119 26625 26541 27023 26631 26154 26029 26008 26632 27010 27041 27244 26976 26715 27017 27714 27655 27103 27088 26968 27770 27616 27481 27279 26918 26503 26547 27467 27305 26259 26048 25743

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.948523	7.9924	0
2	0.88953	7.4953	0
3	0.840212	7.0798	0
4	0.803032	6.7665	0
5	0.759566	6.4002	0
6	0.691573	5.8273	0
7	0.617821	5.2059	1e-06
8	0.540067	4.5507	1.1e-05
9	0.459451	3.8714	0.000119
10	0.387704	3.2669	0.000838
11	0.329985	2.7805	0.003472
12	0.273891	2.3078	0.011963
13	0.184874	1.5578	0.061867
14	0.099845	0.8413	0.201499
15	0.029423	0.2479	0.402456
16	-0.023031	-0.1941	0.423342
17	-0.063931	-0.5387	0.295891
18	-0.115665	-0.9746	0.166531
19	-0.164262	-1.3841	0.085332
20	-0.207946	-1.7522	0.04203
21	-0.2404	-2.0257	0.02328
22	-0.262118	-2.2086	0.015214
23	-0.266041	-2.2417	0.014054
24	-0.26897	-2.2664	0.013239
25	-0.293402	-2.4722	0.007912
26	-0.312697	-2.6348	0.005164
27	-0.319616	-2.6931	0.004413
28	-0.314043	-2.6462	0.005009
29	-0.302782	-2.5513	0.006444
30	-0.306704	-2.5843	0.005907
31	-0.301512	-2.5406	0.006627
32	-0.295195	-2.4874	0.00761
33	-0.296764	-2.5006	0.007355
34	-0.289515	-2.4395	0.008604
35	-0.270513	-2.2794	0.012826
36	-0.247885	-2.0887	0.02016
37	-0.246134	-2.074	0.020855
38	-0.244895	-2.0635	0.02136
39	-0.239196	-2.0155	0.023819
40	-0.224883	-1.8949	0.031089
41	-0.209916	-1.7688	0.040612
42	-0.212607	-1.7915	0.038741
43	-0.207529	-1.7487	0.042335
44	-0.206306	-1.7384	0.043241
45	-0.207783	-1.7508	0.042149
46	-0.202512	-1.7064	0.046153
47	-0.192788	-1.6245	0.054354
48	-0.182123	-1.5346	0.064664

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.948523	7.9924	0
2	-0.101342	-0.8539	0.19801
3	0.07144	0.602	0.274557
4	0.080918	0.6818	0.248783
5	-0.093645	-0.7891	0.216349
6	-0.246173	-2.0743	0.02084
7	-0.06825	-0.5751	0.283527
8	-0.137419	-1.1579	0.125389
9	-0.13878	-1.1694	0.123081
10	0.04558	0.3841	0.35104
11	0.128838	1.0856	0.140662
12	-0.008186	-0.069	0.472601
13	-0.336788	-2.8378	0.002959
14	0.064674	0.545	0.293748
15	-0.000378	-0.0032	0.498732
16	-0.024365	-0.2053	0.418962
17	0.110788	0.9335	0.176858
18	-0.013031	-0.1098	0.456439
19	-0.022831	-0.1924	0.423997
20	-0.017228	-0.1452	0.442496
21	0.062278	0.5248	0.300692
22	-0.046193	-0.3892	0.349135
23	0.095179	0.802	0.212616
24	-0.020664	-0.1741	0.431133
25	-0.180007	-1.5168	0.066883
26	0.017558	0.1479	0.441403
27	0.01928	0.1625	0.435703
28	-0.088084	-0.7422	0.230203
29	-0.003826	-0.0322	0.487187
30	-0.016716	-0.1409	0.444193
31	0.077899	0.6564	0.256848
32	-0.051815	-0.4366	0.331862
33	-0.143474	-1.2089	0.115349
34	0.074316	0.6262	0.266596
35	0.014221	0.1198	0.452477
36	0.000543	0.0046	0.498182
37	-0.066976	-0.5644	0.287147
38	0.061897	0.5215	0.301804
39	-0.066316	-0.5588	0.289032
40	-0.06471	-0.5453	0.293643
41	0.009718	0.0819	0.467484
42	-0.082202	-0.6926	0.245396
43	0.01846	0.1555	0.438417
44	-0.071906	-0.6059	0.273259
45	0.030228	0.2547	0.399843
46	0.004196	0.0354	0.485948
47	-0.01571	-0.1324	0.447532
48	-0.039636	-0.334	0.36969

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/13iqh1293630749.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/13iqh1293630749.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/2wrqk1293630749.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/2wrqk1293630749.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/3wrqk1293630749.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630624hyrenr0iic8xh9q/3wrqk1293630749.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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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