Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 21 »

*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: Tue, 21 Dec 2010 12:03:44 +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/21/t129293290519gynaaxi04oj5z.htm/, Retrieved Tue, 21 Dec 2010 13:01:51 +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/21/t129293290519gynaaxi04oj5z.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 «

695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 707 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841 892 782 813 793 978 775 797 946 594 438 1022 868

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.295168	2.2479	0.014199
2	0.254803	1.9405	0.028591
3	0.345618	2.6321	0.005427
4	0.02247	0.1711	0.432361
5	0.135045	1.0285	0.153998
6	0.307349	2.3407	0.011354
7	0.019913	0.1517	0.439992
8	0.351018	2.6733	0.00487
9	0.193454	1.4733	0.073038
10	0.058341	0.4443	0.329235
11	0.152443	1.161	0.125205
12	-0.189828	-1.4457	0.076823
13	-0.229277	-1.7461	0.043042
14	0.112762	0.8588	0.197002
15	-0.047441	-0.3613	0.359595
16	-0.025248	-0.1923	0.424097
17	0.129092	0.9831	0.164811
18	-0.092227	-0.7024	0.242626
19	-0.07734	-0.589	0.279072
20	-0.004235	-0.0323	0.487191
21	-0.169487	-1.2908	0.100951
22	-0.182033	-1.3863	0.085478
23	-0.08062	-0.614	0.270813
24	-0.184791	-1.4073	0.082333
25	-0.046804	-0.3564	0.3614
26	-0.142198	-1.0829	0.141657
27	-0.258789	-1.9709	0.026758
28	-0.088195	-0.6717	0.25223
29	-0.117982	-0.8985	0.186311
30	-0.283816	-2.1615	0.017399
31	-0.064417	-0.4906	0.312786
32	-0.197447	-1.5037	0.06904
33	-0.198922	-1.5149	0.067608
34	-0.051776	-0.3943	0.347399
35	-0.078321	-0.5965	0.27659
36	-0.064923	-0.4944	0.311431

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.295168	2.2479	0.014199
2	0.183682	1.3989	0.083587
3	0.260755	1.9859	0.025892
4	-0.184909	-1.4082	0.082201
5	0.074528	0.5676	0.286254
6	0.254708	1.9398	0.028636
7	-0.105094	-0.8004	0.213382
8	0.303876	2.3142	0.012108
9	-0.101838	-0.7756	0.220575
10	0.029183	0.2222	0.41245
11	-0.090946	-0.6926	0.245654
12	-0.363774	-2.7704	0.003755
13	-0.112464	-0.8565	0.197624
14	0.148233	1.1289	0.131792
15	0.177945	1.3552	0.090306
16	-0.167243	-1.2737	0.103928
17	0.03368	0.2565	0.399236
18	0.018852	0.1436	0.443167
19	-0.062369	-0.475	0.318288
20	0.107035	0.8152	0.209159
21	0.004182	0.0319	0.487349
22	-0.198442	-1.5113	0.068072
23	-0.039384	-0.2999	0.382646
24	-0.166009	-1.2643	0.105592
25	-0.089246	-0.6797	0.249706
26	-0.100821	-0.7678	0.222852
27	0.00512	0.039	0.484515
28	0.100505	0.7654	0.223561
29	0.027591	0.2101	0.417154
30	-0.096454	-0.7346	0.232779
31	-0.050381	-0.3837	0.351305
32	0.044967	0.3425	0.366621
33	0.104533	0.7961	0.21461
34	-0.100287	-0.7638	0.224052
35	0.080694	0.6145	0.27063
36	0.071864	0.5473	0.293137

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/1j8ci1292933021.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/1j8ci1292933021.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/2uzt21292933021.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/2uzt21292933021.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/3uzt21292933021.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129293290519gynaaxi04oj5z/3uzt21292933021.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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