Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 28 »

*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, 28 Dec 2010 16:35:17 +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/28/t1293553979o52nftsjylaznf0.htm/, Retrieved Tue, 28 Dec 2010 17:33:02 +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/28/t1293553979o52nftsjylaznf0.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 «

11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.493139	4.1844	4e-05
2	0.299328	2.5399	0.006624
3	0.042391	0.3597	0.360064
4	-0.270287	-2.2935	0.012371
5	-0.396917	-3.3679	0.000609
6	-0.442957	-3.7586	0.000172
7	-0.362315	-3.0743	0.00149
8	-0.306288	-2.5989	0.005668
9	0.02369	0.201	0.420626
10	0.18265	1.5498	0.062783
11	0.36771	3.1201	0.0013
12	0.630088	5.3465	1e-06
13	0.364702	3.0946	0.001403
14	0.281332	2.3872	0.009803
15	0.080597	0.6839	0.248121
16	-0.171921	-1.4588	0.074485
17	-0.284638	-2.4152	0.009133
18	-0.371098	-3.1489	0.001193
19	-0.326441	-2.7699	0.003564
20	-0.293631	-2.4915	0.007512
21	-0.027175	-0.2306	0.409143
22	0.15863	1.346	0.091259
23	0.381282	3.2353	0.000918
24	0.542847	4.6062	9e-06
25	0.289859	2.4595	0.008157
26	0.214142	1.8171	0.036685
27	0.017643	0.1497	0.440708
28	-0.21217	-1.8003	0.037999
29	-0.285259	-2.4205	0.009011
30	-0.318965	-2.7065	0.004242
31	-0.286276	-2.4291	0.008816
32	-0.264649	-2.2456	0.013899
33	-0.082574	-0.7007	0.242884
34	0.031934	0.271	0.393595
35	0.200303	1.6996	0.046759
36	0.346557	2.9406	0.002201
37	0.234195	1.9872	0.025352
38	0.231138	1.9613	0.026858
39	0.048413	0.4108	0.341221
40	-0.087849	-0.7454	0.229221
41	-0.168618	-1.4308	0.078411
42	-0.22063	-1.8721	0.032626
43	-0.220457	-1.8706	0.032729
44	-0.225133	-1.9103	0.030038
45	-0.084314	-0.7154	0.238328
46	-0.012761	-0.1083	0.457036
47	0.11899	1.0097	0.158019
48	0.170711	1.4485	0.075904
49	0.065154	0.5529	0.291038
50	0.080721	0.6849	0.247791
51	-0.020174	-0.1712	0.432279
52	-0.082227	-0.6977	0.2438
53	-0.128713	-1.0922	0.139201
54	-0.078031	-0.6621	0.255006
55	-0.138934	-1.1789	0.121161
56	-0.112139	-0.9515	0.17226
57	-0.045593	-0.3869	0.349997
58	0.008349	0.0708	0.471859
59	0.066277	0.5624	0.287801
60	0.101414	0.8605	0.196178

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.493139	4.1844	4e-05
2	0.074182	0.6295	0.265522
3	-0.173855	-1.4752	0.072258
4	-0.343084	-2.9112	0.002395
5	-0.189253	-1.6059	0.05634
6	-0.127689	-1.0835	0.141106
7	-0.046211	-0.3921	0.348065
8	-0.187948	-1.5948	0.05757
9	0.186211	1.5801	0.059239
10	0.059798	0.5074	0.306713
11	0.146466	1.2428	0.108985
12	0.398729	3.3833	0.000581
13	-0.177133	-1.503	0.068603
14	0.056261	0.4774	0.317266
15	0.074661	0.6335	0.2642
16	-0.03261	-0.2767	0.391399
17	0.09178	0.7788	0.219332
18	-0.077008	-0.6534	0.257778
19	0.005875	0.0498	0.48019
20	-0.003698	-0.0314	0.487526
21	-0.017656	-0.1498	0.440665
22	0.171335	1.4538	0.07517
23	0.160582	1.3626	0.08863
24	0.058248	0.4943	0.311316
25	-0.174624	-1.4817	0.071387
26	-0.080462	-0.6827	0.248479
27	0.042357	0.3594	0.36017
28	-0.06632	-0.5627	0.28768
29	0.013961	0.1185	0.453015
30	0.047992	0.4072	0.342524
31	-0.032733	-0.2777	0.391001
32	-0.08028	-0.6812	0.248966
33	-0.182911	-1.5521	0.062517
34	-0.116178	-0.9858	0.163766
35	-0.086044	-0.7301	0.233848
36	-0.042151	-0.3577	0.36082
37	0.039021	0.3311	0.370765
38	0.00724	0.0614	0.475594
39	-0.1061	-0.9003	0.185483
40	0.04899	0.4157	0.339436
41	0.001401	0.0119	0.495274
42	0.060108	0.51	0.305794
43	0.056175	0.4767	0.317523
44	-0.006761	-0.0574	0.477204
45	0.016931	0.1437	0.443084
46	-0.074335	-0.6308	0.265099
47	-0.045549	-0.3865	0.350134
48	-0.036743	-0.3118	0.378055
49	-0.142668	-1.2106	0.115009
50	-0.013048	-0.1107	0.456076
51	0.045443	0.3856	0.350467
52	-0.03136	-0.2661	0.395461
53	-0.119185	-1.0113	0.157626
54	0.060454	0.513	0.304771
55	-0.089766	-0.7617	0.224366
56	0.094181	0.7992	0.213414
57	-0.004384	-0.0372	0.485216
58	0.128086	1.0868	0.140364
59	-0.037847	-0.3211	0.374517
60	-0.068924	-0.5848	0.280243

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/1uwur1293554112.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/1uwur1293554112.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/2ffbe1293554112.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/2ffbe1293554112.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/3ffbe1293554112.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553979o52nftsjylaznf0/3ffbe1293554112.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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