Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 24 »

*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: Fri, 24 Dec 2010 13:37:17 +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/24/t1293197705eznv23yt5589gv0.htm/, Retrieved Fri, 24 Dec 2010 14:35:08 +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/24/t1293197705eznv23yt5589gv0.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 «

6.4 7.7 9.2 8.6 7.4 8.6 6.2 6 6.6 5.1 4.7 5 3.6 1.9 -0.1 -5.7 -5.6 -6.4 -7.7 -8 -11.9 -15.4 -15.5 -13.4 -10.9 -10.8 -7.3 -6.5 -5.1 -5.3 -6.8 -8.4 -8.4 -9.7 -8.8 -9.6 -11.5 -11 -14.9 -16.2 -14.4 -17.3 -15.7 -12.6 -9.4 -8.1 -5.4 -4.6 -4.9 -4 -3.1 -1.3 0 -0.4 3 0.4 1.2 0.6 -1.3 -3.2 -1.8 -3.6 -4.2 -6.9 -8 -7.5 -8.2 -7.6 -3.7 -1.7 -0.7 0.2 0.6 2.2 3.3 5.3 5.5 6.3 7.7 6.5 5.5 6.9 5.7 6.9 6.1 4.8 3.7 5.8 6.8 8.5 7.2 5 4.7 2.3 2.4 0.1 1.9 1.7 2 -1.9 0.5 -1.3 -3.3 -2.8 -8 -13.9 -21.9 -28.8 -27.6 -31.4 -31.8 -29.4 -27.6 -23.6 -22.8 -18.2 -17.8 -14.2 -8.8 -7.9 -7 -7 -3.6 -2.4 -4.9 -7.7 -6.5 -5.1 -3.4 -2.8 0.8

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	0.964347	11.0375	0
2	0.908635	10.3998	0
3	0.831751	9.5198	0
4	0.740944	8.4805	0
5	0.646858	7.4036	0
6	0.546623	6.2564	0
7	0.448412	5.1323	1e-06
8	0.353039	4.0407	4.5e-05
9	0.25987	2.9743	0.001748
10	0.177826	2.0353	0.021918
11	0.103386	1.1833	0.119416
12	0.03747	0.4289	0.334365
13	-0.016926	-0.1937	0.423344
14	-0.056184	-0.6431	0.260657
15	-0.088897	-1.0175	0.155402
16	-0.115731	-1.3246	0.093804
17	-0.136675	-1.5643	0.060077
18	-0.156958	-1.7965	0.037363
19	-0.173348	-1.9841	0.02467
20	-0.190302	-2.1781	0.015594
21	-0.202244	-2.3148	0.01109
22	-0.212023	-2.4267	0.008298
23	-0.221831	-2.539	0.006144
24	-0.230654	-2.64	0.004649
25	-0.242374	-2.7741	0.003172
26	-0.257287	-2.9448	0.001913
27	-0.279246	-3.1961	0.000873
28	-0.30471	-3.4876	0.000332
29	-0.329426	-3.7705	0.000123
30	-0.349368	-3.9987	5.3e-05
31	-0.366128	-4.1905	2.5e-05
32	-0.371292	-4.2496	2e-05
33	-0.374401	-4.2852	1.8e-05
34	-0.369454	-4.2286	2.2e-05
35	-0.360875	-4.1304	3.2e-05
36	-0.34694	-3.9709	5.9e-05
37	-0.323427	-3.7018	0.000157
38	-0.290117	-3.3205	0.000582
39	-0.250855	-2.8712	0.002385
40	-0.203297	-2.3268	0.010754
41	-0.160478	-1.8368	0.034256
42	-0.119557	-1.3684	0.086765
43	-0.08501	-0.973	0.166179
44	-0.063713	-0.7292	0.233581
45	-0.054899	-0.6283	0.265436
46	-0.052768	-0.604	0.273457
47	-0.061899	-0.7085	0.239955
48	-0.075531	-0.8645	0.194448

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964347	11.0375	0
2	-0.304553	-3.4858	0.000334
3	-0.277854	-3.1802	0.000919
4	-0.136249	-1.5594	0.060652
5	0.026624	0.3047	0.380532
6	-0.097854	-1.12	0.132384
7	-0.00479	-0.0548	0.47818
8	-0.020861	-0.2388	0.405832
9	-0.063225	-0.7236	0.235289
10	0.067169	0.7688	0.221703
11	-0.011469	-0.1313	0.447881
12	-0.035524	-0.4066	0.342485
13	0.023834	0.2728	0.392721
14	0.111288	1.2737	0.102504
15	-0.104564	-1.1968	0.116776
16	-0.074828	-0.8564	0.196658
17	0.001519	0.0174	0.493079
18	-0.074799	-0.8561	0.196749
19	-0.00793	-0.0908	0.463909
20	-0.048719	-0.5576	0.289029
21	0.044064	0.5043	0.307437
22	-0.03092	-0.3539	0.361995
23	-0.024565	-0.2812	0.389517
24	-0.049248	-0.5637	0.286972
25	-0.080409	-0.9203	0.179546
26	-0.056956	-0.6519	0.257807
27	-0.124862	-1.4291	0.077676
28	-0.051494	-0.5894	0.278313
29	0.007949	0.091	0.463824
30	0.077387	0.8857	0.188692
31	-0.058266	-0.6669	0.253007
32	0.109414	1.2523	0.106345
33	-0.103837	-1.1885	0.1184
34	0.034589	0.3959	0.346415
35	-0.054698	-0.626	0.266188
36	-0.00103	-0.0118	0.495307
37	0.058499	0.6696	0.25216
38	0.082284	0.9418	0.17402
39	-0.026088	-0.2986	0.382864
40	0.005841	0.0669	0.473399
41	-0.120536	-1.3796	0.08503
42	-0.031776	-0.3637	0.358338
43	-0.045092	-0.5161	0.303328
44	-0.150474	-1.7222	0.043692
45	-0.117346	-1.3431	0.090784
46	0.045396	0.5196	0.302116
47	-0.103879	-1.189	0.118304
48	-0.027442	-0.3141	0.376978

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/1ply91293197835.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/1ply91293197835.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/2icgc1293197835.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/2icgc1293197835.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/3icgc1293197835.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197705eznv23yt5589gv0/3icgc1293197835.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