Home » date » 2010 » Dec » 24 »

Kristof Nagels

*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 15:05:06 +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/t1293202966m7zjzmlv9weh7mq.htm/, Retrieved Fri, 24 Dec 2010 16:02:49 +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/t1293202966m7zjzmlv9weh7mq.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 «

15 14.4 13 13.7 13.6 15.2 12.9 14 14.1 13.2 11.3 13.3 14.4 13.3 11.6 13.2 13.1 14.6 14 14.3 13.8 13.7 11 14.4 15.6 13.7 12.6 13.2 13.3 14.3 14 13.4 13.9 13.7 10.5 14.5 15 13.5 13.5 13.2 13.8 16.2 14.7 13.9 16 14.4 12.3 15.9 15.9 15.5 15.1 14.5 15.1 17.4 16.2 15.6 17.2 14.9 13.8 17.5 16.2 17.5 16.6 16.2 16.6 19.6 15.9 18 18.3 16.3 14.9 18.2 18.4 18.5 16 17.4 17.2 19.6 17.2 18.3 19.3 18.1 16.2 18.4 20.5 19 16.5 18.7 19 19.2 20.5 19.3 20.6 20.1 16.1 20.4 19.7 15.6 14.4 13.7 14.1 15 14.2 13.6 15.4 14.8 12.5 16.2 16.1 16 15.8 15.2 15.7 18.9 17.4 17 19.8 17.7 16 19.6 19.7

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	-0.406324	-3.9811	6.7e-05
2	0.09256	0.9069	0.183367
3	0.369161	3.617	0.000239
4	-0.282376	-2.7667	0.003397
5	0.220378	2.1593	0.016661
6	0.091529	0.8968	0.186034
7	-0.32429	-3.1774	0.001
8	0.255119	2.4996	0.007064
9	-0.206531	-2.0236	0.022896
10	-0.060691	-0.5946	0.276739
11	0.091808	0.8995	0.185311
12	-0.291732	-2.8584	0.002611
13	0.078594	0.7701	0.221578
14	-0.057191	-0.5604	0.288272
15	-0.006826	-0.0669	0.473407
16	-0.078576	-0.7699	0.221629
17	0.01009	0.0989	0.460727
18	0.020669	0.2025	0.419971
19	-0.037097	-0.3635	0.358523
20	0.024375	0.2388	0.405873
21	0.087473	0.8571	0.196775
22	-0.21913	-2.147	0.017155
23	0.346998	3.3999	0.000492
24	-0.193864	-1.8995	0.030252
25	-0.011167	-0.1094	0.456551
26	0.180276	1.7663	0.040259
27	-0.186859	-1.8308	0.035114
28	0.122213	1.1974	0.117042
29	0.035902	0.3518	0.362891
30	-0.14584	-1.4289	0.078135
31	0.169826	1.6639	0.049692
32	-0.082645	-0.8097	0.210043
33	-0.02473	-0.2423	0.40453
34	0.0983	0.9631	0.168948
35	-0.13743	-1.3465	0.09065
36	0.033065	0.324	0.373334
37	0.032366	0.3171	0.37592
38	-0.05748	-0.5632	0.287309
39	0.031829	0.3119	0.377913
40	-0.052223	-0.5117	0.305026
41	0.078258	0.7668	0.222551
42	-0.045863	-0.4494	0.327093
43	-0.029169	-0.2858	0.387823
44	0.128268	1.2568	0.105944
45	-0.155112	-1.5198	0.065926
46	0.130159	1.2753	0.102641
47	0.026965	0.2642	0.396097
48	-0.124961	-1.2244	0.111906
49	0.143028	1.4014	0.082162
50	-0.069479	-0.6808	0.248833
51	-0.040308	-0.3949	0.346885
52	0.127759	1.2518	0.106847
53	-0.183094	-1.7939	0.037985
54	0.093056	0.9118	0.182091
55	0.008565	0.0839	0.466647
56	-0.120595	-1.1816	0.120144
57	0.071068	0.6963	0.243956
58	-0.03303	-0.3236	0.373463
59	-0.098335	-0.9635	0.168864
60	0.098469	0.9648	0.168537

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.406324	-3.9811	6.7e-05
2	-0.086884	-0.8513	0.198364
3	0.452252	4.4311	1.2e-05
4	0.059877	0.5867	0.279401
5	0.061208	0.5997	0.275055
6	0.079687	0.7808	0.218431
7	-0.28235	-2.7665	0.003399
8	-0.142047	-1.3918	0.083604
9	-0.202955	-1.9885	0.024799
10	-0.022941	-0.2248	0.411315
11	0.013394	0.1312	0.447931
12	-0.113199	-1.1091	0.135076
13	-0.041431	-0.4059	0.342845
14	-0.084137	-0.8244	0.205885
15	0.242002	2.3711	0.009866
16	-0.104925	-1.0281	0.153254
17	-0.024565	-0.2407	0.405155
18	-0.013152	-0.1289	0.448866
19	-0.07612	-0.7458	0.228798
20	-0.059923	-0.5871	0.279249
21	0.042867	0.42	0.337707
22	-0.165302	-1.6196	0.054297
23	0.204231	2.001	0.024105
24	-0.024692	-0.2419	0.404675
25	-0.05986	-0.5865	0.279455
26	-0.087162	-0.854	0.197614
27	0.038209	0.3744	0.354479
28	0.025046	0.2454	0.403336
29	-0.070669	-0.6924	0.245176
30	0.07815	0.7657	0.222864
31	0.004291	0.042	0.483275
32	-0.000414	-0.0041	0.498387
33	0.007933	0.0777	0.469105
34	-0.112029	-1.0977	0.137551
35	0.054709	0.536	0.296587
36	-0.145674	-1.4273	0.078368
37	0.031659	0.3102	0.378543
38	-0.037052	-0.363	0.358689
39	0.156433	1.5327	0.064316
40	-0.054601	-0.535	0.296949
41	0.118757	1.1636	0.12374
42	-0.023927	-0.2344	0.407572
43	-0.077868	-0.7629	0.223684
44	0.024472	0.2398	0.405509
45	-0.040597	-0.3978	0.345842
46	-0.034947	-0.3424	0.366396
47	0.095734	0.938	0.175299
48	-0.010328	-0.1012	0.459805
49	-0.019055	-0.1867	0.426146
50	-0.023528	-0.2305	0.409085
51	0.023532	0.2306	0.409071
52	-0.042117	-0.4127	0.340388
53	-0.031413	-0.3078	0.379456
54	-0.024279	-0.2379	0.406239
55	0.01479	0.1449	0.442541
56	-0.017979	-0.1762	0.430271
57	-0.014344	-0.1405	0.444265
58	-0.053651	-0.5257	0.300163
59	0.035989	0.3526	0.362575
60	-0.098839	-0.9684	0.167635

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/112nl1293203102.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/112nl1293203102.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/2cbmo1293203102.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/2cbmo1293203102.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/3cbmo1293203102.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293202966m7zjzmlv9weh7mq/3cbmo1293203102.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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