Home » date » 2010 » Dec » 28 »

Autocorrelation Function

*Unverified author*

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 12:17:07 +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/t1293538665z04ana7vxtr1if7.htm/, Retrieved Tue, 28 Dec 2010 13:17:47 +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/t1293538665z04ana7vxtr1if7.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 «

-697.3 -143.8 -137.4 -26.9 559.2 630.2 1070.9 -820.8 993.3 741.7 603.6 -145.8 -35.1 395.1 523.1 462.3 183.4 791.5 344.8 -217 406.7 228.6 -580.1 -1550.4 -1447.5 -40.1 -1033.5 -925.6 -347.8 -447.7 -102.6 -2062.2 -929.7 -720.7 -1541.8 -1432.3 -1216.2 -212.8 -378.2 76.9 -101.3 220.4 495.6 -1035.2 61.8 -734.8 -6.9 -1061.1 -854.6 -186.5 244 -992.6 -335.2 316.8 477.6 -572.1

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	0.415675	3.1106	0.001468
2	0.342184	2.5607	0.006585
3	0.320451	2.398	0.009921
4	0.416107	3.1139	0.001454
5	0.227924	1.7056	0.04681
6	-0.06329	-0.4736	0.318806
7	0.130975	0.9801	0.165619
8	0.207787	1.5549	0.062798
9	0.123899	0.9272	0.178907
10	0.012151	0.0909	0.463937
11	0.102313	0.7656	0.223554
12	0.26812	2.0064	0.024824
13	-0.014073	-0.1053	0.458252
14	-0.155829	-1.1661	0.124255
15	-0.182436	-1.3652	0.088821
16	-0.093954	-0.7031	0.242457
17	-0.19172	-1.4347	0.078466
18	-0.43166	-3.2302	0.001036
19	-0.248901	-1.8626	0.033883
20	-0.119041	-0.8908	0.188419
21	-0.152296	-1.1397	0.129635
22	-0.197176	-1.4755	0.072835
23	-0.192338	-1.4393	0.077812
24	0.075764	0.567	0.286502
25	-0.114076	-0.8537	0.198463
26	-0.226374	-1.694	0.047907
27	-0.171628	-1.2843	0.102154
28	-0.114342	-0.8557	0.197917
29	-0.088727	-0.664	0.254716
30	-0.240725	-1.8014	0.03851
31	-0.094722	-0.7088	0.240684
32	-0.01027	-0.0769	0.469506
33	0.017956	0.1344	0.446796
34	-0.015581	-0.1166	0.4538
35	-0.021468	-0.1607	0.436473
36	0.111114	0.8315	0.204611
37	-0.031445	-0.2353	0.407411
38	-0.013502	-0.101	0.459939
39	-0.073769	-0.552	0.291561
40	0.026234	0.1963	0.422536
41	-0.031388	-0.2349	0.407576
42	-0.075202	-0.5628	0.287922
43	-0.056341	-0.4216	0.337458
44	0.045632	0.3415	0.367009
45	0.023658	0.177	0.430057
46	-0.014586	-0.1091	0.456737
47	-0.013051	-0.0977	0.461273
48	0.06107	0.457	0.324717
49	0.019522	0.1461	0.442189
50	0.003291	0.0246	0.49022
51	0.009888	0.074	0.47064
52	0.003474	0.026	0.489677
53	-0.007931	-0.0594	0.476442
54	-0.012867	-0.0963	0.461817
55	0.005524	0.0413	0.483587
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.415675	3.1106	0.001468
2	0.204782	1.5324	0.065521
3	0.154214	1.154	0.126695
4	0.263118	1.969	0.026955
5	-0.071015	-0.5314	0.298613
6	-0.376032	-2.814	0.00337
7	0.143426	1.0733	0.14387
8	0.196647	1.4716	0.073367
9	0.026667	0.1996	0.421274
10	0.028064	0.21	0.417209
11	0.01743	0.1304	0.448345
12	0.061365	0.4592	0.323928
13	-0.263869	-1.9746	0.026625
14	-0.241989	-1.8109	0.037762
15	-0.192036	-1.4371	0.078132
16	-0.053328	-0.3991	0.34568
17	0.10309	0.7715	0.221841
18	-0.110683	-0.8283	0.205514
19	0.003701	0.0277	0.489002
20	0.084358	0.6313	0.265213
21	-0.05701	-0.4266	0.335645
22	0.072061	0.5393	0.295924
23	-0.102384	-0.7662	0.223395
24	0.117746	0.8811	0.191008
25	0.011802	0.0883	0.46497
26	-0.094029	-0.7037	0.242283
27	0.05403	0.4043	0.343758
28	-0.132594	-0.9922	0.162674
29	0.01889	0.1414	0.444045
30	0.098034	0.7336	0.23312
31	-0.042932	-0.3213	0.3746
32	-0.084002	-0.6286	0.266078
33	-0.044671	-0.3343	0.369706
34	0.011012	0.0824	0.467307
35	-0.026182	-0.1959	0.422689
36	-0.082109	-0.6144	0.270705
37	-0.086358	-0.6462	0.26038
38	0.111449	0.834	0.203911
39	-0.008669	-0.0649	0.474252
40	0.079831	0.5974	0.276325
41	-0.17839	-1.3349	0.093648
42	-0.001758	-0.0132	0.494775
43	-0.091889	-0.6876	0.247261
44	0.028552	0.2137	0.415793
45	0.032643	0.2443	0.403955
46	-0.080238	-0.6004	0.275315
47	0.081863	0.6126	0.271309
48	0.053393	0.3996	0.345502
49	-0.042415	-0.3174	0.376059
50	0.074468	0.5573	0.289783
51	-0.031566	-0.2362	0.407062
52	-0.076754	-0.5744	0.284008
53	-0.027393	-0.205	0.419162
54	-0.007409	-0.0554	0.47799
55	-0.010452	-0.0782	0.468968
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293538665z04ana7vxtr1if7/1cewv1293538625.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293538665z04ana7vxtr1if7/1cewv1293538625.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293538665z04ana7vxtr1if7/2cewv1293538625.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293538665z04ana7vxtr1if7/2cewv1293538625.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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 (par2 == 0) {

x <- log(x)

} else {

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

}

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

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

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

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

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