Home » date » 2009 » Dec » 21 »

Autocorrelation function D=d=Lambda=1

*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: Mon, 21 Dec 2009 07:21:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/21/t1261405362r2wtzoyfs5y21i6.htm/, Retrieved Mon, 21 Dec 2009 15:22:44 +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/2009/Dec/21/t1261405362r2wtzoyfs5y21i6.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.63046	-4.368	3.3e-05
2	0.041743	0.2892	0.386835
3	0.357567	2.4773	0.008406
4	-0.338586	-2.3458	0.011583
5	0.092308	0.6395	0.262759
6	0.159441	1.1046	0.137411
7	-0.28961	-2.0065	0.025229
8	0.249962	1.7318	0.044867
9	-0.14779	-1.0239	0.155503
10	-0.036374	-0.252	0.401055
11	0.199246	1.3804	0.086927
12	-0.227815	-1.5783	0.060527
13	0.09389	0.6505	0.259239
14	0.033308	0.2308	0.40924
15	-0.01944	-0.1347	0.446712
16	-0.068554	-0.475	0.318486
17	0.104033	0.7208	0.237276
18	-0.037173	-0.2575	0.398931
19	-0.073469	-0.509	0.306538
20	0.116664	0.8083	0.211462
21	0.020964	0.1452	0.442564
22	-0.27128	-1.8795	0.033128
23	0.386715	2.6792	0.005039
24	-0.270757	-1.8759	0.033381
25	0.038445	0.2664	0.395552
26	0.150703	1.0441	0.150835
27	-0.179395	-1.2429	0.109973
28	0.045295	0.3138	0.377511
29	0.099473	0.6892	0.247018
30	-0.149936	-1.0388	0.152054
31	0.125789	0.8715	0.193912
32	-0.063934	-0.4429	0.329897
33	-0.055718	-0.386	0.350591
34	0.152328	1.0554	0.148272
35	-0.178022	-1.2334	0.111721
36	0.070178	0.4862	0.314516
37	0.019725	0.1367	0.445936
38	-0.056343	-0.3904	0.349001
39	0.006165	0.0427	0.483055
40	0.052111	0.361	0.359827
41	-0.055467	-0.3843	0.351231
42	0.028755	0.1992	0.421465
43	0.010431	0.0723	0.471345
44	-0.010072	-0.0698	0.472329
45	0.010888	0.0754	0.470091
46	-0.007384	-0.0512	0.479706
47	0.001454	0.0101	0.496003
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
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	-0.63046	-4.368	3.3e-05
2	-0.590414	-4.0905	8.2e-05
3	0.069277	0.48	0.316715
4	0.181106	1.2547	0.107824
5	0.050208	0.3479	0.364737
6	0.076898	0.5328	0.298328
7	-0.15577	-1.0792	0.142945
8	-0.004259	-0.0295	0.48829
9	-0.144808	-1.0033	0.160384
10	-0.176135	-1.2203	0.114156
11	0.069525	0.4817	0.31611
12	0.080789	0.5597	0.289136
13	0.032728	0.2267	0.410791
14	-0.173932	-1.205	0.117048
15	0.128279	0.8887	0.189287
16	-0.008887	-0.0616	0.47558
17	-0.050866	-0.3524	0.363036
18	0.007253	0.0502	0.480067
19	-0.08568	-0.5936	0.277781
20	0.04098	0.2839	0.388846
21	0.223638	1.5494	0.063926
22	-0.251141	-1.74	0.044137
23	-0.033175	-0.2298	0.409596
24	-0.012122	-0.084	0.46671
25	0.115118	0.7976	0.214526
26	-0.008511	-0.059	0.476612
27	0.053126	0.3681	0.357222
28	-0.055546	-0.3848	0.351031
29	-0.125452	-0.8692	0.194544
30	0.043119	0.2987	0.383215
31	0.004309	0.0299	0.488153
32	0.011673	0.0809	0.467939
33	-0.020642	-0.143	0.44344
34	-0.071315	-0.4941	0.31175
35	-0.115739	-0.8019	0.213292
36	-0.1221	-0.8459	0.200894
37	-0.090407	-0.6264	0.267024
38	-0.078034	-0.5406	0.295628
39	0.043741	0.303	0.381582
40	0.015049	0.1043	0.458698
41	-0.027953	-0.1937	0.423627
42	0.076382	0.5292	0.299556
43	0.064147	0.4444	0.329366
44	-0.177849	-1.2322	0.111942
45	0.007436	0.0515	0.479564
46	-0.05062	-0.3507	0.363673
47	0.05836	0.4043	0.343882
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
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/2009/Dec/21/t1261405362r2wtzoyfs5y21i6/1u5ka1261405300.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261405362r2wtzoyfs5y21i6/1u5ka1261405300.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261405362r2wtzoyfs5y21i6/2n1c31261405300.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261405362r2wtzoyfs5y21i6/2n1c31261405300.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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