Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 22 »

*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: Wed, 22 Dec 2010 14:25:47 +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/22/t12930281483fp8awg75crzc50.htm/, Retrieved Wed, 22 Dec 2010 15:29:09 +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/22/t12930281483fp8awg75crzc50.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 «

13.193 15.234 14.718 16.961 13.945 15.876 16.226 18.316 16.748 17.904 17.209 18.950 17.225 18.710 17.236 18.687 17.580 19.568 17.381 19.580 17.260 18.661 15.658 18.674 15.908 17.475 17.725 19.562 16.368 19.555 17.743 19.867 15.703 19.324 18.162 19.074 15.323 19.704 18.375 18.352 13.927 17.795 16.761 18.902 16.239 19.158 18.279 15.698 16.239 18.431 18.414 19.801 14.995 18.706 18.232 19.409 16.263 19.017 20.298 19.891 15.203 17.845 17.502 18.532 15.737 17.770 17.224 17.601 14.940 18.507 17.635 19.392 15.699 17.661 18.243 19.643 15.770 17.344 17.229 17.322 16.152 17.919 16.918 18.114 16.308 17.759 16.021 17.952 15.954 17.762 16.610 17.751 15.458 18.106 15.990 15.349 13.185 15.409 16.007 16.633 14.800 15.974 15.693

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.363992	3.6217	0.000232
2	0.142213	1.415	0.080104
3	-0.075009	-0.7463	0.22862
4	-0.322744	-3.2113	0.000891
5	0.031131	0.3097	0.378703
6	0.012989	0.1292	0.448715
7	0.125542	1.2491	0.107281
8	0.025674	0.2555	0.39945
9	-0.132777	-1.3211	0.094754
10	-0.035751	-0.3557	0.361403
11	-0.113808	-1.1324	0.130105
12	-0.051267	-0.5101	0.305558
13	0.037531	0.3734	0.354814
14	-0.0442	-0.4398	0.330524
15	-0.007137	-0.071	0.471766
16	-0.040149	-0.3995	0.345201
17	0.042241	0.4203	0.33759
18	0.105138	1.0461	0.149029
19	0.093642	0.9317	0.176872
20	0.122399	1.2179	0.113087
21	-0.029635	-0.2949	0.384359
22	-0.026516	-0.2638	0.396231
23	-0.065863	-0.6553	0.256889
24	-0.018554	-0.1846	0.426956
25	0.103173	1.0266	0.153566
26	-0.001664	-0.0166	0.493414
27	0.043679	0.4346	0.332399
28	-0.080626	-0.8022	0.212175
29	0.004147	0.0413	0.483586
30	0.024187	0.2407	0.405161
31	-0.059535	-0.5924	0.277478
32	0.047035	0.468	0.32041
33	-0.120723	-1.2012	0.116274
34	-0.07588	-0.755	0.226021
35	-0.005273	-0.0525	0.479132
36	-0.048109	-0.4787	0.316613
37	0.037381	0.3719	0.355368
38	0.021811	0.217	0.41432
39	-0.013041	-0.1298	0.44851
40	0.041694	0.4149	0.339573
41	-0.01	-0.0995	0.46047
42	0.086502	0.8607	0.195745
43	0.074329	0.7396	0.230657
44	-0.013173	-0.1311	0.447995
45	0.051597	0.5134	0.304415
46	-0.041953	-0.4174	0.338634
47	0.035027	0.3485	0.364098
48	0.068042	0.677	0.24999
49	0.032102	0.3194	0.375046
50	-0.00733	-0.0729	0.471003
51	-0.127111	-1.2647	0.104466
52	-0.124282	-1.2366	0.109582
53	-0.110955	-1.104	0.136136
54	0.034579	0.3441	0.365767
55	0.11135	1.1079	0.13529
56	0.07327	0.729	0.233852
57	0.020817	0.2071	0.418169
58	-0.05815	-0.5786	0.282091
59	-0.087367	-0.8693	0.193396
60	-0.057318	-0.5703	0.284882

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.363992	3.6217	0.000232
2	0.011207	0.1115	0.455719
3	-0.150187	-1.4943	0.069134
4	-0.295147	-2.9367	0.002063
5	0.327501	3.2586	0.000767
6	-0.051837	-0.5158	0.303581
7	0.047971	0.4773	0.317099
8	-0.196396	-1.9541	0.026754
9	0.030591	0.3044	0.380739
10	0.038357	0.3816	0.351772
11	-0.036505	-0.3632	0.358609
12	-0.14075	-1.4004	0.082253
13	0.092534	0.9207	0.179723
14	-0.047451	-0.4721	0.318936
15	-0.020954	-0.2085	0.417637
16	-0.056579	-0.563	0.287369
17	0.170371	1.6952	0.046593
18	0.012182	0.1212	0.451886
19	0.046535	0.463	0.322185
20	-0.021002	-0.209	0.41745
21	-0.005897	-0.0587	0.476663
22	0.034159	0.3399	0.367333
23	-0.064931	-0.6461	0.259868
24	0.040185	0.3998	0.345068
25	0.077712	0.7732	0.220614
26	-0.081308	-0.809	0.210227
27	0.003349	0.0333	0.486741
28	-0.057594	-0.5731	0.283954
29	0.235481	2.343	0.010565
30	-0.148016	-1.4727	0.071996
31	-0.05643	-0.5615	0.287872
32	-0.001477	-0.0147	0.494152
33	0.034488	0.3432	0.366105
34	-0.094102	-0.9363	0.175698
35	0.007347	0.0731	0.470937
36	-0.034873	-0.347	0.364672
37	0.017282	0.172	0.431911
38	0.008514	0.0847	0.466331
39	-0.057088	-0.568	0.285656
40	0.085966	0.8553	0.197211
41	0.03898	0.3878	0.349483
42	0.035477	0.353	0.362421
43	-0.036425	-0.3624	0.358905
44	-0.017171	-0.1709	0.432344
45	0.051209	0.5095	0.305761
46	0.005325	0.053	0.478926
47	0.026629	0.265	0.395798
48	0.031823	0.3166	0.376095
49	0.000431	0.0043	0.498293
50	-0.101477	-1.0097	0.157554
51	-0.039231	-0.3903	0.34856
52	-0.006627	-0.0659	0.473778
53	0.028967	0.2882	0.38689
54	0.047165	0.4693	0.31995
55	0.016625	0.1654	0.434476
56	-0.02622	-0.2609	0.397363
57	0.001601	0.0159	0.493662
58	0.030286	0.3013	0.381894
59	-0.088197	-0.8776	0.191156
60	-0.012544	-0.1248	0.450462

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930281483fp8awg75crzc50/1m6pp1293027944.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930281483fp8awg75crzc50/1m6pp1293027944.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930281483fp8awg75crzc50/2m6pp1293027944.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930281483fp8awg75crzc50/2m6pp1293027944.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; 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 (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