Home » date » 2008 » Dec » 21 »

400 random numbers: Autocorrelation Plot

*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: Sun, 21 Dec 2008 14:08:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229893799k7y8eefk7p4vozq.htm/, Retrieved Sun, 21 Dec 2008 22:10:01 +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/2008/Dec/21/t1229893799k7y8eefk7p4vozq.htm/},
    year = {2008},
}
@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 = {2008},
    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:

s0800650 Jan Werkhoven

Dataseries X:

» Textbox « » Textfile « » CSV «

63 59 10 21 12 63 61 59 70 26 74 82 40 39 28 92 2 54 25 40 96 4 29 22 14 47 15 80 92 22 57 42 53 72 15 65 29 7 84 1 36 56 86 65 75 85 12 11 68 79 90 71 68 23 6 97 6 65 18 78 14 98 79 30 74 1 36 25 41 93 39 77 51 67 51 85 71 71 74 45 47 83 82 23 73 67 14 84 40 67 52 23 4 56 81 75 37 30 56 51 67 50 67 59 17 53 44 6 49 84 52 37 4 53 52 43 94 50 39 61 96 2 38 11 82 40 46 99 81 39 88 66 24 27 23 54 85 66 48 18 57 78 90 15 72 5 25 97 37 39 22 88 39 30 79 7 91 36 14 91 34 10 71 28 40 92 47 34 60 79 23 26 29 3 97 52 48 15 62 96 12 31 72 45 75 54 45 64 9 41 85 11 59 11 21 95 45 88 47 18 100 46 27 2 79 69 33 31 34 31 63 94 26 92 80 70 88 57 54 70 80 17 53 86 95 58 8 28 48 2 69 2 52 57 60 22 90 35 87 42 29 6 3 88 17 1 62 3 26 12 74 39 2 8 66 43 86 33 63 36 69 73 8 74 64 6 98 93 60 93 55 4 42 79 2 36 8 79 2 80 79 37 28 54 21 72 84 11 34 70 12 9 76 60 7 43 70 54 13 55 95 49 69 30 11 66 19 47 44 32 51 57 2 39 83 70 10 82 67 24 0 9 58 62 77 56 36 16 38 41 18 46 4 12 16 82 48 58 79 94 62 62 99 14 85 87 61 27 96 10 24 40 16 59 18 79 91 38 75 4 85 4 19 40 1 10 61 33 53 46 86 83 56 72 66 60 36 7 87 42 98 53 85 18 70 22 12 35 94 5 56 42 0 58 18 66 67 68 76 59

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	-0.095516	-1.9103	0.028404
2	-0.00951	-0.1902	0.424621
3	0.079598	1.592	0.056092
4	-0.066619	-1.3324	0.091746
5	0.011544	0.2309	0.40876
6	-0.030146	-0.6029	0.27345
7	0.021245	0.4249	0.335571
8	-0.050738	-1.0148	0.155415
9	-0.069776	-1.3955	0.081816
10	0.080749	1.615	0.053552
11	-0.046015	-0.9203	0.178983
12	-0.041933	-0.8387	0.201079
13	0.052623	1.0525	0.146613
14	0.004451	0.089	0.464554
15	-0.051248	-1.025	0.153002
16	0.011759	0.2352	0.407097
17	-0.046108	-0.9222	0.1785
18	0.053797	1.0759	0.141302
19	-0.07838	-1.5676	0.058883
20	0.033309	0.6662	0.252843
21	-0.036204	-0.7241	0.234722
22	0.021442	0.4288	0.334132
23	0.013562	0.2712	0.393172
24	-0.077984	-1.5597	0.059812
25	0.006432	0.1286	0.448855
26	-0.026319	-0.5264	0.299457
27	0.025417	0.5083	0.30575
28	-1.5e-05	-3e-04	0.499883
29	-0.065326	-1.3065	0.096064
30	0.024791	0.4958	0.310145
31	0.001381	0.0276	0.488987
32	0.060375	1.2075	0.113978
33	0.036645	0.7329	0.232025
34	-0.019821	-0.3964	0.346
35	-0.015942	-0.3188	0.375008
36	-0.010629	-0.2126	0.41588
37	-0.038655	-0.7731	0.219962
38	0.033922	0.6784	0.24894
39	0.013075	0.2615	0.396918
40	-0.032847	-0.6569	0.2558
41	-0.011397	-0.2279	0.409907
42	0.052878	1.0576	0.145448
43	0.051942	1.0388	0.149752
44	-0.032593	-0.6519	0.257436
45	0.027834	0.5567	0.289027
46	0.061989	1.2398	0.10789
47	-0.092478	-1.8496	0.032557
48	-0.069997	-1.3999	0.081152
49	0.102997	2.0599	0.020026
50	-0.048677	-0.9735	0.165436
51	0.01152	0.2304	0.408951
52	-0.101625	-2.0325	0.021382
53	0.010126	0.2025	0.419807
54	0.053437	1.0687	0.142918
55	-0.025145	-0.5029	0.307658
56	0.105164	2.1033	0.018032
57	-0.017079	-0.3416	0.366425
58	-0.000924	-0.0185	0.492636
59	0.076456	1.5291	0.063513
60	0.01323	0.2646	0.395726

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.095516	-1.9103	0.028404
2	-0.018805	-0.3761	0.353518
3	0.077612	1.5522	0.060699
4	-0.052494	-1.0499	0.147204
5	0.002087	0.0417	0.483363
6	-0.036629	-0.7326	0.232119
7	0.024829	0.4966	0.309878
8	-0.052692	-1.0538	0.146297
9	-0.074549	-1.491	0.068377
10	0.060807	1.2161	0.112325
11	-0.024461	-0.4892	0.312474
12	-0.045192	-0.9038	0.183314
13	0.027891	0.5578	0.288641
14	0.022581	0.4516	0.325891
15	-0.050872	-1.0174	0.154778
16	-0.004446	-0.0889	0.464597
17	-0.056208	-1.1242	0.130809
18	0.057559	1.1512	0.125173
19	-0.070991	-1.4198	0.078221
20	0.015661	0.3132	0.377138
21	-0.048751	-0.975	0.16507
22	0.048617	0.9723	0.165734
23	-0.012275	-0.2455	0.403101
24	-0.073105	-1.4621	0.072249
25	-0.016326	-0.3265	0.372101
26	-0.026176	-0.5235	0.30045
27	0.029898	0.598	0.2751
28	-0.018316	-0.3663	0.357163
29	-0.055925	-1.1185	0.132012
30	-0.00127	-0.0254	0.489878
31	0.013468	0.2694	0.393894
32	0.053439	1.0688	0.142908
33	0.037165	0.7433	0.228868
34	-0.015046	-0.3009	0.381819
35	-0.02769	-0.5538	0.290011
36	-0.028673	-0.5735	0.283328
37	-0.03139	-0.6278	0.265247
38	0.019095	0.3819	0.351369
39	0.034282	0.6856	0.24667
40	-0.040095	-0.8019	0.211543
41	-0.025325	-0.5065	0.306395
42	0.063069	1.2614	0.103954
43	0.058515	1.1703	0.121287
44	-0.022439	-0.4488	0.326915
45	-0.004695	-0.0939	0.462616
46	0.064744	1.2949	0.098054
47	-0.058565	-1.1713	0.121089
48	-0.106817	-2.1363	0.016629
49	0.085553	1.7111	0.043923
50	-0.011905	-0.2381	0.40596
51	0.03581	0.7162	0.237145
52	-0.152227	-3.0445	0.001242
53	0.001898	0.038	0.484868
54	0.076171	1.5234	0.064222
55	0.001927	0.0385	0.484639
56	0.057082	1.1416	0.127145
57	0.01617	0.3234	0.373283
58	0.034585	0.6917	0.244766
59	0.035234	0.7047	0.240712
60	0.026807	0.5361	0.29608

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229893799k7y8eefk7p4vozq/1e7ud1229893710.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229893799k7y8eefk7p4vozq/1e7ud1229893710.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229893799k7y8eefk7p4vozq/2ncfk1229893710.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229893799k7y8eefk7p4vozq/2ncfk1229893710.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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