Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 25 »

*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: Sat, 25 Dec 2010 12:49:36 +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/25/t1293281399756uh1o8hllhs7g.htm/, Retrieved Sat, 25 Dec 2010 13:49:59 +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/25/t1293281399756uh1o8hllhs7g.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 «

130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135 124 118 121 121

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.796786	6.2231	0
2	0.478397	3.7364	0.000207
3	0.228707	1.7863	0.039514
4	0.112767	0.8807	0.190958
5	0.106004	0.8279	0.205471
6	0.113549	0.8868	0.189323
7	0.075288	0.588	0.279345
8	0.046847	0.3659	0.357857
9	0.097819	0.764	0.22391
10	0.245924	1.9207	0.029722
11	0.452037	3.5305	0.000398
12	0.560379	4.3767	2.4e-05
13	0.370963	2.8973	0.00261
14	0.102426	0.8	0.213416
15	-0.102724	-0.8023	0.212746
16	-0.194546	-1.5194	0.066908
17	-0.198327	-1.549	0.063279
18	-0.19889	-1.5534	0.062753
19	-0.247575	-1.9336	0.028902
20	-0.281506	-2.1986	0.015854
21	-0.251075	-1.961	0.027227
22	-0.134696	-1.052	0.148472
23	0.034792	0.2717	0.393373
24	0.131203	1.0247	0.154769
25	0.00461	0.036	0.485697
26	-0.16718	-1.3057	0.098275
27	-0.286362	-2.2366	0.014491
28	-0.32393	-2.53	0.007003
29	-0.301576	-2.3554	0.010868
30	-0.284974	-2.2257	0.014869
31	-0.302176	-2.3601	0.010743
32	-0.308061	-2.406	0.009586
33	-0.262924	-2.0535	0.022159
34	-0.158545	-1.2383	0.110179
35	-0.020039	-0.1565	0.438074
36	0.059897	0.4678	0.320792
37	-0.005962	-0.0466	0.481506
38	-0.099128	-0.7742	0.220897
39	-0.158644	-1.2391	0.110037
40	-0.160367	-1.2525	0.107582
41	-0.12309	-0.9614	0.170082
42	-0.094045	-0.7345	0.232725
43	-0.088135	-0.6884	0.246919
44	-0.079018	-0.6172	0.269715
45	-0.049512	-0.3867	0.350163
46	0.006811	0.0532	0.478874
47	0.078236	0.611	0.27172
48	0.117556	0.9181	0.18108
49	0.080474	0.6285	0.266004
50	0.025327	0.1978	0.421927
51	-0.012202	-0.0953	0.462196
52	-0.014601	-0.114	0.454791
53	0.009043	0.0706	0.471962
54	0.026757	0.209	0.417579
55	0.02149	0.1678	0.433631
56	0.013629	0.1064	0.457788
57	0.004506	0.0352	0.48602
58	0.002065	0.0161	0.493593
59	0.003511	0.0274	0.489105
60	0.00201	0.0157	0.493764

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.796786	6.2231	0
2	-0.42853	-3.3469	0.000702
3	0.085972	0.6715	0.252231
4	0.092404	0.7217	0.236618
5	0.071058	0.555	0.290469
6	-0.066897	-0.5225	0.301614
7	-0.071257	-0.5565	0.28994
8	0.125816	0.9827	0.164829
9	0.191395	1.4948	0.070055
10	0.228074	1.7813	0.039919
11	0.273164	2.1335	0.018458
12	-0.029211	-0.2281	0.410148
13	-0.601835	-4.7005	8e-06
14	0.185992	1.4526	0.075723
15	-0.072258	-0.5643	0.287293
16	-0.146578	-1.1448	0.128379
17	-0.107361	-0.8385	0.202507
18	-0.054739	-0.4275	0.335251
19	-0.109933	-0.8586	0.196961
20	-0.036817	-0.2876	0.387332
21	-0.070317	-0.5492	0.292438
22	0.005568	0.0435	0.482726
23	-0.044616	-0.3485	0.364347
24	0.03577	0.2794	0.390453
25	-0.045961	-0.359	0.360429
26	0.099174	0.7746	0.220792
27	-0.021314	-0.1665	0.434171
28	-0.032861	-0.2567	0.399155
29	-0.005146	-0.0402	0.484035
30	0.037669	0.2942	0.384801
31	0.051433	0.4017	0.344654
32	-0.064093	-0.5006	0.309234
33	0.03466	0.2707	0.393765
34	-0.060669	-0.4738	0.318653
35	-0.054534	-0.4259	0.33583
36	-0.008421	-0.0658	0.473887
37	0.110119	0.8601	0.196563
38	-0.115631	-0.9031	0.18501
39	-0.022944	-0.1792	0.429189
40	0.051512	0.4023	0.344427
41	0.019052	0.1488	0.441099
42	-0.013951	-0.109	0.456794
43	0.055166	0.4309	0.334045
44	-0.024036	-0.1877	0.425856
45	-0.070332	-0.5493	0.292399
46	-0.045703	-0.357	0.36118
47	-0.022154	-0.173	0.431601
48	0.014427	0.1127	0.455328
49	0.014149	0.1105	0.456185
50	-0.105581	-0.8246	0.206401
51	-0.005323	-0.0416	0.483486
52	0.015359	0.12	0.452454
53	-0.009895	-0.0773	0.469327
54	-0.033584	-0.2623	0.396988
55	-0.088674	-0.6926	0.245605
56	0.042245	0.3299	0.371287
57	-0.107604	-0.8404	0.201979
58	-0.037412	-0.2922	0.385563
59	-0.052623	-0.411	0.341257
60	-0.003317	-0.0259	0.489708

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/16eph1293281372.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/16eph1293281372.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/2yn621293281372.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/2yn621293281372.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/3yn621293281372.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293281399756uh1o8hllhs7g/3yn621293281372.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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