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autocorrelation

*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, 12 Dec 2009 06:36:00 -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/12/t1260625033ejqxlyl9mqjvbqz.htm/, Retrieved Sat, 12 Dec 2009 14:37:15 +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/12/t1260625033ejqxlyl9mqjvbqz.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 «

593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274 560576 548854 531673 525919 511038 498662 555362 564591 541657 527070 509846 514258 516922 507561 492622 490243 469357 477580 528379 533590 517945 506174 501866 516141 528222 532638 536322 536535 523597 536214 586570

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	0.220173	1.7055	0.046641
2	-0.222616	-1.7244	0.044894
3	-0.262838	-2.0359	0.023089
4	-0.181764	-1.4079	0.082155
5	0.081547	0.6317	0.265004
6	0.218472	1.6923	0.047891
7	0.08047	0.6233	0.267719
8	-0.226669	-1.7558	0.042116
9	-0.263116	-2.0381	0.022978
10	-0.209417	-1.6221	0.055009
11	0.28768	2.2284	0.014808
12	0.73014	5.6556	0
13	0.095784	0.7419	0.230509
14	-0.226375	-1.7535	0.042312
15	-0.233897	-1.8118	0.037514
16	-0.177837	-1.3775	0.086735
17	0.044602	0.3455	0.365469
18	0.134141	1.039	0.151475
19	0.023351	0.1809	0.428536
20	-0.232716	-1.8026	0.038236
21	-0.240087	-1.8597	0.033916
22	-0.163883	-1.2694	0.104595
23	0.236042	1.8284	0.036233
24	0.497753	3.8556	0.000142
25	0.016588	0.1285	0.449096
26	-0.199679	-1.5467	0.063596
27	-0.17113	-1.3256	0.095004
28	-0.119586	-0.9263	0.178998
29	0.043165	0.3344	0.369639
30	0.074936	0.5804	0.281893
31	0.001085	0.0084	0.496662
32	-0.191374	-1.4824	0.071736
33	-0.17799	-1.3787	0.086553
34	-0.067865	-0.5257	0.300525
35	0.169539	1.3132	0.09705
36	0.29006	2.2468	0.014172
37	-0.004493	-0.0348	0.486176
38	-0.092735	-0.7183	0.237673
39	-0.100969	-0.7821	0.218616
40	-0.027524	-0.2132	0.415947
41	0.034395	0.2664	0.395412
42	0.044793	0.347	0.364916
43	0.004285	0.0332	0.486816
44	-0.093231	-0.7222	0.236499
45	-0.077837	-0.6029	0.274416
46	-0.011318	-0.0877	0.465217
47	0.098742	0.7649	0.223678
48	0.136992	1.0611	0.146441
49	-0.018841	-0.1459	0.44223
50	-0.039544	-0.3063	0.380215
51	-0.036402	-0.282	0.389468
52	-4e-06	0	0.499987
53	0.003256	0.0252	0.489982
54	0.004725	0.0366	0.485462
55	-0.003167	-0.0245	0.490254
56	-0.043885	-0.3399	0.367546
57	-0.01259	-0.0975	0.461319
58	0.015706	0.1217	0.451789
59	0.042959	0.3328	0.370239
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.220173	1.7055	0.046641
2	-0.284904	-2.2069	0.015581
3	-0.15685	-1.215	0.114572
4	-0.162016	-1.255	0.107177
5	0.067569	0.5234	0.301315
6	0.085424	0.6617	0.255352
7	-0.013463	-0.1043	0.458647
8	-0.21263	-1.647	0.052391
9	-0.119785	-0.9279	0.178601
10	-0.226946	-1.7579	0.041931
11	0.292747	2.2676	0.013484
12	0.605602	4.691	8e-06
13	-0.146714	-1.1364	0.130145
14	0.006369	0.0493	0.480407
15	0.023576	0.1826	0.427857
16	-0.113897	-0.8822	0.190583
17	-0.088853	-0.6883	0.246972
18	-0.20925	-1.6208	0.055148
19	-0.049231	-0.3813	0.352149
20	-0.021852	-0.1693	0.433078
21	-0.011949	-0.0926	0.463282
22	-0.031729	-0.2458	0.403349
23	-0.162685	-1.2602	0.106246
24	-0.046898	-0.3633	0.358841
25	-0.030329	-0.2349	0.407531
26	-0.079172	-0.6133	0.27101
27	0.039987	0.3097	0.378917
28	0.025772	0.1996	0.421223
29	0.053613	0.4153	0.339708
30	-0.041093	-0.3183	0.37568
31	-0.006143	-0.0476	0.481104
32	-0.007151	-0.0554	0.478005
33	-0.024299	-0.1882	0.42567
34	0.064511	0.4997	0.309557
35	-0.127028	-0.984	0.164544
36	-0.148193	-1.1479	0.127783
37	0.056242	0.4356	0.332327
38	0.05208	0.4034	0.344042
39	-0.066966	-0.5187	0.302933
40	0.047777	0.3701	0.356315
41	-0.039771	-0.3081	0.379549
42	0.050255	0.3893	0.349227
43	-0.008133	-0.063	0.474987
44	0.069066	0.535	0.29732
45	0.020954	0.1623	0.435805
46	-0.008475	-0.0656	0.47394
47	0.039119	0.303	0.381462
48	-0.06034	-0.4674	0.320956
49	-0.112085	-0.8682	0.194371
50	-0.029321	-0.2271	0.41055
51	-0.058939	-0.4565	0.324826
52	-0.084602	-0.6553	0.257383
53	-0.056502	-0.4377	0.331601
54	-0.007023	-0.0544	0.478399
55	-0.047234	-0.3659	0.357874
56	-0.053147	-0.4117	0.341022
57	0.010893	0.0844	0.466518
58	-0.002678	-0.0207	0.491759
59	0.047641	0.369	0.356703
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260625033ejqxlyl9mqjvbqz/11v0p1260624959.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260625033ejqxlyl9mqjvbqz/11v0p1260624959.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260625033ejqxlyl9mqjvbqz/23z3p1260624959.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260625033ejqxlyl9mqjvbqz/23z3p1260624959.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (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

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