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*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: Tue, 28 Dec 2010 08:43:45 +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/28/t1293525688k3p5ocpb1r6bz05.htm/, Retrieved Tue, 28 Dec 2010 09:41:31 +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/28/t1293525688k3p5ocpb1r6bz05.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 «

547.344 554.788 562.325 560.854 555.332 543.599 536.662 542.722 593.530 610.763 612.613 611.324 594.167 595.454 590.865 589.379 584.428 573.100 567.456 569.028 620.735 628.884 628.232 612.117 595.404 597.141 593.408 590.072 579.799 574.205 572.775 572.942 619.567 625.809 619.916 587.625 565.742 557.274 560.576 548.854 531.673 525.919 511.038 498.662 555.362 564.591 541.657 527.070 509.846 514.258 516.922 507.561 492.622 490.243 469.357 477.580 528.379 533.590 517.945 506.174 501.866 516.141 528.222 532.638 536.322 536.535 523.597 536.214 586.570 596.594 580.523 564.478 557.560 575.093 580.112 574.761 563.250 551.531 537.034 544.686 600.991 604.378 586.111 563.668 548.604

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	11 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.214548	1.8205	0.036419
2	0.285278	2.4207	0.009008
3	0.290569	2.4656	0.008032
4	0.189513	1.6081	0.056098
5	0.129005	1.0946	0.138661
6	0.163972	1.3913	0.084202
7	0.080476	0.6829	0.248442
8	0.129022	1.0948	0.13863
9	0.073972	0.6277	0.266102
10	-0.096887	-0.8221	0.206864
11	0.168565	1.4303	0.078475
12	-0.151243	-1.2833	0.101744
13	-0.120669	-1.0239	0.154652
14	0.054673	0.4639	0.322055
15	-0.069197	-0.5872	0.279468
16	-0.09923	-0.842	0.201289
17	-0.040712	-0.3454	0.365382
18	-0.092236	-0.7827	0.218199
19	-0.029699	-0.252	0.400877
20	-0.07502	-0.6366	0.263213
21	-0.202263	-1.7163	0.045208
22	-0.064647	-0.5486	0.292505
23	-0.113136	-0.96	0.170136
24	-0.247171	-2.0973	0.019739
25	-0.072659	-0.6165	0.269743
26	-0.188656	-1.6008	0.0569
27	-0.235501	-1.9983	0.024731
28	-0.180769	-1.5339	0.064721
29	-0.093536	-0.7937	0.214996
30	-0.129269	-1.0969	0.138174
31	-0.005635	-0.0478	0.480998
32	-0.096252	-0.8167	0.20839
33	0.044133	0.3745	0.354573
34	-0.051135	-0.4339	0.33283
35	0.019841	0.1684	0.433389
36	-0.01889	-0.1603	0.436553
37	-0.024712	-0.2097	0.417252
38	-0.013548	-0.115	0.4544
39	-0.017597	-0.1493	0.44086
40	0.032852	0.2788	0.390614
41	-0.045998	-0.3903	0.348731
42	0.051745	0.4391	0.330962
43	-0.016522	-0.1402	0.444448
44	0.022851	0.1939	0.423402
45	-0.051371	-0.4359	0.332107
46	-0.05256	-0.446	0.328473
47	-0.026513	-0.225	0.411321
48	-0.006989	-0.0593	0.476438

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.214548	1.8205	0.036419
2	0.250791	2.128	0.018379
3	0.21355	1.812	0.037076
4	0.05954	0.5052	0.307477
5	-0.023438	-0.1989	0.42146
6	0.044641	0.3788	0.352977
7	-0.020319	-0.1724	0.431799
8	0.057147	0.4849	0.314608
9	-0.004626	-0.0393	0.484398
10	-0.196506	-1.6674	0.049889
11	0.171403	1.4544	0.07509
12	-0.204202	-1.7327	0.043714
13	-0.113175	-0.9603	0.170054
14	0.138662	1.1766	0.121618
15	-0.017392	-0.1476	0.441546
16	-0.035034	-0.2973	0.383556
17	-0.040023	-0.3396	0.367572
18	-0.013859	-0.1176	0.453357
19	0.053332	0.4525	0.326122
20	-0.060747	-0.5155	0.303908
21	-0.111302	-0.9444	0.174055
22	-0.084807	-0.7196	0.237046
23	0.023174	0.1966	0.422331
24	-0.12737	-1.0808	0.141703
25	-0.04333	-0.3677	0.357098
26	-0.058579	-0.4971	0.310332
27	-0.098641	-0.837	0.202681
28	-0.081886	-0.6948	0.244701
29	0.112833	0.9574	0.170779
30	0.009412	0.0799	0.468283
31	0.118873	1.0087	0.158256
32	0.011468	0.0973	0.461375
33	0.045817	0.3888	0.349296
34	-0.123969	-1.0519	0.148179
35	0.152051	1.2902	0.100556
36	-0.124017	-1.0523	0.148087
37	-0.127576	-1.0825	0.141318
38	0.014197	0.1205	0.452225
39	-0.088389	-0.75	0.227848
40	-0.01583	-0.1343	0.44676
41	-0.006756	-0.0573	0.477223
42	0.022323	0.1894	0.425149
43	0.037339	0.3168	0.376144
44	-0.031314	-0.2657	0.395613
45	-0.023194	-0.1968	0.422266
46	-0.14399	-1.2218	0.112885
47	0.05878	0.4988	0.309732
48	-0.016921	-0.1436	0.443117

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/1mmce1293525814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/1mmce1293525814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/2xvtz1293525814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/2xvtz1293525814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/3xvtz1293525814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525688k3p5ocpb1r6bz05/3xvtz1293525814.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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

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