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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: Mon, 13 Dec 2010 09:59:22 +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/13/t129223440558kd9mkoxyee7h6.htm/, Retrieved Mon, 13 Dec 2010 11:00:05 +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/13/t129223440558kd9mkoxyee7h6.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 «

31293 30236 30160 32436 30695 27525 26434 25739 25204 24977 24320 22680 22052 21467 21383 21777 21928 21814 22937 23595 20830 19650 19195 19644 18483 18079 19178 18391 18441 18584 20108 20148 19394 17745 17696 17032 16438 15683 15594 15713 15937 16171 15928 16348 15579 15305 15648 14954 15137 15839 16050 15168 17064 16005 14886 14931 14544 13812

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.027018	0.1812	0.428497
2	-0.129154	-0.8664	0.195436
3	-0.234797	-1.5751	0.061123
4	-0.02222	-0.1491	0.441088
5	-0.032196	-0.216	0.414992
6	0.076041	0.5101	0.306237
7	0.14538	0.9752	0.167327
8	-0.195052	-1.3085	0.098682
9	0.106531	0.7146	0.239264
10	-0.163883	-1.0994	0.138729
11	-2.2e-05	-1e-04	0.499942
12	-0.143882	-0.9652	0.169804
13	0.190499	1.2779	0.103918
14	-0.047453	-0.3183	0.375855
15	0.083811	0.5622	0.288377
16	0.088758	0.5954	0.277277
17	-0.045918	-0.308	0.379742
18	0.014547	0.0976	0.461347
19	-0.16105	-1.0804	0.142869
20	0.104462	0.7008	0.243532
21	-0.137138	-0.92	0.181252
22	0.107719	0.7226	0.236832
23	0.049093	0.3293	0.371718
24	-0.082554	-0.5538	0.291232
25	-0.224366	-1.5051	0.069644
26	0.085153	0.5712	0.285345
27	0.125056	0.8389	0.20298
28	-0.057107	-0.3831	0.351731
29	0.046145	0.3096	0.379165
30	0.003719	0.0249	0.490103
31	0.038334	0.2572	0.399116
32	0.019708	0.1322	0.447706
33	0.106889	0.717	0.23853
34	-0.045635	-0.3061	0.38046
35	-0.0198	-0.1328	0.447464
36	-0.02452	-0.1645	0.435044
37	-0.130251	-0.8738	0.193446
38	-0.022051	-0.1479	0.441531
39	0.020965	0.1406	0.444391
40	-0.009823	-0.0659	0.473878
41	-0.029161	-0.1956	0.422895
42	0.018412	0.1235	0.451125
43	0.002973	0.0199	0.492087
44	-0.003184	-0.0214	0.491527
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.027018	0.1812	0.428497
2	-0.129979	-0.8719	0.193939
3	-0.231418	-1.5524	0.063786
4	-0.034134	-0.229	0.409963
5	-0.09817	-0.6585	0.256771
6	0.014408	0.0967	0.461717
7	0.125298	0.8405	0.202529
8	-0.232746	-1.5613	0.062729
9	0.191593	1.2852	0.102641
10	-0.207049	-1.3889	0.085845
11	-0.030601	-0.2053	0.41914
12	-0.135699	-0.9103	0.183758
13	0.094977	0.6371	0.263636
14	-0.123992	-0.8318	0.204967
15	0.137873	0.9249	0.17998
16	0.029124	0.1954	0.422992
17	0.057217	0.3838	0.351457
18	0.017042	0.1143	0.454745
19	-0.098365	-0.6599	0.256356
20	0.037353	0.2506	0.401642
21	-0.099807	-0.6695	0.25329
22	-0.055202	-0.3703	0.356445
23	0.16107	1.0805	0.142841
24	-0.259293	-1.7394	0.044401
25	-0.096676	-0.6485	0.259972
26	0.161565	1.0838	0.142111
27	-0.073945	-0.496	0.31114
28	-0.016074	-0.1078	0.457305
29	-0.01581	-0.1061	0.458004
30	0.041334	0.2773	0.391418
31	0.021823	0.1464	0.442133
32	0.085161	0.5713	0.285328
33	-0.029135	-0.1954	0.422964
34	0.170312	1.1425	0.129646
35	-0.091302	-0.6125	0.271654
36	-0.056146	-0.3766	0.354106
37	-0.044908	-0.3013	0.382304
38	-0.055366	-0.3714	0.356039
39	-0.086223	-0.5784	0.282939
40	-0.003117	-0.0209	0.491704
41	-0.055044	-0.3692	0.356838
42	0.036188	0.2428	0.40465
43	-0.044014	-0.2953	0.384577
44	0.022002	0.1476	0.44166
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t129223440558kd9mkoxyee7h6/17amw1292234350.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t129223440558kd9mkoxyee7h6/17amw1292234350.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t129223440558kd9mkoxyee7h6/27amw1292234350.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t129223440558kd9mkoxyee7h6/27amw1292234350.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 (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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