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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: Wed, 29 Dec 2010 13:49:41 +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/29/t129363057134nu6hmfbiwu7sp.htm/, Retrieved Wed, 29 Dec 2010 14:49:31 +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/29/t129363057134nu6hmfbiwu7sp.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 «

60178 53200 59909 55970 47682 50173 43090 36031 42143 48478 36046 31060 54874 60051 71622 66526 50140 55973 40393 38483 42879 47875 40578 31027 62027 56493 65566 62653 53470 59600 42542 42018 44038 44988 43309 26843 69770 64886 79354 63025 54003 55926 45629 40361 43039 44570 43269 25563 68707 60223 74283 61232 61531 65305 51699 44599 35221 55066 45335 28702 69517 69240 71525 77740 62107 65450 51493 43067 49172 54483 38158 27898 58648 56000 62381 59849 48345 55376 45400 38389 44098 48290 41267 31238

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	0.420109	3.5647	0.000326
2	0.3955	3.3559	0.000633
3	0.196534	1.6676	0.049865
4	0.177195	1.5036	0.068535
5	0.172175	1.461	0.074189
6	0.172617	1.4647	0.073678
7	-0.008135	-0.069	0.472579
8	0.056332	0.478	0.317052
9	-0.03124	-0.2651	0.395853
10	-0.08631	-0.7324	0.233161
11	-0.127409	-1.0811	0.141629
12	-0.335342	-2.8455	0.002886
13	-0.223056	-1.8927	0.031209
14	-0.018201	-0.1544	0.438847
15	0.037053	0.3144	0.377061
16	-0.00603	-0.0512	0.479667
17	-0.055907	-0.4744	0.318329
18	-0.208755	-1.7713	0.040367
19	-0.080742	-0.6851	0.247734
20	-0.139756	-1.1859	0.119786
21	0.021904	0.1859	0.426537
22	-0.048861	-0.4146	0.339833
23	0.130666	1.1087	0.135617
24	0.046148	0.3916	0.348262
25	0.129611	1.0998	0.137545
26	0.008478	0.0719	0.471426
27	0.003869	0.0328	0.48695
28	-0.026901	-0.2283	0.410045
29	0.094657	0.8032	0.212254
30	0.102419	0.8691	0.193853
31	0.08726	0.7404	0.230725
32	0.018518	0.1571	0.437791
33	-0.022123	-0.1877	0.425813
34	-0.0803	-0.6814	0.248913
35	-0.087812	-0.7451	0.229315
36	-0.137086	-1.1632	0.124291
37	-0.078032	-0.6621	0.255002
38	-0.053879	-0.4572	0.324459
39	-0.009288	-0.0788	0.468701
40	0.004934	0.0419	0.483362
41	-0.072755	-0.6173	0.269478
42	-0.081385	-0.6906	0.246026
43	-0.069867	-0.5928	0.277574
44	0.070963	0.6021	0.274487
45	-0.032911	-0.2793	0.390424
46	0.080211	0.6806	0.249149
47	0.033705	0.286	0.38785
48	0.056651	0.4807	0.316095
49	0.060886	0.5166	0.303498
50	0.029645	0.2515	0.401054
51	-0.029535	-0.2506	0.401413
52	-0.007689	-0.0652	0.47408
53	-0.003458	-0.0293	0.488337
54	0.043209	0.3666	0.357483
55	-0.012514	-0.1062	0.457865
56	-0.112337	-0.9532	0.171837
57	-0.101872	-0.8644	0.195116
58	-0.109342	-0.9278	0.178306
59	-0.134895	-1.1446	0.128078
60	-0.122742	-1.0415	0.150564

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.420109	3.5647	0.000326
2	0.265946	2.2566	0.013534
3	-0.048555	-0.412	0.340781
4	0.030577	0.2595	0.398013
5	0.094004	0.7976	0.213849
6	0.059826	0.5076	0.306627
7	-0.196134	-1.6643	0.050204
8	0.051394	0.4361	0.332036
9	-0.012857	-0.1091	0.456716
10	-0.144895	-1.2295	0.111449
11	-0.084367	-0.7159	0.238192
12	-0.279332	-2.3702	0.010229
13	0.049196	0.4174	0.338799
14	0.316212	2.6831	0.004521
15	0.124375	1.0554	0.147395
16	-0.139207	-1.1812	0.120703
17	-0.068017	-0.5771	0.282823
18	-0.150415	-1.2763	0.102973
19	-0.032663	-0.2772	0.391227
20	-0.085771	-0.7278	0.234552
21	0.200844	1.7042	0.046326
22	-0.032353	-0.2745	0.392235
23	0.185851	1.577	0.05959
24	-0.092302	-0.7832	0.218037
25	-0.053116	-0.4507	0.326777
26	0.111373	0.945	0.173902
27	0.047338	0.4017	0.344556
28	-0.106633	-0.9048	0.184293
29	-0.029136	-0.2472	0.402719
30	-0.023889	-0.2027	0.419969
31	-0.102988	-0.8739	0.192545
32	-0.031348	-0.266	0.395502
33	0.153059	1.2988	0.099087
34	-0.046062	-0.3909	0.34853
35	0.011786	0.1	0.460308
36	-0.1196	-1.0148	0.15679
37	-0.058533	-0.4967	0.310469
38	0.014185	0.1204	0.452266
39	0.159497	1.3534	0.090085
40	-0.040287	-0.3418	0.366731
41	-0.013098	-0.1111	0.455906
42	-0.024823	-0.2106	0.416885
43	-0.003281	-0.0278	0.488932
44	0.088005	0.7467	0.228824
45	-0.061793	-0.5243	0.300829
46	-0.001297	-0.011	0.495626
47	0.078366	0.665	0.254101
48	-0.093812	-0.796	0.214318
49	-0.010353	-0.0878	0.465121
50	0.014674	0.1245	0.450629
51	0.080731	0.685	0.247764
52	-0.099908	-0.8477	0.199694
53	-0.024045	-0.204	0.419452
54	-0.070891	-0.6015	0.274689
55	-0.096068	-0.8152	0.208833
56	-0.056227	-0.4771	0.317367
57	0.079364	0.6734	0.251417
58	-0.080321	-0.6815	0.248856
59	0.03604	0.3058	0.380315
60	-0.086725	-0.7359	0.232095

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/1eayl1293630577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/1eayl1293630577.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/27jf61293630577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/27jf61293630577.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/37jf61293630577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363057134nu6hmfbiwu7sp/37jf61293630577.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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