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Autocorrelation function

*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: Fri, 17 Dec 2010 09:14:56 +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/17/t1292577350xk5jdqagsdg8s69.htm/, Retrieved Fri, 17 Dec 2010 10:15:51 +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/17/t1292577350xk5jdqagsdg8s69.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 «

15561600 14917500 14805920 16958000 17605000 17131200 18474600 17286700 18574400 18056000 19701600 19061700 19681900 34521200 19922700 20177900 19759900 23076700 22532000 22029400 22587000 23256600 22680300 21916400 19640200 18813100 18730000 18154700 17848800 18077500 17133100 16602600 15878900 15789100 15422000 14661400 15879200 14339300 13169600 14528900 13375800 12309900 11933900 10061900 12609600 11156500 12187200 11284300 10177000 10970720 10820680 11492390 14573750 13992820 14727070 15685360 16736210 17950180 17002730 17415160 17929810 17865790 19202360 19085000 18188880 18466410 18520400 20025500 20636100 20672000 22589100 21864800 22750100 22548746 21325495 21556563 21415269 20401054 19062253 19085706 19279967 18552045 17800733 17142490 17593173 17633859 17336613 17008347 17951965 14520929 16941217 15436824 14744261 14248004 11540953 12881661 15185757 13554339 13575106 12238400 13303614 14151478 1417 etc...

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.799384	8.1521	0
2	0.765961	7.8113	0
3	0.728086	7.425	0
4	0.69404	7.0779	0
5	0.650442	6.6332	0
6	0.562864	5.7401	0
7	0.512307	5.2245	0
8	0.448121	4.57	7e-06
9	0.369024	3.7633	0.000139
10	0.289466	2.952	0.001951
11	0.175741	1.7922	0.038003
12	0.094056	0.9592	0.169844
13	0.037455	0.382	0.351632
14	-0.022781	-0.2323	0.408372
15	-0.091401	-0.9321	0.176719
16	-0.148754	-1.517	0.06615
17	-0.228459	-2.3298	0.010873
18	-0.293571	-2.9938	0.001721
19	-0.369403	-3.7672	0.000137
20	-0.427777	-4.3625	1.5e-05
21	-0.481143	-4.9067	2e-06
22	-0.530552	-5.4106	0
23	-0.537246	-5.4789	0
24	-0.578126	-5.8958	0
25	-0.607629	-6.1966	0
26	-0.599312	-6.1118	0
27	-0.612007	-6.2413	0
28	-0.604572	-6.1654	0
29	-0.586229	-5.9784	0
30	-0.578038	-5.8949	0
31	-0.511942	-5.2208	0
32	-0.48741	-4.9706	1e-06
33	-0.424921	-4.3334	1.7e-05
34	-0.379785	-3.8731	9.4e-05
35	-0.346214	-3.5307	0.00031
36	-0.28777	-2.9347	0.002055
37	-0.252493	-2.5749	0.005716
38	-0.192478	-1.9629	0.026164
39	-0.109653	-1.1182	0.133019
40	-0.063962	-0.6523	0.257829
41	-0.005959	-0.0608	0.47583
42	0.044699	0.4558	0.324728
43	0.099517	1.0149	0.15626
44	0.160711	1.6389	0.052124
45	0.185617	1.8929	0.030573
46	0.235289	2.3995	0.009099
47	0.271288	2.7666	0.003353
48	0.303387	3.094	0.001269

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.799384	8.1521	0
2	0.351667	3.5863	0.000256
3	0.158045	1.6117	0.055024
4	0.078465	0.8002	0.212713
5	0.003122	0.0318	0.487329
6	-0.16873	-1.7207	0.044138
7	-0.072524	-0.7396	0.230604
8	-0.077953	-0.795	0.214221
9	-0.122396	-1.2482	0.107381
10	-0.112758	-1.1499	0.12641
11	-0.212677	-2.1689	0.016185
12	-0.139789	-1.4256	0.078494
13	0.004261	0.0435	0.482711
14	0.040693	0.415	0.339504
15	0.010869	0.1108	0.455977
16	0.036887	0.3762	0.353776
17	-0.101487	-1.035	0.151541
18	-0.112032	-1.1425	0.127934
19	-0.142544	-1.4537	0.074524
20	-0.112383	-1.1461	0.127194
21	-0.101137	-1.0314	0.152374
22	-0.098355	-1.003	0.159087
23	0.029077	0.2965	0.383709
24	-0.039665	-0.4045	0.343336
25	-0.037103	-0.3784	0.352962
26	0.094741	0.9662	0.1681
27	0.030601	0.3121	0.377805
28	0.008321	0.0849	0.466268
29	0.028174	0.2873	0.387221
30	-0.102598	-1.0463	0.148923
31	0.041254	0.4207	0.337419
32	-0.043276	-0.4413	0.329945
33	0.029508	0.3009	0.382036
34	0.022118	0.2256	0.410992
35	-0.044314	-0.4519	0.326135
36	-0.042944	-0.4379	0.331168
37	-0.075098	-0.7659	0.222749
38	-0.022132	-0.2257	0.410938
39	0.096405	0.9831	0.16391
40	0.008347	0.0851	0.466164
41	-0.022566	-0.2301	0.40922
42	-0.021379	-0.218	0.413919
43	-0.027826	-0.2838	0.388576
44	0.039717	0.405	0.343141
45	-0.032658	-0.333	0.369886
46	-0.013241	-0.135	0.446425
47	-0.067089	-0.6842	0.247694
48	-0.072292	-0.7372	0.23132

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/1h60y1292577292.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/1h60y1292577292.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/2sxi01292577292.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/2sxi01292577292.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/3sxi01292577292.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292577350xk5jdqagsdg8s69/3sxi01292577292.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; 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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