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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sat, 15 Jan 2011 10:11:09 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa.htm/, Retrieved Sat, 15 Jan 2011 11:15:40 +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/2011/Jan/15/t1295086537ucd98oe7vhmxrfa.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

52347 52407 50570 50442 50590 50040 50476 50268 50595 48708 48547 48196 48375 47915 46462 46132 46308 46532 46817 46824 46263 45992 46404 46995 48102 48719 47912 48430 50141 50608 51005 51857 52513 52406 53634 55165 57294 58026 56701 58706 60103 61153 62395 63850 64534 65765 66954 65741 65474 60687 59227 59373 59995 59532 59696 59507 60210 58782 59372 58827 60481 59508 56565 56201 56193 56431 56316 55316 54795 53310 51848 50618 52026 50120 46825 46374 45441 45392 45032 44302 42880 42101 41886 41415 43228 41633 39375 38603 37847 36881 36700 36477 35684 35896 37109 37612 39570 39518 37970 38343 37966 38942 39304 39438 38999 38110 40024 41050 42239 42313 41159 42067 42515 43554 45018 45797 46749 47291 48800 50566 54884 54002 51813 52751 54461 55364 56900 57795

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	'Gwilym Jenkins' @ www.wessa.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.305579	3.4437	0.000389
2	0.093059	1.0487	0.148149
3	0.099239	1.1184	0.13276
4	0.139981	1.5775	0.058584
5	0.246438	2.7772	0.003157
6	0.259211	2.9212	0.002064
7	0.220903	2.4895	0.007043
8	0.083847	0.9449	0.17325
9	0.059711	0.6729	0.251115
10	-0.017302	-0.195	0.422858
11	0.136377	1.5369	0.063404
12	0.464146	5.2307	0
13	0.122478	1.3803	0.084966
14	-0.049741	-0.5606	0.288045
15	-0.035662	-0.4019	0.344219
16	-0.029052	-0.3274	0.371954
17	0.113452	1.2785	0.101695
18	0.119073	1.3419	0.091013
19	0.070389	0.7932	0.214559
20	-0.046921	-0.5288	0.298944
21	-0.074571	-0.8404	0.20114
22	-0.149941	-1.6897	0.046765
23	-0.035201	-0.3967	0.346127
24	0.276271	3.1134	0.001143
25	-0.055751	-0.6283	0.265474
26	-0.189836	-2.1393	0.017161
27	-0.145101	-1.6352	0.052242
28	-0.163738	-1.8452	0.033666
29	-0.036496	-0.4113	0.340776
30	-0.051913	-0.585	0.279783
31	-0.088741	-1.0001	0.159591
32	-0.174139	-1.9624	0.025949
33	-0.185479	-2.0902	0.019295
34	-0.285866	-3.2216	0.00081
35	-0.149091	-1.6802	0.047691
36	0.163841	1.8464	0.033582
37	-0.148025	-1.6682	0.048874
38	-0.191127	-2.1539	0.016568
39	-0.183064	-2.063	0.020574
40	-0.14353	-1.6175	0.054125
41	-0.092199	-1.039	0.150382
42	-0.064898	-0.7314	0.232953
43	-0.100089	-1.1279	0.130735
44	-0.2087	-2.3519	0.010107
45	-0.234394	-2.6415	0.004646
46	-0.309285	-3.4855	0.000338
47	-0.124959	-1.4082	0.080754
48	0.132449	1.4926	0.069008

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.305579	3.4437	0.000389
2	-0.000352	-0.004	0.498419
3	0.078203	0.8813	0.189911
4	0.097664	1.1006	0.136573
5	0.193328	2.1787	0.0156
6	0.147544	1.6627	0.049416
7	0.113195	1.2756	0.102206
8	-0.036497	-0.4113	0.340772
9	-0.006026	-0.0679	0.472983
10	-0.133719	-1.5069	0.067156
11	0.090559	1.0206	0.154704
12	0.392479	4.423	1e-05
13	-0.160911	-1.8134	0.036067
14	-0.120828	-1.3617	0.087858
15	-0.035773	-0.4031	0.343762
16	-0.099661	-1.1231	0.131751
17	0.043302	0.488	0.3132
18	-0.020956	-0.2362	0.406845
19	-0.01821	-0.2052	0.418868
20	-0.040588	-0.4574	0.324081
21	-0.045422	-0.5119	0.30481
22	-0.076332	-0.8602	0.195643
23	-0.036099	-0.4068	0.342416
24	0.16569	1.8672	0.032088
25	-0.169203	-1.9068	0.029402
26	-0.082067	-0.9248	0.178399
27	0.019445	0.2191	0.41345
28	-0.093091	-1.0491	0.148067
29	-0.023392	-0.2636	0.396252
30	-0.079394	-0.8947	0.186313
31	-0.048953	-0.5517	0.291071
32	-0.031422	-0.3541	0.361922
33	-0.038497	-0.4338	0.332569
34	-0.09648	-1.0873	0.139487
35	-0.002142	-0.0241	0.490392
36	0.128036	1.4429	0.075757
37	-0.110294	-1.2429	0.108088
38	0.07263	0.8185	0.207304
39	-0.012507	-0.1409	0.444069
40	0.048733	0.5492	0.291919
41	-0.091323	-1.0292	0.152681
42	0.000512	0.0058	0.497703
43	-0.021837	-0.2461	0.403005
44	-0.123737	-1.3944	0.082809
45	-0.107029	-1.2062	0.115001
46	-0.072909	-0.8216	0.206409
47	0.041642	0.4693	0.319838
48	0.039171	0.4414	0.329824

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/1yhjh1295086267.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/1yhjh1295086267.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/21whr1295086267.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/21whr1295086267.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/3ns981295086267.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295086537ucd98oe7vhmxrfa/3ns981295086267.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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 (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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