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autocorrelation

*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 17:26:10 +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/t1293643499zrw0925frp5da9c.htm/, Retrieved Wed, 29 Dec 2010 18:25:02 +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/t1293643499zrw0925frp5da9c.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 «

5.921 4.561 4.399 4.249 4.211 4.081 4.131 4.071 3.841 4.109 4.354 4.402 4.954 4.137 4.561 4.210 4.429 4.190 4.196 4.226 3.878 3.931 4.115 4.679 5.385 4.387 4.552 4.325 4.179 4.054 4.075 4.147 4.046 4.368 4.097 4.821 4.965 4.425 4.601 4.521 4.193 4.039 4.099 4.109 4.024 4.245 4.252 5.136 5.037 4.230 4.408 4.119 4.083 4.010 4.148 3.952 3.843 4.164 4.075 4.708

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.333781	2.5855	0.006086
2	0.150922	1.169	0.123505
3	-0.066373	-0.5141	0.304526
4	-0.224566	-1.7395	0.043539
5	-0.27677	-2.1439	0.018053
6	-0.332845	-2.5782	0.006202
7	-0.264073	-2.0455	0.022599
8	-0.261568	-2.0261	0.023604
9	-0.044381	-0.3438	0.366108
10	0.081119	0.6283	0.266082
11	0.267858	2.0748	0.02115
12	0.580894	4.4996	1.6e-05
13	0.141706	1.0976	0.138372
14	0.13197	1.0222	0.155386
15	-0.071421	-0.5532	0.291083
16	-0.177743	-1.3768	0.086847
17	-0.244019	-1.8902	0.031784
18	-0.287931	-2.2303	0.01474
19	-0.201622	-1.5618	0.061802
20	-0.215824	-1.6718	0.049889
21	-0.032964	-0.2553	0.399669
22	0.051651	0.4001	0.345257
23	0.330889	2.5631	0.006451
24	0.502554	3.8928	0.000126
25	0.092554	0.7169	0.238102
26	0.071077	0.5506	0.291991
27	-0.096216	-0.7453	0.229505
28	-0.15957	-1.236	0.110633
29	-0.182423	-1.413	0.081405
30	-0.191744	-1.4852	0.071358
31	-0.131323	-1.0172	0.156565
32	-0.139235	-1.0785	0.142562
33	0.02235	0.1731	0.431569
34	0.006743	0.0522	0.479258
35	0.266418	2.0637	0.021691
36	0.286922	2.2225	0.015016
37	0.076864	0.5954	0.276913
38	0.076976	0.5963	0.276625
39	-0.041946	-0.3249	0.373189
40	-0.100239	-0.7764	0.220268
41	-0.118657	-0.9191	0.180859
42	-0.11101	-0.8599	0.196639
43	-0.076466	-0.5923	0.277937
44	-0.092898	-0.7196	0.237287
45	0.014885	0.1153	0.454297
46	0.024216	0.1876	0.425921
47	0.244171	1.8913	0.031705
48	0.189801	1.4702	0.073367

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.333781	2.5855	0.006086
2	0.044466	0.3444	0.365861
3	-0.145857	-1.1298	0.131528
4	-0.193572	-1.4994	0.069506
5	-0.150467	-1.1655	0.124213
6	-0.206719	-1.6012	0.057288
7	-0.141185	-1.0936	0.139247
8	-0.235757	-1.8262	0.036401
9	-0.03578	-0.2772	0.391308
10	-0.041355	-0.3203	0.374915
11	0.091113	0.7058	0.241534
12	0.431842	3.345	0.000711
13	-0.302534	-2.3434	0.01122
14	0.040383	0.3128	0.377757
15	-0.053923	-0.4177	0.338834
16	-0.078379	-0.6071	0.273031
17	-0.033477	-0.2593	0.39814
18	-0.090327	-0.6997	0.243419
19	0.00501	0.0388	0.484587
20	-0.074934	-0.5804	0.281897
21	-0.107334	-0.8314	0.20452
22	-0.02122	-0.1644	0.434998
23	0.146714	1.1364	0.130146
24	0.134889	1.0448	0.150142
25	-0.195654	-1.5155	0.067445
26	-0.118313	-0.9164	0.181551
27	0.018928	0.1466	0.441964
28	-0.051573	-0.3995	0.345478
29	0.054159	0.4195	0.33817
30	0.000121	9e-04	0.499627
31	0.015807	0.1224	0.451481
32	0.02852	0.2209	0.412956
33	-0.039683	-0.3074	0.379808
34	-0.146182	-1.1323	0.131003
35	-0.011823	-0.0916	0.463667
36	-0.062748	-0.486	0.314352
37	0.093561	0.7247	0.235721
38	-0.041393	-0.3206	0.374803
39	0.034655	0.2684	0.394642
40	0.002594	0.0201	0.492019
41	0.022394	0.1735	0.431436
42	0.017207	0.1333	0.447208
43	6.4e-05	5e-04	0.499802
44	0.013222	0.1024	0.459382
45	0.035076	0.2717	0.393393
46	0.018595	0.144	0.442977
47	-0.0149	-0.1154	0.454251
48	0.027299	0.2115	0.416622

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/1u9041293643565.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/1u9041293643565.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/2m1z71293643565.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/2m1z71293643565.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/3xazs1293643565.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643499zrw0925frp5da9c/3xazs1293643565.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 = 0 ; 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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