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paper autocorrelation function graan

*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: Thu, 10 Dec 2009 10:03:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464722edpq8mfqsitunei.htm/, Retrieved Thu, 10 Dec 2009 18:05:24 +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/2009/Dec/10/t1260464722edpq8mfqsitunei.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

108,2 108,8 110,2 109,5 109,5 116 111,2 112,1 114 119,1 114,1 115,1 115,4 110,8 116 119,2 126,5 127,8 131,3 140,3 137,3 143 134,5 139,9 159,3 170,4 175 175,8 180,9 180,3 169,6 172,3 184,8 177,7 184,6 211,4 215,3 215,9 244,7 259,3 289 310,9 321 315,1 333,2 314,1 284,7 273,9 216 196,4 190,9 206,4 196,3 199,5 198,9 214,4 214,2 187,6 180,6 172,2 187,2

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.964302	7.5314	0
2	0.91146	7.1187	0
3	0.845596	6.6043	0
4	0.768704	6.0038	0
5	0.687334	5.3682	1e-06
6	0.610716	4.7698	6e-06
7	0.538048	4.2023	4.4e-05
8	0.474487	3.7059	0.000228
9	0.424587	3.3161	0.00077
10	0.372939	2.9127	0.0025
11	0.325792	2.5445	0.006745
12	0.277666	2.1686	0.017009
13	0.230575	1.8008	0.038335
14	0.184177	1.4385	0.077706
15	0.141851	1.1079	0.136129
16	0.09604	0.7501	0.228039
17	0.046951	0.3667	0.357556
18	-0.000171	-0.0013	0.49947
19	-0.045411	-0.3547	0.362029
20	-0.088403	-0.6904	0.246265
21	-0.134224	-1.0483	0.149312
22	-0.175351	-1.3695	0.087926
23	-0.213163	-1.6649	0.050535
24	-0.24671	-1.9269	0.029329
25	-0.270614	-2.1136	0.019325
26	-0.288422	-2.2526	0.013945
27	-0.306712	-2.3955	0.009841
28	-0.324826	-2.537	0.006878
29	-0.341427	-2.6666	0.004898
30	-0.354578	-2.7693	0.003715
31	-0.370004	-2.8898	0.002666
32	-0.38307	-2.9919	0.001999
33	-0.389984	-3.0459	0.001712
34	-0.395757	-3.091	0.001503
35	-0.396521	-3.0969	0.001477
36	-0.39167	-3.059	0.001648

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964302	7.5314	0
2	-0.262675	-2.0516	0.022256
3	-0.166973	-1.3041	0.09855
4	-0.136792	-1.0684	0.144779
5	-0.040846	-0.319	0.375401
6	0.073356	0.5729	0.284399
7	0.001899	0.0148	0.494106
8	0.058531	0.4571	0.324597
9	0.093701	0.7318	0.233539
10	-0.181486	-1.4174	0.08072
11	-0.00785	-0.0613	0.475656
12	-0.098642	-0.7704	0.222012
13	0.004053	0.0317	0.487426
14	0.008115	0.0634	0.474834
15	0.025407	0.1984	0.421683
16	-0.094048	-0.7345	0.232717
17	-0.103979	-0.8121	0.209944
18	-0.032752	-0.2558	0.399481
19	0.010355	0.0809	0.467904
20	-0.020463	-0.1598	0.436774
21	-0.098516	-0.7694	0.222303
22	0.024491	0.1913	0.424469
23	-0.014417	-0.1126	0.45536
24	-0.044998	-0.3514	0.363233
25	0.082111	0.6413	0.261862
26	-0.014677	-0.1146	0.454556
27	-0.103464	-0.8081	0.211093
28	-0.081974	-0.6402	0.262207
29	-0.047491	-0.3709	0.355991
30	0.070882	0.5536	0.290936
31	-0.096633	-0.7547	0.226658
32	0.041081	0.3209	0.374708
33	0.078115	0.6101	0.272032
34	-0.113059	-0.883	0.190346
35	-0.017004	-0.1328	0.447392
36	0.017242	0.1347	0.44666

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464722edpq8mfqsitunei/1cz5q1260464626.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464722edpq8mfqsitunei/1cz5q1260464626.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464722edpq8mfqsitunei/2gv8o1260464626.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464722edpq8mfqsitunei/2gv8o1260464626.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; 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 (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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