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Paper

*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: Tue, 15 Dec 2009 20:22:45 -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/16/t1260933821cc4elrtgu4tp0xm.htm/, Retrieved Wed, 16 Dec 2009 04:23:43 +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/16/t1260933821cc4elrtgu4tp0xm.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 «

102,1 102,86 102,99 103,73 105,02 104,43 104,63 104,93 105,87 105,66 106,76 106 107,22 107,33 107,11 108,86 107,72 107,88 108,38 107,72 108,41 109,9 111,45 112,18 113,34 113,46 114,06 115,54 116,39 115,94 116,97 115,94 115,91 116,43 116,26 116,35 117,9 117,7 117,53 117,86 117,65 116,51 115,93 115,31 115 115,45 115,83

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	-0.063528	-0.4309	0.334289
2	0.134839	0.9145	0.182605
3	0.27701	1.8788	0.03331
4	-0.162285	-1.1007	0.138383
5	-0.062827	-0.4261	0.336006
6	0.162852	1.1045	0.137557
7	-0.099902	-0.6776	0.250721
8	-0.088287	-0.5988	0.276124
9	0.141313	0.9584	0.171427
10	-0.098645	-0.669	0.253406
11	-0.054259	-0.368	0.35728
12	0.177938	1.2068	0.116833
13	-0.07355	-0.4988	0.310134
14	-0.035776	-0.2426	0.404681
15	0.055734	0.378	0.353582
16	-0.203257	-1.3786	0.08735
17	-0.171607	-1.1639	0.125234
18	0.09472	0.6424	0.261895
19	-0.206699	-1.4019	0.083829
20	-0.073719	-0.5	0.309734
21	-0.024805	-0.1682	0.433567
22	-0.077986	-0.5289	0.299701
23	0.006532	0.0443	0.482428
24	0.160789	1.0905	0.140581
25	-0.021489	-0.1457	0.442379
26	0.086364	0.5857	0.280454
27	-0.002437	-0.0165	0.493441
28	-0.041077	-0.2786	0.390902
29	-0.009041	-0.0613	0.475686
30	-0.010678	-0.0724	0.471291
31	-0.086853	-0.5891	0.27935
32	0.070198	0.4761	0.318126
33	-0.005824	-0.0395	0.48433
34	-0.061915	-0.4199	0.338245
35	0.03144	0.2132	0.416043
36	0.012062	0.0818	0.467578

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.063528	-0.4309	0.334289
2	0.131333	0.8907	0.18885
3	0.299141	2.0289	0.024141
4	-0.153778	-1.043	0.151206
5	-0.190882	-1.2946	0.100956
6	0.138901	0.9421	0.175538
7	0.067194	0.4557	0.325364
8	-0.138775	-0.9412	0.175755
9	0.019548	0.1326	0.447552
10	0.025977	0.1762	0.43046
11	-0.023469	-0.1592	0.437115
12	0.088394	0.5995	0.275885
13	0.003609	0.0245	0.490288
14	-0.056434	-0.3828	0.351832
15	-0.072678	-0.4929	0.312205
16	-0.150371	-1.0199	0.156563
17	-0.154695	-1.0492	0.149785
18	0.111203	0.7542	0.227281
19	-0.046599	-0.3161	0.376697
20	-0.10683	-0.7246	0.236196
21	-0.170688	-1.1577	0.126488
22	0.085237	0.5781	0.283007
23	0.144962	0.9832	0.165332
24	0.109413	0.7421	0.230907
25	-0.076147	-0.5165	0.304005
26	0.031183	0.2115	0.416718
27	-0.087753	-0.5952	0.277324
28	0.021663	0.1469	0.441916
29	0.035398	0.2401	0.405666
30	-0.020854	-0.1414	0.44407
31	-0.133985	-0.9087	0.184115
32	0.032542	0.2207	0.413147
33	0.037119	0.2518	0.401176
34	-0.021378	-0.145	0.442674
35	-0.083939	-0.5693	0.285961
36	-0.070568	-0.4786	0.31724

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260933821cc4elrtgu4tp0xm/1h8ld1260933764.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260933821cc4elrtgu4tp0xm/1h8ld1260933764.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260933821cc4elrtgu4tp0xm/2dp081260933764.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260933821cc4elrtgu4tp0xm/2dp081260933764.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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