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*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, 16 Dec 2009 09:16:25 -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/t1260980638t5pp3cnvn9p0ayl.htm/, Retrieved Wed, 16 Dec 2009 17:24:01 +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/t1260980638t5pp3cnvn9p0ayl.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 «

98,8 100,5 110,4 96,4 101,9 106,2 81 94,7 101 109,4 102,3 90,7 96,2 96,1 106 103,1 102 104,7 86 92,1 106,9 112,6 101,7 92 97,4 97 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3

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	-0.060373	-0.4183	0.338806
2	0.00248	0.0172	0.493182
3	0.282459	1.9569	0.028093
4	-0.202054	-1.3999	0.083991
5	0.204574	1.4173	0.081423
6	0.142307	0.9859	0.164556
7	-0.300128	-2.0793	0.021476
8	-0.116228	-0.8053	0.212322
9	0.004092	0.0284	0.488749
10	-0.258998	-1.7944	0.039525
11	-0.08011	-0.555	0.290729
12	-0.012157	-0.0842	0.466615
13	-0.326559	-2.2625	0.014116
14	0.094304	0.6534	0.258321
15	0.041593	0.2882	0.38723
16	-0.217892	-1.5096	0.06885
17	0.187608	1.2998	0.099941
18	-0.016322	-0.1131	0.455219
19	-0.183623	-1.2722	0.10472
20	0.226627	1.5701	0.061478
21	0.060573	0.4197	0.338302
22	-0.035253	-0.2442	0.404042
23	0.323086	2.2384	0.014934
24	-0.085102	-0.5896	0.279112
25	-0.080365	-0.5568	0.29013
26	0.194803	1.3496	0.091733
27	-0.082166	-0.5693	0.285916
28	0.077552	0.5373	0.296774
29	-0.036764	-0.2547	0.400017
30	-0.220886	-1.5303	0.066248
31	0.013658	0.0946	0.462503
32	-0.045517	-0.3153	0.376931
33	-0.064557	-0.4473	0.328349
34	-0.134789	-0.9338	0.177528
35	-0.042357	-0.2935	0.385218
36	-0.012112	-0.0839	0.466737

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.060373	-0.4183	0.338806
2	-0.001169	-0.0081	0.496785
3	0.283573	1.9646	0.027629
4	-0.183354	-1.2703	0.105048
5	0.209898	1.4542	0.076197
6	0.077517	0.5371	0.296855
7	-0.22878	-1.585	0.059763
8	-0.311083	-2.1552	0.018093
9	0.026532	0.1838	0.427466
10	-0.170956	-1.1844	0.12104
11	-0.175658	-1.217	0.114778
12	0.025609	0.1774	0.42996
13	-0.10758	-0.7453	0.229851
14	0.054664	0.3787	0.353281
15	0.02078	0.144	0.443065
16	-0.07854	-0.5441	0.294432
17	0.012761	0.0884	0.46496
18	-0.027871	-0.1931	0.423848
19	-0.245736	-1.7025	0.047564
20	-0.052582	-0.3643	0.358617
21	0.11531	0.7989	0.214145
22	0.014176	0.0982	0.461087
23	0.170866	1.1838	0.121162
24	0.006589	0.0457	0.481888
25	-0.050992	-0.3533	0.362711
26	-0.14751	-1.022	0.155957
27	-0.039361	-0.2727	0.393128
28	0.048865	0.3385	0.368214
29	-0.250108	-1.7328	0.044777
30	-0.092198	-0.6388	0.263006
31	0.09607	0.6656	0.254429
32	-0.08167	-0.5658	0.287075
33	0.05709	0.3955	0.347102
34	-0.088933	-0.6161	0.270354
35	-0.022767	-0.1577	0.437664
36	0.061638	0.427	0.335628

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260980638t5pp3cnvn9p0ayl/1afus1260980180.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260980638t5pp3cnvn9p0ayl/1afus1260980180.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260980638t5pp3cnvn9p0ayl/2yp7j1260980180.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260980638t5pp3cnvn9p0ayl/2yp7j1260980180.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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