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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: Fri, 27 Nov 2009 05:02:07 -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/Nov/27/t1259323687a6s5bijdo7gf32g.htm/, Retrieved Fri, 27 Nov 2009 13:08:09 +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/Nov/27/t1259323687a6s5bijdo7gf32g.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 «

17 14 15 16 16 15 13 12 13 13 12 10 14 14 15 16 16 15 15 13 15 15 15 13 16 16 14 16 15 14 15 15 14 13 12 13 12 9 10 8 11 8 8 8 4 6 8 10 5 6 5 9 8 6 9 11 11 8 11 11 13

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	0.821024	6.4124	0
2	0.764774	5.9731	0
3	0.72721	5.6797	0
4	0.724326	5.6572	0
5	0.65213	5.0933	2e-06
6	0.549719	4.2934	3.2e-05
7	0.499375	3.9002	0.000121
8	0.456425	3.5648	0.000357
9	0.426303	3.3295	0.00074
10	0.32264	2.5199	0.007186
11	0.294148	2.2974	0.012522
12	0.255616	1.9964	0.025178
13	0.191003	1.4918	0.070455
14	0.110302	0.8615	0.196172
15	0.078644	0.6142	0.270673
16	0.016772	0.131	0.448106
17	-0.086797	-0.6779	0.250197
18	-0.102603	-0.8014	0.213019
19	-0.154435	-1.2062	0.116203
20	-0.157177	-1.2276	0.112158
21	-0.204828	-1.5998	0.05741
22	-0.211988	-1.6557	0.051462
23	-0.24374	-1.9037	0.030837
24	-0.236442	-1.8467	0.034824
25	-0.229427	-1.7919	0.039056
26	-0.244075	-1.9063	0.030663
27	-0.225438	-1.7607	0.041649
28	-0.250173	-1.9539	0.02765
29	-0.26194	-2.0458	0.022547
30	-0.231915	-1.8113	0.037508
31	-0.214907	-1.6785	0.049185
32	-0.249731	-1.9505	0.02786
33	-0.241322	-1.8848	0.032113
34	-0.237237	-1.8529	0.034369
35	-0.241656	-1.8874	0.031934
36	-0.254863	-1.9905	0.025508

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.821024	6.4124	0
2	0.27827	2.1734	0.016823
3	0.15156	1.1837	0.120558
4	0.188979	1.476	0.072548
5	-0.100439	-0.7845	0.217904
6	-0.231627	-1.8091	0.037685
7	-0.042703	-0.3335	0.369941
8	-0.023836	-0.1862	0.426467
9	0.070412	0.5499	0.292185
10	-0.139274	-1.0878	0.140489
11	0.076412	0.5968	0.276427
12	-0.003398	-0.0265	0.489458
13	-0.148867	-1.1627	0.124742
14	-0.115323	-0.9007	0.185646
15	0.052063	0.4066	0.342854
16	-0.144085	-1.1253	0.132427
17	-0.234666	-1.8328	0.035857
18	0.179606	1.4028	0.082878
19	-0.008905	-0.0695	0.472391
20	0.06274	0.49	0.312942
21	0.064372	0.5028	0.308471
22	0.090497	0.7068	0.241189
23	-0.164046	-1.2812	0.102479
24	-0.035383	-0.2763	0.391607
25	0.139537	1.0898	0.14004
26	-0.018191	-0.1421	0.443744
27	-0.043248	-0.3378	0.368344
28	0.010291	0.0804	0.468099
29	-0.090702	-0.7084	0.240696
30	0.045926	0.3587	0.360532
31	0.003287	0.0257	0.489802
32	-0.081336	-0.6353	0.26382
33	-0.047529	-0.3712	0.355881
34	-0.136275	-1.0643	0.145685
35	-0.079285	-0.6192	0.269034
36	-0.078705	-0.6147	0.270518

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323687a6s5bijdo7gf32g/1zbc51259323326.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323687a6s5bijdo7gf32g/1zbc51259323326.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323687a6s5bijdo7gf32g/2xjny1259323326.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323687a6s5bijdo7gf32g/2xjny1259323326.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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