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ACF(2)

*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, 25 Nov 2009 08:43:27 -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/25/t1259163897i3vdpvnn8ynakem.htm/, Retrieved Wed, 25 Nov 2009 16:44:59 +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/25/t1259163897i3vdpvnn8ynakem.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 «

2.085 2.053 2.077 2.058 2.057 2.076 2.07 2.062 2.073 2.061 2.094 2.067 2.086 2.276 2.326 2.349 2.52 2.628 2.577 2.698 2.814 2.968 3.041 3.278 3.328 3.5 3.563 3.569 3.69 3.819 3.79 3.956 4.063 4.047 4.029 3.941 4.022 3.879 4.022 4.028 4.091 3.987 4.01 4.007 4.191 4.299 4.273 3.82 3.15 2.486 1.812 1.257 1.062 0.842 0.782 0.698 0.358 0.347 0.363 0.359 0.355

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	0.964427	6.751	0
2	0.900488	6.3034	0
3	0.816861	5.718	0
4	0.727059	5.0894	3e-06
5	0.635962	4.4517	2.5e-05
6	0.550751	3.8553	0.000169
7	0.46191	3.2334	0.001096
8	0.370259	2.5918	0.006273
9	0.278143	1.947	0.028639
10	0.192345	1.3464	0.092182
11	0.120382	0.8427	0.201754
12	0.066496	0.4655	0.321828
13	0.026347	0.1844	0.427219
14	-0.002434	-0.017	0.493238
15	-0.027153	-0.1901	0.42502
16	-0.056788	-0.3975	0.346356
17	-0.090728	-0.6351	0.26416
18	-0.126771	-0.8874	0.189601
19	-0.159032	-1.1132	0.135522
20	-0.192058	-1.3444	0.092504
21	-0.21991	-1.5394	0.065074
22	-0.24726	-1.7308	0.044888
23	-0.274083	-1.9186	0.030437
24	-0.301159	-2.1081	0.02008
25	-0.320459	-2.2432	0.014719
26	-0.336135	-2.3529	0.011342
27	-0.343259	-2.4028	0.010051
28	-0.344574	-2.412	0.009827
29	-0.339903	-2.3793	0.010642
30	-0.332598	-2.3282	0.012037
31	-0.32405	-2.2683	0.013875
32	-0.313229	-2.1926	0.016557
33	-0.300618	-2.1043	0.020252
34	-0.284569	-1.992	0.02598
35	-0.265412	-1.8579	0.034599
36	-0.242677	-1.6987	0.047855

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964427	6.751	0
2	-0.424018	-2.9681	0.002313
3	-0.190149	-1.331	0.094667
4	0.02038	0.1427	0.443572
5	-0.020261	-0.1418	0.443898
6	0.0382	0.2674	0.395141
7	-0.19974	-1.3982	0.084178
8	-0.094633	-0.6624	0.255398
9	-0.005191	-0.0363	0.485582
10	0.054407	0.3808	0.352481
11	0.111898	0.7833	0.218615
12	0.053152	0.3721	0.355725
13	-0.043695	-0.3059	0.380501
14	-0.001512	-0.0106	0.495798
15	-0.062378	-0.4366	0.332143
16	-0.156244	-1.0937	0.139715
17	-0.061982	-0.4339	0.333142
18	-0.05152	-0.3606	0.359959
19	0.037863	0.265	0.396046
20	-0.125359	-0.8775	0.192244
21	0.030702	0.2149	0.415364
22	-0.020875	-0.1461	0.442212
23	-0.007084	-0.0496	0.480327
24	0.003715	0.026	0.48968
25	0.071451	0.5002	0.309603
26	-0.082544	-0.5778	0.283021
27	-0.011012	-0.0771	0.469435
28	-0.044957	-0.3147	0.377163
29	-0.020755	-0.1453	0.442542
30	-0.022056	-0.1544	0.438969
31	-0.067695	-0.4739	0.318851
32	0.043741	0.3062	0.38038
33	-0.035097	-0.2457	0.40348
34	0.019606	0.1372	0.445701
35	0.02838	0.1987	0.421676
36	0.018231	0.1276	0.449487

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259163897i3vdpvnn8ynakem/165511259163805.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259163897i3vdpvnn8ynakem/165511259163805.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259163897i3vdpvnn8ynakem/2ubpf1259163805.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259163897i3vdpvnn8ynakem/2ubpf1259163805.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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