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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: Thu, 17 Dec 2009 19:24:21 -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/18/t1261103164vlgcpwxf6iitz2v.htm/, Retrieved Fri, 18 Dec 2009 03:26:06 +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/18/t1261103164vlgcpwxf6iitz2v.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 «

9.0 9.1 8.7 8.2 7.9 7.9 9.1 9.4 9.4 9.1 9.0 9.3 9.9 9.8 9.3 8.3 8.0 8.5 10.4 11.1 10.9 10.0 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9.0 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9.0 9.0 9.0 9.8 10.0 9.8 9.3 9.0 9.0 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8.0

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.573169	3.9294	0.000139
2	-0.042103	-0.2886	0.387062
3	-0.566512	-3.8838	0.00016
4	-0.646782	-4.4341	2.8e-05
5	-0.368078	-2.5234	0.007531
6	0.049312	0.3381	0.368409
7	0.279244	1.9144	0.030834
8	0.306761	2.1031	0.020421
9	0.19366	1.3277	0.09535
10	0.002143	0.0147	0.49417
11	-0.0998	-0.6842	0.248607
12	-0.169861	-1.1645	0.125048
13	-0.143666	-0.9849	0.164852
14	-0.018028	-0.1236	0.451083
15	0.037776	0.259	0.398391
16	0.102873	0.7053	0.242064
17	0.084467	0.5791	0.282651
18	0.006809	0.0467	0.481484
19	-0.113924	-0.781	0.219352
20	-0.12887	-0.8835	0.190734
21	-0.071778	-0.4921	0.312475
22	0.067902	0.4655	0.321857
23	0.190386	1.3052	0.099086
24	0.176762	1.2118	0.115819
25	0.082451	0.5653	0.287295
26	-0.080746	-0.5536	0.291251
27	-0.221319	-1.5173	0.067946
28	-0.212355	-1.4558	0.076044
29	-0.098757	-0.677	0.250849
30	0.086609	0.5938	0.27776
31	0.216453	1.4839	0.072252
32	0.267203	1.8319	0.036657
33	0.147657	1.0123	0.158292
34	-0.010451	-0.0717	0.471592
35	-0.220181	-1.5095	0.068934
36	-0.283866	-1.9461	0.028818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.573169	3.9294	0.000139
2	-0.551956	-3.784	0.000218
3	-0.455542	-3.123	0.001531
4	-0.082076	-0.5627	0.288161
5	-0.107297	-0.7356	0.232817
6	-0.112286	-0.7698	0.222636
7	-0.242363	-1.6616	0.05163
8	-0.068179	-0.4674	0.321182
9	0.031578	0.2165	0.414772
10	-0.162343	-1.113	0.135691
11	0.009469	0.0649	0.474259
12	-0.150088	-1.029	0.154384
13	-0.06031	-0.4135	0.340574
14	0.106576	0.7306	0.234311
15	-0.253955	-1.741	0.044111
16	0.083521	0.5726	0.284826
17	-0.062925	-0.4314	0.334079
18	-0.153597	-1.053	0.148861
19	-0.169144	-1.1596	0.126037
20	-0.135157	-0.9266	0.179436
21	-0.037262	-0.2555	0.399744
22	-0.129859	-0.8903	0.188929
23	-0.035452	-0.243	0.404514
24	-0.056703	-0.3887	0.349614
25	-0.04099	-0.281	0.389966
26	-0.019216	-0.1317	0.447877
27	-0.242961	-1.6657	0.051217
28	-0.035776	-0.2453	0.403659
29	-0.113423	-0.7776	0.220355
30	-0.09605	-0.6585	0.256719
31	-0.091144	-0.6249	0.267545
32	0.017783	0.1219	0.451742
33	0.03434	0.2354	0.407451
34	-0.035597	-0.244	0.404131
35	-0.129906	-0.8906	0.188843
36	0.014023	0.0961	0.461912

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261103164vlgcpwxf6iitz2v/19ytf1261103059.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261103164vlgcpwxf6iitz2v/19ytf1261103059.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261103164vlgcpwxf6iitz2v/2i0wt1261103059.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261103164vlgcpwxf6iitz2v/2i0wt1261103059.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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