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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: Tue, 24 Nov 2009 06:46:01 -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/24/t1259070393vuo48f3xooooevn.htm/, Retrieved Tue, 24 Nov 2009 14:46:35 +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/24/t1259070393vuo48f3xooooevn.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 «

11 8 6 10 11 10 9 8 11 10 12 13 13 13 13 13 12 13 12 13 12 14 11 12 13 13 12 10 9 10 10 9 7 11 11 12 13 13 12 12 10 12 12 12 10 13 13 11 13 12 11 12 12 11 10 9 10 9 6 7 5 8 5 5 5 1 3 5 7 2 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	0.792233	6.6755	0
2	0.680565	5.7345	0
3	0.652932	5.5017	0
4	0.62687	5.2821	1e-06
5	0.541242	4.5606	1e-05
6	0.412801	3.4783	0.000433
7	0.351602	2.9627	0.002074
8	0.259846	2.1895	0.015924
9	0.192583	1.6227	0.05454
10	0.158951	1.3393	0.092365
11	0.097816	0.8242	0.206289
12	0.04438	0.3739	0.354778
13	-0.04114	-0.3467	0.364939
14	-0.085373	-0.7194	0.237138
15	-0.085309	-0.7188	0.237303
16	-0.118855	-1.0015	0.159996
17	-0.179882	-1.5157	0.067016
18	-0.166056	-1.3992	0.083052
19	-0.176657	-1.4885	0.070518
20	-0.144488	-1.2175	0.113726
21	-0.133737	-1.1269	0.131792
22	-0.103073	-0.8685	0.194021
23	-0.102987	-0.8678	0.194217
24	-0.09987	-0.8415	0.201442
25	-0.021877	-0.1843	0.427138
26	0.001153	0.0097	0.496137
27	-0.030866	-0.2601	0.397778
28	-0.04151	-0.3498	0.363773
29	-0.035382	-0.2981	0.383236
30	0.002829	0.0238	0.490523
31	-0.001751	-0.0148	0.494134
32	-0.021578	-0.1818	0.428122
33	-0.006332	-0.0534	0.4788
34	-0.016934	-0.1427	0.443472
35	-0.010741	-0.0905	0.464071
36	-0.03203	-0.2699	0.394015

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.792233	6.6755	0
2	0.14215	1.1978	0.117494
3	0.213224	1.7967	0.038322
4	0.103005	0.8679	0.194178
5	-0.091719	-0.7728	0.221092
6	-0.206988	-1.7441	0.042734
7	-0.022929	-0.1932	0.423675
8	-0.164709	-1.3879	0.084759
9	0.004136	0.0348	0.48615
10	0.09584	0.8076	0.21102
11	-0.024875	-0.2096	0.417291
12	0.002682	0.0226	0.491018
13	-0.140988	-1.188	0.119398
14	-0.076784	-0.647	0.25986
15	0.062589	0.5274	0.299784
16	-0.020057	-0.169	0.433138
17	-0.078224	-0.6591	0.255972
18	0.170745	1.4387	0.077311
19	-0.093612	-0.7888	0.21643
20	0.137154	1.1557	0.125843
21	0.021903	0.1846	0.427051
22	0.022156	0.1867	0.426218
23	-0.074979	-0.6318	0.26478
24	-0.007938	-0.0669	0.47343
25	0.096407	0.8123	0.209655
26	0.001442	0.0122	0.495169
27	-0.145247	-1.2239	0.112523
28	-0.033988	-0.2864	0.387709
29	-0.050631	-0.4266	0.335472
30	0.023416	0.1973	0.422074
31	0.052249	0.4403	0.330543
32	-0.041479	-0.3495	0.363872
33	0.084581	0.7127	0.239186
34	-0.065957	-0.5558	0.290059
35	0.012115	0.1021	0.459491
36	-0.112195	-0.9454	0.173837

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259070393vuo48f3xooooevn/13hn01259070359.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259070393vuo48f3xooooevn/13hn01259070359.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259070393vuo48f3xooooevn/20pt91259070359.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259070393vuo48f3xooooevn/20pt91259070359.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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