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Paper

*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: Mon, 21 Dec 2009 13:57:27 -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/Dec/21/t12614290732sao1ctpxp73vg3.htm/, Retrieved Mon, 21 Dec 2009 21:57:56 +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/21/t12614290732sao1ctpxp73vg3.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 «

25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	0.646195	3.8229	0.00026
2	0.060744	0.3594	0.360741
3	-0.446848	-2.6436	0.006096
4	-0.602135	-3.5623	0.000542
5	-0.409686	-2.4237	0.010334
6	-0.006279	-0.0371	0.485289
7	0.375478	2.2214	0.016446
8	0.496383	2.9366	0.002916
9	0.317936	1.8809	0.034161
10	-0.085848	-0.5079	0.307361
11	-0.427555	-2.5295	0.008041
12	-0.572103	-3.3846	0.000885
13	-0.336756	-1.9923	0.027093
14	0.0178	0.1053	0.458367
15	0.304887	1.8037	0.039943
16	0.333587	1.9735	0.028186
17	0.197801	1.1702	0.124912
18	0.007705	0.0456	0.481951
19	-0.191351	-1.132	0.132656
20	-0.238749	-1.4125	0.083323
21	-0.169069	-1.0002	0.162034
22	-0.001599	-0.0095	0.496253
23	0.135267	0.8003	0.214482
24	0.177852	1.0522	0.149962
25	0.108744	0.6433	0.262099
26	-0.001212	-0.0072	0.49716
27	-0.119435	-0.7066	0.24225
28	-0.145513	-0.8609	0.197585
29	-0.106132	-0.6279	0.267077
30	-0.0535	-0.3165	0.376747
31	0.030546	0.1807	0.428819
32	0.086527	0.5119	0.305968
33	0.084539	0.5001	0.310055
34	0.03178	0.188	0.425975
35	NA	NA	NA
36	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.646195	3.8229	0.00026
2	-0.612645	-3.6245	0.000455
3	-0.314052	-1.858	0.035802
4	-0.006658	-0.0394	0.484402
5	-0.014199	-0.084	0.466766
6	0.105326	0.6231	0.268623
7	0.145295	0.8596	0.197936
8	-0.028137	-0.1665	0.434375
9	-0.02619	-0.1549	0.438878
10	-0.208398	-1.2329	0.112916
11	-0.060329	-0.3569	0.361651
12	-0.220358	-1.3037	0.10043
13	0.192414	1.1383	0.131356
14	-0.203358	-1.2031	0.11851
15	-0.063947	-0.3783	0.353741
16	-0.150506	-0.8904	0.189664
17	0.153336	0.9072	0.185265
18	0.096259	0.5695	0.286336
19	-0.111835	-0.6616	0.256272
20	0.066672	0.3944	0.347826
21	-0.102151	-0.6043	0.27476
22	-0.084852	-0.502	0.309408
23	0.021318	0.1261	0.450179
24	-0.156762	-0.9274	0.180031
25	0.097844	0.5789	0.283198
26	-0.119753	-0.7085	0.241673
27	-0.091602	-0.5419	0.295653
28	-0.004604	-0.0272	0.489213
29	-0.043736	-0.2587	0.398675
30	-0.017414	-0.103	0.459266
31	-0.034889	-0.2064	0.418835
32	0.005865	0.0347	0.486258
33	-0.161032	-0.9527	0.173643
34	0.041417	0.245	0.403933
35	NA	NA	NA
36	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614290732sao1ctpxp73vg3/126gh1261429045.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614290732sao1ctpxp73vg3/126gh1261429045.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614290732sao1ctpxp73vg3/2qqt51261429045.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614290732sao1ctpxp73vg3/2qqt51261429045.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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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