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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, 03 Dec 2009 05:09:45 -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/03/t12598422262i82nnexjzpl027.htm/, Retrieved Thu, 03 Dec 2009 13:10:31 +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/03/t12598422262i82nnexjzpl027.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 «

128,7 136,9 156,9 109,1 122,3 123,9 90,9 77,9 120,3 118,9 125,5 98,9 102,9 105,9 117,6 113,6 115,9 118,9 77,6 81,2 123,1 136,6 112,1 95,1 96,3 105,7 115,8 105,7 105,7 111,1 82,4 60 107,3 99,3 113,5 108,9 100,2 103,9 138,7 120,2 100,2 143,2 70,9 85,2 133 136,6 117,9 106,3 122,3 125,5 148,4 126,3 99,6 140,4 80,3 92,6 138,5 110,9 119,6 105 109 129,4 148,6 101,4 134,8 143,7 81,6 90,3 141,5 140,7 140,2 100,2 125,7 119,6 134,7 109 116,3 146,9 97,4 89,4 132,1 139,8 129 112,5 121,9 121,7 123,1 131,6 119,3 132,5 98,3 85,1 131,7 129,3 90,7 78,6 68,9 79,1 83,5 74,1 59,7 93,3 61,3 56,6 98,5

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	0.354651	3.6341	0.000217
2	0.056622	0.5802	0.281512
3	0.231718	2.3744	0.009697
4	0.210667	2.1587	0.016576
5	0.201683	2.0666	0.020614
6	0.203663	2.0869	0.019658
7	0.117609	1.2051	0.11543
8	0.085501	0.8761	0.191481
9	0.020643	0.2115	0.416445
10	-0.212085	-2.1732	0.016005
11	0.021702	0.2224	0.412227
12	0.433935	4.4465	1.1e-05
13	-0.007654	-0.0784	0.46882
14	-0.252051	-2.5827	0.005589
15	-0.060961	-0.6247	0.266773
16	-0.066993	-0.6865	0.246963
17	-0.046119	-0.4726	0.318748
18	-0.034282	-0.3513	0.363038
19	-0.010939	-0.1121	0.455483
20	-0.02138	-0.2191	0.413505
21	-0.063604	-0.6517	0.257994
22	-0.258555	-2.6494	0.004655
23	-0.022629	-0.2319	0.408543
24	0.346254	3.548	0.000291
25	-0.036339	-0.3724	0.355188
26	-0.268179	-2.748	0.003529
27	-0.107669	-1.1033	0.136215
28	-0.086305	-0.8844	0.18926
29	-0.094194	-0.9652	0.168332
30	-0.098093	-1.0052	0.158567
31	-0.084658	-0.8675	0.193826
32	-0.113274	-1.1607	0.124195
33	-0.11113	-1.1387	0.128701
34	-0.221666	-2.2714	0.012581
35	-0.076188	-0.7807	0.218369
36	0.253887	2.6016	0.00531

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.354651	3.6341	0.000217
2	-0.079105	-0.8106	0.209717
3	0.274075	2.8084	0.002969
4	0.037561	0.3849	0.350551
5	0.16416	1.6821	0.047757
6	0.061834	0.6336	0.263856
7	0.001262	0.0129	0.494855
8	-0.003254	-0.0333	0.486731
9	-0.104332	-1.0691	0.14374
10	-0.313663	-3.2141	0.000869
11	0.174444	1.7875	0.03837
12	0.437809	4.4862	9e-06
13	-0.30305	-3.1053	0.001222
14	-0.176162	-1.8051	0.036961
15	-0.015773	-0.1616	0.435954
16	-0.053613	-0.5494	0.291961
17	-0.008047	-0.0825	0.467221
18	-0.044404	-0.455	0.325023
19	0.15938	1.6332	0.052716
20	-0.050575	-0.5182	0.302692
21	0.041959	0.43	0.334055
22	-0.059493	-0.6096	0.271716
23	0.058628	0.6008	0.274649
24	0.09949	1.0195	0.155163
25	-0.152561	-1.5633	0.060497
26	-0.12744	-1.3059	0.097225
27	-0.093585	-0.959	0.169891
28	-0.001214	-0.0124	0.495049
29	-0.046894	-0.4805	0.315929
30	-0.052925	-0.5423	0.294373
31	-0.017959	-0.184	0.427176
32	-0.091258	-0.9351	0.175937
33	0.127667	1.3082	0.096832
34	0.111362	1.1411	0.128207
35	-0.07876	-0.8071	0.210731
36	0.011089	0.1136	0.454876

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598422262i82nnexjzpl027/1p0wp1259842182.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598422262i82nnexjzpl027/1p0wp1259842182.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598422262i82nnexjzpl027/2wy061259842182.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598422262i82nnexjzpl027/2wy061259842182.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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