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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, 26 Nov 2009 11:35:46 -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/26/t1259260589yas1qfbtaei6li2.htm/, Retrieved Thu, 26 Nov 2009 19:36:32 +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/26/t1259260589yas1qfbtaei6li2.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 «

110,5 110,8 104,2 88,9 89,8 90 93,9 91,3 87,8 99,7 73,5 79,2 96,9 95,2 95,6 89,7 92,8 88 101,1 92,7 95,8 103,8 81,8 87,1 105,9 108,1 102,6 93,7 103,5 100,6 113,3 102,4 102,1 106,9 87,3 93,1 109,1 120,3 104,9 92,6 109,8 111,4 117,9 121,6 117,8 124,2 106,8 102,7 116,8 113,6 96,1 85 83,2 84,9 83 79,6 83,2 83,8 82,8 71,4

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	0.633074	4.9038	4e-06
2	0.398772	3.0889	0.001521
3	0.38314	2.9678	0.002152
4	0.37581	2.911	0.002525
5	0.341304	2.6437	0.005224
6	0.205791	1.5941	0.058089
7	0.155536	1.2048	0.11651
8	-0.010487	-0.0812	0.467765
9	-0.174592	-1.3524	0.090664
10	-0.30106	-2.332	0.011538
11	-0.159473	-1.2353	0.110772
12	0.079549	0.6162	0.270051
13	-0.143283	-1.1099	0.135742
14	-0.312037	-2.417	0.009352
15	-0.229668	-1.779	0.040153
16	-0.12197	-0.9448	0.174281
17	-0.081969	-0.6349	0.263945
18	-0.098273	-0.7612	0.224754
19	-0.07034	-0.5449	0.293936
20	-0.126249	-0.9779	0.166019
21	-0.210683	-1.6319	0.053965
22	-0.26819	-2.0774	0.021027
23	-0.136671	-1.0587	0.147001
24	0.012741	0.0987	0.460857
25	-0.133543	-1.0344	0.152546
26	-0.289445	-2.242	0.014334
27	-0.23251	-1.801	0.038363
28	-0.123484	-0.9565	0.171328
29	-0.128867	-0.9982	0.161095
30	-0.120442	-0.9329	0.177294
31	-0.113299	-0.8776	0.191827
32	-0.141661	-1.0973	0.138446
33	-0.187635	-1.4534	0.07566
34	-0.186746	-1.4465	0.076617
35	-0.085487	-0.6622	0.255196
36	0.041682	0.3229	0.37396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.633074	4.9038	4e-06
2	-0.003354	-0.026	0.489678
3	0.22023	1.7059	0.0466
4	0.087446	0.6774	0.250391
5	0.068272	0.5288	0.299435
6	-0.136894	-1.0604	0.146611
7	0.029481	0.2284	0.410072
8	-0.307607	-2.3827	0.010185
9	-0.193832	-1.5014	0.069246
10	-0.294832	-2.2838	0.01297
11	0.312353	2.4195	0.009295
12	0.441768	3.4219	0.000563
13	-0.262852	-2.036	0.023084
14	-0.185823	-1.4394	0.07762
15	0.097256	0.7533	0.227096
16	0.008822	0.0683	0.472873
17	-0.087773	-0.6799	0.249595
18	-0.146639	-1.1359	0.130266
19	-0.145907	-1.1302	0.131447
20	-0.050373	-0.3902	0.348891
21	0.055388	0.429	0.334718
22	0.042917	0.3324	0.370361
23	-0.022575	-0.1749	0.430887
24	-0.124669	-0.9657	0.16904
25	0.064827	0.5021	0.3087
26	0.011044	0.0855	0.466056
27	-0.06713	-0.52	0.302492
28	-0.093017	-0.7205	0.237004
29	-0.170683	-1.3221	0.095576
30	-0.004528	-0.0351	0.486069
31	-0.078393	-0.6072	0.272994
32	-0.060211	-0.4664	0.321312
33	-0.04134	-0.3202	0.374957
34	0.066894	0.5182	0.303126
35	-0.08082	-0.626	0.266834
36	0.111951	0.8672	0.194653

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260589yas1qfbtaei6li2/1apg11259260544.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260589yas1qfbtaei6li2/1apg11259260544.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260589yas1qfbtaei6li2/2ohcn1259260544.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260589yas1qfbtaei6li2/2ohcn1259260544.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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