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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 12:35:12 -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/t1259091362jcz12uf44gq1x1a.htm/, Retrieved Tue, 24 Nov 2009 20:36:04 +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/t1259091362jcz12uf44gq1x1a.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 «

111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 91 93,2 103,1 94,1 91,8 102,7

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	0.483185	3.3823	0.00071
2	0.56938	3.9857	0.000112
3	0.595325	4.1673	6.2e-05
4	0.324708	2.273	0.013725
5	0.341219	2.3885	0.010406
6	0.260038	1.8203	0.037414
7	0.089159	0.6241	0.267724
8	0.13543	0.948	0.173889
9	0.021901	0.1533	0.439394
10	0.017759	0.1243	0.450787
11	0.075209	0.5265	0.300471
12	-0.063253	-0.4428	0.32994
13	0.004819	0.0337	0.486614
14	-0.003045	-0.0213	0.491541
15	-0.024305	-0.1701	0.432802
16	-0.078157	-0.5471	0.293397
17	0.001362	0.0095	0.496215
18	-0.071051	-0.4974	0.31058
19	-0.097173	-0.6802	0.249785
20	-0.051341	-0.3594	0.360424
21	-0.104001	-0.728	0.235037
22	-0.196613	-1.3763	0.087495
23	-0.023425	-0.164	0.435212
24	-0.205677	-1.4397	0.07815
25	-0.133703	-0.9359	0.176952
26	-0.110286	-0.772	0.22191
27	-0.23232	-1.6262	0.055157
28	-0.161503	-1.1305	0.131879
29	-0.143937	-1.0076	0.159308
30	-0.226929	-1.5885	0.059303
31	-0.180646	-1.2645	0.106012
32	-0.201785	-1.4125	0.082062
33	-0.225362	-1.5775	0.060554
34	-0.145059	-1.0154	0.157448
35	-0.235224	-1.6466	0.053023
36	-0.164422	-1.151	0.127668

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.483185	3.3823	0.00071
2	0.438223	3.0676	0.001755
3	0.369801	2.5886	0.006325
4	-0.208472	-1.4593	0.075431
5	-0.166601	-1.1662	0.124588
6	-0.076952	-0.5387	0.296278
7	-0.112717	-0.789	0.216951
8	0.047582	0.3331	0.37025
9	-0.000125	-9e-04	0.499652
10	0.09383	0.6568	0.257189
11	0.144079	1.0086	0.159071
12	-0.111505	-0.7805	0.219416
13	-0.08795	-0.6157	0.270487
14	-0.052197	-0.3654	0.358201
15	0.09163	0.6414	0.262123
16	-0.155957	-1.0917	0.140152
17	0.072053	0.5044	0.308132
18	0.027858	0.195	0.423097
19	-0.06205	-0.4344	0.33297
20	-0.029581	-0.2071	0.418407
21	-0.036314	-0.2542	0.400203
22	-0.202746	-1.4192	0.081082
23	0.2053	1.4371	0.078523
24	-0.071941	-0.5036	0.308403
25	0.01167	0.0817	0.467613
26	-0.067428	-0.472	0.319512
27	-0.066201	-0.4634	0.322563
28	-0.161429	-1.13	0.131989
29	0.088984	0.6229	0.268124
30	0.014424	0.101	0.459994
31	-0.094848	-0.6639	0.254922
32	-0.040466	-0.2833	0.389085
33	0.035913	0.2514	0.401283
34	-0.043447	-0.3041	0.381157
35	-0.05134	-0.3594	0.360428
36	-0.030857	-0.216	0.414941

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259091362jcz12uf44gq1x1a/19ig11259091310.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259091362jcz12uf44gq1x1a/19ig11259091310.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259091362jcz12uf44gq1x1a/2tm1j1259091310.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259091362jcz12uf44gq1x1a/2tm1j1259091310.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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