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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: Mon, 14 Dec 2009 03:13:26 -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/14/t1260785734qtud04t9406lwv0.htm/, Retrieved Mon, 14 Dec 2009 11:15:37 +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/14/t1260785734qtud04t9406lwv0.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 «

95,1 97,0 112,7 102,9 97,4 111,4 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 99,0 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102,0 106,0 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100,0 110,7 112,8 109,8 117,3 109,1 115,9 96,0 99,8 116,8 115,7 99,4 94,3

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	-0.629949	-4.3187	4e-05
2	0.077601	0.532	0.298613
3	0.186879	1.2812	0.103208
4	-0.190481	-1.3059	0.098976
5	0.072634	0.498	0.310419
6	0.064655	0.4433	0.329809
7	-0.129494	-0.8878	0.189594
8	0.074757	0.5125	0.305348
9	0.041383	0.2837	0.38894
10	-0.117001	-0.8021	0.213261
11	0.117782	0.8075	0.211732
12	-0.06748	-0.4626	0.322885
13	0.029238	0.2004	0.420999
14	-0.058093	-0.3983	0.346119
15	0.109984	0.754	0.227301
16	-0.123043	-0.8435	0.2016
17	0.056994	0.3907	0.348882
18	0.06578	0.451	0.327043
19	-0.127466	-0.8739	0.193319
20	0.068766	0.4714	0.319755
21	0.082431	0.5651	0.28734
22	-0.28277	-1.9386	0.029286
23	0.393881	2.7003	0.0048
24	-0.2787	-1.9107	0.031079
25	0.021052	0.1443	0.442931
26	0.130557	0.8951	0.18766
27	-0.108244	-0.7421	0.230864
28	0.027526	0.1887	0.425566
29	0.02974	0.2039	0.419662
30	-0.023859	-0.1636	0.435387
31	-0.030837	-0.2114	0.416741
32	0.074407	0.5101	0.306181
33	-0.105243	-0.7215	0.237084
34	0.088817	0.6089	0.272761
35	-0.08724	-0.5981	0.276327
36	0.061541	0.4219	0.337509

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.629949	-4.3187	4e-05
2	-0.529267	-3.6285	0.00035
3	-0.165301	-1.1332	0.131429
4	-0.106078	-0.7272	0.235345
5	-0.081184	-0.5566	0.290232
6	0.049753	0.3411	0.367279
7	-0.007089	-0.0486	0.480721
8	-0.052904	-0.3627	0.359232
9	0.039629	0.2717	0.393528
10	-0.021486	-0.1473	0.441763
11	0.030257	0.2074	0.418285
12	-0.006688	-0.0459	0.481811
13	0.061304	0.4203	0.338098
14	-0.098625	-0.6761	0.251133
15	0.030851	0.2115	0.416704
16	-0.037825	-0.2593	0.398263
17	-0.06264	-0.4294	0.334783
18	0.069084	0.4736	0.318984
19	0.033466	0.2294	0.409765
20	-0.035818	-0.2456	0.403548
21	0.129873	0.8904	0.188902
22	-0.240634	-1.6497	0.052836
23	0.117689	0.8068	0.211913
24	0.013009	0.0892	0.464658
25	-0.008756	-0.06	0.476194
26	-0.092871	-0.6367	0.263708
27	0.002727	0.0187	0.492581
28	0.018148	0.1244	0.450759
29	-0.013626	-0.0934	0.462984
30	0.060065	0.4118	0.341184
31	0.008746	0.06	0.476222
32	-0.028544	-0.1957	0.422849
33	-0.058601	-0.4017	0.344846
34	-0.073536	-0.5041	0.308261
35	-0.142957	-0.9801	0.166036
36	-0.166002	-1.1381	0.130433

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260785734qtud04t9406lwv0/1pkci1260785605.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260785734qtud04t9406lwv0/1pkci1260785605.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260785734qtud04t9406lwv0/2rhng1260785605.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260785734qtud04t9406lwv0/2rhng1260785605.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 2.0 ; par3 = 1 ; 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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