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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: Fri, 18 Dec 2009 07:15:41 -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/18/t1261145784xf0u8no1krjlb1x.htm/, Retrieved Fri, 18 Dec 2009 15:16:26 +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/18/t1261145784xf0u8no1krjlb1x.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 «

97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 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 99 100.7 115.5 100.7 109.9 114.6 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 82.6 89.1 104.5

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.224408	2.0197	0.023362
2	-0.053888	-0.485	0.314497
3	0.13897	1.2507	0.107318
4	0.039425	0.3548	0.361821
5	0.290734	2.6166	0.005296
6	0.399328	3.594	0.000279
7	0.184902	1.6641	0.049977
8	-0.019677	-0.1771	0.429939
9	-0.047543	-0.4279	0.334935
10	-0.253637	-2.2827	0.012534
11	0.041163	0.3705	0.356
12	0.558169	5.0235	1e-06
13	-0.03746	-0.3371	0.368441
14	-0.233379	-2.1004	0.019402
15	-0.122952	-1.1066	0.135878
16	-0.162919	-1.4663	0.073223
17	0.086586	0.7793	0.219045
18	0.13484	1.2136	0.114222
19	0.036574	0.3292	0.371439
20	-0.112873	-1.0159	0.156362
21	-0.155368	-1.3983	0.082918
22	-0.290649	-2.6158	0.005307
23	-0.01315	-0.1184	0.453041
24	0.379007	3.4111	0.000506
25	-0.07307	-0.6576	0.256319
26	-0.244673	-2.2021	0.015252
27	-0.167742	-1.5097	0.067508
28	-0.175819	-1.5824	0.058731
29	0.01699	0.1529	0.439425
30	0.060242	0.5422	0.294592
31	-0.016774	-0.151	0.440188
32	-0.161068	-1.4496	0.075513
33	-0.178867	-1.6098	0.055666
34	-0.241881	-2.1769	0.016198
35	-0.071856	-0.6467	0.259826
36	0.272592	2.4533	0.00815

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.224408	2.0197	0.023362
2	-0.109775	-0.988	0.163054
3	0.188686	1.6982	0.046657
4	-0.053994	-0.4859	0.31416
5	0.361055	3.2495	0.000842
6	0.249522	2.2457	0.013724
7	0.169035	1.5213	0.066038
8	-0.110936	-0.9984	0.160523
9	-0.091568	-0.8241	0.206149
10	-0.522988	-4.7069	5e-06
11	-0.084203	-0.7578	0.225378
12	0.486259	4.3763	1.8e-05
13	-0.124532	-1.1208	0.132845
14	-0.01924	-0.1732	0.431479
15	-0.086551	-0.779	0.219137
16	0.109084	0.9818	0.164571
17	-0.093573	-0.8422	0.201089
18	-0.133853	-1.2047	0.115918
19	0.063197	0.5688	0.285543
20	-0.0464	-0.4176	0.338671
21	0.061652	0.5549	0.290256
22	-0.042992	-0.3869	0.349913
23	0.024798	0.2232	0.411977
24	0.004697	0.0423	0.483192
25	-0.038535	-0.3468	0.364815
26	-0.111992	-1.0079	0.158246
27	-0.066524	-0.5987	0.275517
28	-0.063449	-0.571	0.284778
29	-0.066535	-0.5988	0.275482
30	0.013845	0.1246	0.450572
31	-0.025233	-0.2271	0.41046
32	-0.034186	-0.3077	0.379561
33	0.045041	0.4054	0.343136
34	0.135753	1.2218	0.112668
35	-0.128239	-1.1541	0.125917
36	-0.00358	-0.0322	0.487187

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261145784xf0u8no1krjlb1x/1vtod1261145738.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261145784xf0u8no1krjlb1x/1vtod1261145738.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261145784xf0u8no1krjlb1x/2idfr1261145738.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261145784xf0u8no1krjlb1x/2idfr1261145738.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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