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Paper(3) - (Partial) Autocorrelation Function

*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, 25 Dec 2009 04:16:54 -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/25/t126173999898uk2u7at3eqorx.htm/, Retrieved Fri, 25 Dec 2009 12:20:01 +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/25/t126173999898uk2u7at3eqorx.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:

P3 - P(ACF)

Dataseries X:

» Textbox « » Textfile « » CSV «

2,3 2,3 2,6 3,1 2,8 2,5 2,9 3,1 3,1 3,2 2,5 2,6 2,9 2,6 2,4 1,7 2 2,2 1,9 1,6 1,6 1,2 1,2 1,5 1,6 1,7 1,8 1,8 1,8 1,3 1,3 1,4 1,1 1,5 2,2 2,9 3,1 3,5 3,6 4,4 4,2 5,2 5,8 5,9 5,4 5,5 4,7 3,1 2,6 2,3 1,9 0,6 0,6 -0,4 -1,1 -1,7 -0,8 -1,2 -1 -0,1

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	17 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.937015	7.2581	0
2	0.835952	6.4753	0
3	0.710627	5.5045	0
4	0.565099	4.3772	2.4e-05
5	0.380941	2.9508	0.002258
6	0.210941	1.6339	0.053754
7	0.047055	0.3645	0.358388
8	-0.111014	-0.8599	0.19663
9	-0.261497	-2.0256	0.023633
10	-0.376174	-2.9138	0.002505
11	-0.468342	-3.6278	0.000296
12	-0.549841	-4.2591	3.7e-05
13	-0.578633	-4.4821	1.7e-05
14	-0.559038	-4.3303	2.9e-05
15	-0.517208	-4.0063	8.6e-05
16	-0.470526	-3.6447	0.00028
17	-0.399374	-3.0935	0.001501
18	-0.333638	-2.5843	0.006104
19	-0.273408	-2.1178	0.019172
20	-0.224718	-1.7407	0.043435
21	-0.161811	-1.2534	0.107464
22	-0.106588	-0.8256	0.206143
23	-0.057629	-0.4464	0.328459
24	-0.011925	-0.0924	0.463356
25	0.035462	0.2747	0.392249
26	0.063565	0.4924	0.312128
27	0.081654	0.6325	0.264735
28	0.100635	0.7795	0.21937
29	0.121491	0.9411	0.175222
30	0.140764	1.0904	0.139959
31	0.161482	1.2508	0.107926
32	0.189984	1.4716	0.073176
33	0.206858	1.6023	0.057169
34	0.210497	1.6305	0.054117
35	0.205244	1.5898	0.058567
36	0.196817	1.5245	0.066314

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.937015	7.2581	0
2	-0.344634	-2.6695	0.004879
3	-0.183208	-1.4191	0.080519
4	-0.178814	-1.3851	0.085577
5	-0.394905	-3.0589	0.001659
6	0.168962	1.3088	0.097801
7	-0.129787	-1.0053	0.159388
8	-0.121892	-0.9442	0.174435
9	-0.051542	-0.3992	0.345567
10	-0.016541	-0.1281	0.449238
11	-0.053795	-0.4167	0.339196
12	-0.205218	-1.5896	0.058589
13	0.35916	2.782	0.003605
14	-0.004028	-0.0312	0.487607
15	-0.074878	-0.58	0.282042
16	-0.099091	-0.7676	0.222881
17	-0.167473	-1.2972	0.099757
18	-0.198524	-1.5378	0.064682
19	-0.027219	-0.2108	0.416866
20	-0.071227	-0.5517	0.291593
21	0.060836	0.4712	0.319591
22	0.061548	0.4767	0.317637
23	-0.046767	-0.3623	0.359216
24	-0.066047	-0.5116	0.305405
25	-0.035115	-0.272	0.393277
26	0.008502	0.0659	0.473855
27	-0.02235	-0.1731	0.431568
28	0.033512	0.2596	0.398037
29	0.06535	0.5062	0.307286
30	-0.052234	-0.4046	0.343604
31	-0.028046	-0.2172	0.414377
32	-0.031983	-0.2477	0.402591
33	-0.115155	-0.892	0.187981
34	-0.004035	-0.0313	0.487585
35	0.036188	0.2803	0.390102
36	-0.014246	-0.1104	0.456249

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/25/t126173999898uk2u7at3eqorx/1w6xq1261739795.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/25/t126173999898uk2u7at3eqorx/1w6xq1261739795.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/25/t126173999898uk2u7at3eqorx/2vk1h1261739795.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/25/t126173999898uk2u7at3eqorx/2vk1h1261739795.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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