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Paper: (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: Thu, 17 Dec 2009 05:52:26 -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/17/t1261054459cbn2jp1j17i3v3w.htm/, Retrieved Thu, 17 Dec 2009 13:54:22 +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/17/t1261054459cbn2jp1j17i3v3w.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:

SHW Paper: (Partial) Autocorrelation function

Dataseries X:

» Textbox « » Textfile « » CSV «

15.5 15.1 11.7 16.3 16.7 15 14.9 14.6 15.3 17.9 16.4 15.4 17.9 15.9 13.9 17.8 17.9 17.4 16.7 16 16.6 19.1 17.8 17.2 18.6 16.3 15.1 19.2 17.7 19.1 18 17.5 17.8 21.1 17.2 19.4 19.8 17.6 16.2 19.5 19.9 20 17.3 18.9 18.6 21.4 18.6 19.8 20.8 19.6 17.7 19.8 22.2 20.7 17.9 20.9 21.2 21.4 23 21.3 23.9 22.4 18.3 22.8 22.3 17.8 16.4 16 16.4 17.7 16.6 16.2 18.3

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	0.613349	5.2405	1e-06
2	0.467784	3.9967	7.6e-05
3	0.54173	4.6285	8e-06
4	0.504458	4.3101	2.5e-05
5	0.435229	3.7186	0.000195
6	0.42295	3.6137	0.000276
7	0.254194	2.1718	0.016559
8	0.310866	2.656	0.004852
9	0.217107	1.855	0.03382
10	0.085263	0.7285	0.234324
11	0.209591	1.7907	0.03874
12	0.386917	3.3058	0.000735
13	0.154071	1.3164	0.096082
14	0.063695	0.5442	0.293977
15	0.105217	0.899	0.185812
16	0.145795	1.2457	0.108434
17	0.106994	0.9142	0.181823
18	0.114592	0.9791	0.165387
19	0.04914	0.4199	0.337913
20	0.066397	0.5673	0.286128
21	-0.014879	-0.1271	0.449594
22	-0.078018	-0.6666	0.253568
23	0.021494	0.1836	0.427402
24	0.12266	1.048	0.149045
25	-0.017222	-0.1471	0.441712
26	-0.119799	-1.0236	0.15471
27	-0.088926	-0.7598	0.224916
28	-0.017617	-0.1505	0.440384
29	-0.088646	-0.7574	0.225626
30	-0.083108	-0.7101	0.239959
31	-0.0978	-0.8356	0.203052
32	-0.1305	-1.115	0.134255
33	-0.179228	-1.5313	0.065006
34	-0.19608	-1.6753	0.049077
35	-0.183053	-1.564	0.061071
36	-0.069485	-0.5937	0.277282

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.613349	5.2405	1e-06
2	0.146821	1.2544	0.106843
3	0.338963	2.8961	0.002491
4	0.100558	0.8592	0.196531
5	0.056985	0.4869	0.313902
6	0.051533	0.4403	0.33051
7	-0.258116	-2.2053	0.01529
8	0.16036	1.3701	0.087426
9	-0.246861	-2.1092	0.01918
10	-0.079032	-0.6753	0.250824
11	0.244774	2.0913	0.019988
12	0.394609	3.3715	0.000599
13	-0.196349	-1.6776	0.048851
14	-0.210748	-1.8006	0.037946
15	-0.066905	-0.5716	0.284663
16	0.009145	0.0781	0.468969
17	-0.115706	-0.9886	0.163065
18	0.147873	1.2634	0.105228
19	0.127054	1.0856	0.140625
20	-0.097304	-0.8314	0.20424
21	-0.094635	-0.8086	0.210697
22	0.007297	0.0623	0.475229
23	0.02428	0.2075	0.418117
24	-0.085514	-0.7306	0.233672
25	0.085419	0.7298	0.233918
26	-0.067834	-0.5796	0.281993
27	-0.078779	-0.6731	0.251509
28	0.039992	0.3417	0.366781
29	-0.100707	-0.8604	0.196182
30	-0.004622	-0.0395	0.484305
31	-0.030444	-0.2601	0.397755
32	0.00444	0.0379	0.48492
33	-0.001603	-0.0137	0.494556
34	0.003421	0.0292	0.48838
35	-0.10958	-0.9363	0.176115
36	0.003003	0.0257	0.4898

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054459cbn2jp1j17i3v3w/11qx01261054344.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054459cbn2jp1j17i3v3w/11qx01261054344.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054459cbn2jp1j17i3v3w/2la5t1261054344.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054459cbn2jp1j17i3v3w/2la5t1261054344.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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