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(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, 26 Nov 2009 02:42:54 -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/Nov/26/t1259228771c25ptdq4uel33lf.htm/, Retrieved Thu, 26 Nov 2009 10:46:13 +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/26/t1259228771c25ptdq4uel33lf.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 «

1.4 1 -0.8 -2.9 -0.7 -0.7 1.5 3 3.2 3.1 3.9 1 1.3 0.8 1.2 2.9 3.9 4.5 4.5 3.3 2 1.5 1 2.1 3 4 5.1 4.5 4.2 3.3 2.7 1.8 1.4 0.5 -0.4 0.8 0.7 1.9 2 1.1 0.9 0.4 0.7 2.1 2.8 3.9 3.5 2 2 1.5 2.5 3.1 2.7 2.8 2.5 3 3.2 2.8 2.4 2 1.8 1.1 -1.5 -3.7

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.719206	5.7536	0
2	0.400778	3.2062	0.00105
3	0.103386	0.8271	0.20563
4	-0.13139	-1.0511	0.148578
5	-0.192757	-1.5421	0.063995
6	-0.151056	-1.2084	0.115661
7	-0.065622	-0.525	0.300706
8	0.079564	0.6365	0.263357
9	0.12398	0.9918	0.162506
10	0.073576	0.5886	0.279097
11	-0.01729	-0.1383	0.445212
12	-0.162625	-1.301	0.098962
13	-0.236087	-1.8887	0.031733
14	-0.273689	-2.1895	0.016106
15	-0.285341	-2.2827	0.012889
16	-0.221913	-1.7753	0.040301
17	-0.152494	-1.22	0.11348
18	-0.042913	-0.3433	0.366247
19	0.051705	0.4136	0.340262
20	0.060709	0.4857	0.314428
21	-0.004079	-0.0326	0.487036
22	-0.10429	-0.8343	0.203602
23	-0.204878	-1.639	0.053058
24	-0.229368	-1.8349	0.035581
25	-0.16407	-1.3126	0.097009
26	-0.037596	-0.3008	0.382284
27	0.12342	0.9874	0.163593
28	0.228641	1.8291	0.03602
29	0.273067	2.1845	0.016296
30	0.219084	1.7527	0.042224
31	0.144755	1.158	0.125576
32	0.05048	0.4038	0.343837
33	-0.006368	-0.0509	0.479763
34	-0.043655	-0.3492	0.364028
35	-0.044869	-0.359	0.360405
36	-0.009211	-0.0737	0.470746

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.719206	5.7536	0
2	-0.241284	-1.9303	0.029003
3	-0.17788	-1.423	0.07979
4	-0.132331	-1.0586	0.14687
5	0.10833	0.8666	0.194689
6	0.038257	0.3061	0.380276
7	0.007716	0.0617	0.475487
8	0.135353	1.0828	0.141474
9	-0.100384	-0.8031	0.212453
10	-0.100932	-0.8075	0.211198
11	-0.050929	-0.4074	0.342525
12	-0.119561	-0.9565	0.171212
13	0.014077	0.1126	0.455343
14	-0.11177	-0.8942	0.187294
15	-0.099177	-0.7934	0.215233
16	-0.022238	-0.1779	0.429681
17	-0.054817	-0.4385	0.331236
18	0.097521	0.7802	0.219084
19	-0.002879	-0.023	0.490847
20	-0.058742	-0.4699	0.319999
21	-0.132999	-1.064	0.145666
22	-0.100989	-0.8079	0.211068
23	-0.056723	-0.4538	0.325758
24	-0.022565	-0.1805	0.428658
25	0.065067	0.5205	0.302242
26	0.025329	0.2026	0.420031
27	0.028847	0.2308	0.409113
28	-0.012149	-0.0972	0.46144
29	0.034364	0.2749	0.392133
30	-0.026763	-0.2141	0.415573
31	0.08884	0.7107	0.239919
32	-0.036609	-0.2929	0.385283
33	0.010492	0.0839	0.466683
34	-0.090212	-0.7217	0.236555
35	-0.038204	-0.3056	0.38044
36	0.013698	0.1096	0.456541

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259228771c25ptdq4uel33lf/1gpux1259228572.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259228771c25ptdq4uel33lf/1gpux1259228572.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259228771c25ptdq4uel33lf/253ur1259228572.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259228771c25ptdq4uel33lf/253ur1259228572.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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