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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: Fri, 18 Dec 2009 08:30:44 -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/t1261150305o5huy8aogwbw4w3.htm/, Retrieved Fri, 18 Dec 2009 16:31:47 +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/t1261150305o5huy8aogwbw4w3.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 «

12.1 12 11.8 12.7 12.3 11.9 12 12.3 12.8 12.4 12.3 12.7 12.7 12.9 13 12.2 12.3 12.8 12.8 12.8 12.2 12.6 12.8 12.5 12.4 12.3 11.9 11.7 12 12.1 11.7 11.8 11.8 11.8 11.3 11.3 11.3 11.2 11.4 12.2 12.9 13.1 13.5 13.6 14.4 14.1 15.1 15.8 15.9 15.4 15.5 14.8 13.2 12.7 12.1 11.9 10.6 10.7 9.8 9 8.3 9.3 9 9.1 10

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	0.176337	1.4107	0.081588
2	0.155608	1.2449	0.10886
3	0.227402	1.8192	0.036778
4	0.270808	2.1665	0.017003
5	-0.046958	-0.3757	0.354206
6	-0.017302	-0.1384	0.445174
7	0.097906	0.7832	0.218185
8	-0.077678	-0.6214	0.268265
9	-0.210653	-1.6852	0.048408
10	-0.17075	-1.366	0.08836
11	0.008583	0.0687	0.472735
12	-0.508456	-4.0677	6.6e-05
13	-0.278757	-2.2301	0.014629
14	-0.098664	-0.7893	0.216423
15	-0.017447	-0.1396	0.444717
16	-0.192867	-1.5429	0.063888
17	-0.046919	-0.3753	0.354321
18	0.05481	0.4385	0.331256
19	-0.03695	-0.2956	0.384246
20	-0.083966	-0.6717	0.252087
21	0.005226	0.0418	0.483392
22	0.148848	1.1908	0.119068
23	-0.02173	-0.1738	0.431271
24	-0.027196	-0.2176	0.414229
25	0.154672	1.2374	0.110235
26	0.086646	0.6932	0.245357
27	-0.0681	-0.5448	0.293893
28	0.048484	0.3879	0.349699
29	0.082412	0.6593	0.256035
30	0.019963	0.1597	0.43681
31	-0.076089	-0.6087	0.272435
32	0.07158	0.5726	0.284448
33	0.114388	0.9151	0.181785
34	-0.023955	-0.1916	0.424317
35	-0.073659	-0.5893	0.278877
36	0.136968	1.0957	0.138649

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.176337	1.4107	0.081588
2	0.12851	1.0281	0.153892
3	0.189765	1.5181	0.066954
4	0.209545	1.6764	0.049273
5	-0.1723	-1.3784	0.08644
6	-0.099689	-0.7975	0.214052
7	0.050055	0.4004	0.345083
8	-0.111348	-0.8908	0.18819
9	-0.155458	-1.2437	0.10908
10	-0.140447	-1.1236	0.132695
11	0.089203	0.7136	0.239026
12	-0.448453	-3.5876	0.000323
13	-0.098714	-0.7897	0.216305
14	0.071147	0.5692	0.285614
15	0.176384	1.4111	0.081533
16	0.1038	0.8304	0.2047
17	-0.043935	-0.3515	0.363193
18	-0.046879	-0.375	0.354439
19	-0.0449	-0.3592	0.360315
20	-0.101202	-0.8096	0.210581
21	-0.156497	-1.252	0.107568
22	-0.001057	-0.0085	0.496639
23	0.090862	0.7269	0.234969
24	-0.283098	-2.2648	0.01346
25	-0.001989	-0.0159	0.493678
26	0.02395	0.1916	0.424331
27	0.085357	0.6829	0.24858
28	0.139115	1.1129	0.134953
29	-0.035363	-0.2829	0.389082
30	0.022906	0.1832	0.427591
31	-0.133203	-1.0656	0.145299
32	-0.051658	-0.4133	0.340397
33	-0.035448	-0.2836	0.388822
34	0.04232	0.3386	0.368025
35	0.021358	0.1709	0.432433
36	-0.070805	-0.5664	0.286538

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261150305o5huy8aogwbw4w3/12p4n1261150242.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261150305o5huy8aogwbw4w3/12p4n1261150242.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261150305o5huy8aogwbw4w3/2ti4u1261150242.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261150305o5huy8aogwbw4w3/2ti4u1261150242.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

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