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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: Sat, 05 Dec 2009 11:52:26 -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/05/t12600391956q0pmw338z4da0k.htm/, Retrieved Sat, 05 Dec 2009 19:53:17 +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/05/t12600391956q0pmw338z4da0k.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 «

8 8.2 8.3 8.1 7.4 7.3 7.7 8 8 7.7 6.9 6.6 6.9 7.5 7.9 7.7 6.5 6.1 6.4 6.8 7.1 7.3 7.2 7 7 7 7.3 7.5 7.2 7.7 8 7.9 8 8 7.9 7.9 8 8.1 8.1 8.2 8 8.3 8.5 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 7.9 8.1 8.2 8.5 8.6 8.5 8.3 8.2 8.7 9.3 9.3 8.8 7.4 7.2 7.5 8.3 8.8 8.9 8.6 8.4 8.4 8.4 8.4 8.3 7.6 7.6 7.9 8 8.2 8.3 8.2 8.1 8 7.8 7.6 7.5 6.8 6.9 7.1 7.3 7.4 7.6 7.6 7.5 7.5 6.8 6.4 6.2 6 6.3 6.3 6.1 6.1 6.3 6.6 6.8 7 7.1 7.3 6.8 6.3 6.4 6.7 6.8 7.2 7.5 7.7 7.8 8.1

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.383101	4.1967	2.6e-05
2	-0.186304	-2.0409	0.021729
3	-0.466187	-5.1068	1e-06
4	-0.371928	-4.0743	4.2e-05
5	0.025272	0.2768	0.391189
6	0.345275	3.7823	0.000122
7	0.204257	2.2375	0.013549
8	-0.110512	-1.2106	0.114214
9	-0.256813	-2.8133	0.002866
10	-0.205669	-2.253	0.013038
11	0.083859	0.9186	0.180066
12	0.487004	5.3349	0
13	0.167824	1.8384	0.034237
14	-0.020707	-0.2268	0.410468
15	-0.136515	-1.4954	0.068712
16	-0.159591	-1.7482	0.041491
17	-0.033409	-0.366	0.357515
18	0.078699	0.8621	0.195174
19	-0.025954	-0.2843	0.388331
20	-0.128367	-1.4062	0.081125
21	-0.116489	-1.2761	0.102197
22	-0.087554	-0.9591	0.169716
23	0.065342	0.7158	0.237757
24	0.290244	3.1795	0.000939
25	0.007392	0.081	0.467799
26	-0.063123	-0.6915	0.245299
27	-0.067566	-0.7401	0.230329
28	-0.067572	-0.7402	0.230309
29	0.000766	0.0084	0.496661
30	0.028265	0.3096	0.37869
31	-0.041514	-0.4548	0.325051
32	-0.126877	-1.3899	0.083571
33	-0.060105	-0.6584	0.255766
34	-0.016316	-0.1787	0.429225
35	0.075729	0.8296	0.204216
36	0.210096	2.3015	0.011545
37	-0.061621	-0.675	0.250481
38	-0.103201	-1.1305	0.130258
39	-0.0594	-0.6507	0.258245
40	0.027454	0.3007	0.382065
41	0.123254	1.3502	0.08975
42	0.113621	1.2447	0.107841
43	-0.080119	-0.8777	0.190941
44	-0.29318	-3.2116	0.000847
45	-0.225666	-2.472	0.007418
46	-0.050479	-0.553	0.290656
47	0.236079	2.5861	0.005451
48	0.426138	4.6681	4e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.383101	4.1967	2.6e-05
2	-0.390362	-4.2762	1.9e-05
3	-0.300608	-3.293	0.000651
4	-0.161206	-1.7659	0.039976
5	0.086299	0.9454	0.173187
6	0.120361	1.3185	0.094926
7	-0.161887	-1.7734	0.039351
8	-0.137564	-1.5069	0.067227
9	-0.008401	-0.092	0.463413
10	-0.052247	-0.5723	0.284083
11	0.072097	0.7898	0.215607
12	0.375909	4.1179	3.5e-05
13	-0.339315	-3.717	0.000154
14	0.343293	3.7606	0.000132
15	0.12371	1.3552	0.088953
16	0.002506	0.0275	0.489073
17	-0.008925	-0.0978	0.461141
18	-0.093688	-1.0263	0.153407
19	-0.063284	-0.6932	0.244748
20	-0.065259	-0.7149	0.238039
21	-0.138621	-1.5185	0.065757
22	-0.103275	-1.1313	0.130088
23	-0.020384	-0.2233	0.411844
24	0.00126	0.0138	0.494507
25	-0.154045	-1.6875	0.047055
26	-0.009808	-0.1074	0.457308
27	0.024993	0.2738	0.392362
28	-0.044689	-0.4895	0.312676
29	-0.031634	-0.3465	0.364773
30	-0.064036	-0.7015	0.242181
31	0.098872	1.0831	0.14047
32	-0.124501	-1.3638	0.087585
33	0.091001	0.9969	0.160417
34	0.054281	0.5946	0.276609
35	-0.021092	-0.231	0.408836
36	0.08581	0.94	0.174553
37	-0.100887	-1.1052	0.135649
38	-0.024058	-0.2635	0.396291
39	0.008571	0.0939	0.462677
40	0.058757	0.6437	0.260514
41	0.027995	0.3067	0.379815
42	0.033665	0.3688	0.356469
43	-0.164887	-1.8063	0.036693
44	-0.160287	-1.7559	0.040832
45	-0.119994	-1.3145	0.095598
46	-0.067986	-0.7447	0.22894
47	0.070092	0.7678	0.222053
48	0.023324	0.2555	0.399385

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/05/t12600391956q0pmw338z4da0k/126z31260039145.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t12600391956q0pmw338z4da0k/126z31260039145.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t12600391956q0pmw338z4da0k/2k3z61260039145.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t12600391956q0pmw338z4da0k/2k3z61260039145.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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