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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: Thu, 26 Nov 2009 11:52:35 -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/t1259261701higyly2qq2ucmx8.htm/, Retrieved Thu, 26 Nov 2009 19:55:03 +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/t1259261701higyly2qq2ucmx8.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 «

12.610 10.862 52.929 56.902 81.776 87.876 82.103 72.846 60.632 33.521 15.342 7.758 8.668 13.082 38.157 58.263 81.153 88.476 72.329 75.845 61.108 37.665 12.755 2.793 12.935 19.533 33.404 52.074 70.735 69.702 61.656 82.993 53.990 32.283 15.686 2.713 12.842 19.244 48.488 54.464 84.192 84.458 85.793 75.163 68.212 49.233 24.302 5.402 15.058 33.559 70.358 85.934 94.452 129.305 113.882 107.256 94.274 57.842 26.611 14.521

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	0.570366	3.9516	0.000127
2	0.561008	3.8868	0.000156
3	0.458637	3.1775	0.001299
4	0.452353	3.134	0.00147
5	0.271509	1.8811	0.033018
6	0.260689	1.8061	0.038587
7	0.168585	1.168	0.12429
8	0.136477	0.9455	0.17456
9	0.211654	1.4664	0.074533
10	0.135282	0.9373	0.176658
11	0.218406	1.5132	0.068398
12	0.078593	0.5445	0.294306
13	0.124044	0.8594	0.197196
14	0.138657	0.9606	0.170772
15	0.134143	0.9294	0.178675
16	-0.006753	-0.0468	0.481438
17	-0.026896	-0.1863	0.426482
18	-0.073382	-0.5084	0.30675
19	-0.100282	-0.6948	0.245272
20	-0.144205	-0.9991	0.161383
21	-0.195782	-1.3564	0.090656
22	-0.236324	-1.6373	0.054054
23	-0.262243	-1.8169	0.037742
24	-0.326846	-2.2645	0.01405
25	-0.226503	-1.5693	0.061578
26	-0.29932	-2.0737	0.021746
27	-0.292364	-2.0256	0.024195
28	-0.22857	-1.5836	0.059929
29	-0.105499	-0.7309	0.23419
30	-0.148196	-1.0267	0.154846
31	-0.13069	-0.9054	0.184876
32	-0.135062	-0.9357	0.177046
33	-0.161632	-1.1198	0.134182
34	-0.09153	-0.6341	0.2645
35	-0.150833	-1.045	0.150628
36	-0.148841	-1.0312	0.153807
37	-0.191601	-1.3275	0.095319
38	-0.135054	-0.9357	0.17706
39	-0.184024	-1.275	0.10423
40	-0.105455	-0.7306	0.234284
41	-0.140898	-0.9762	0.166937
42	-0.090878	-0.6296	0.265965
43	-0.048659	-0.3371	0.368749
44	-0.019105	-0.1324	0.447625
45	-0.011178	-0.0774	0.469295
46	0.002398	0.0166	0.493408
47	-0.004192	-0.029	0.488476
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.570366	3.9516	0.000127
2	0.349336	2.4203	0.009672
3	0.086416	0.5987	0.276091
4	0.116874	0.8097	0.211047
5	-0.171467	-1.188	0.120347
6	-0.014063	-0.0974	0.461396
7	-0.043696	-0.3027	0.3817
8	-0.020685	-0.1433	0.443323
9	0.245104	1.6981	0.047979
10	-0.045934	-0.3182	0.375841
11	0.155298	1.0759	0.143666
12	-0.210522	-1.4585	0.075602
13	-0.061573	-0.4266	0.335791
14	0.162116	1.1232	0.133475
15	-0.054669	-0.3788	0.353268
16	-0.089663	-0.6212	0.268703
17	-0.141745	-0.982	0.165502
18	-0.104044	-0.7208	0.237252
19	0.041196	0.2854	0.388277
20	-0.100627	-0.6972	0.244531
21	0.016105	0.1116	0.45581
22	-0.114061	-0.7902	0.216639
23	-0.107114	-0.7421	0.230819
24	-0.186523	-1.2923	0.101225
25	0.136125	0.9431	0.175176
26	-0.021421	-0.1484	0.44132
27	0.016795	0.1164	0.453926
28	0.093288	0.6463	0.260577
29	0.102226	0.7082	0.24111
30	0.007619	0.0528	0.479061
31	-0.067621	-0.4685	0.320778
32	-0.058898	-0.4081	0.342524
33	-0.042663	-0.2956	0.384413
34	0.094465	0.6545	0.257965
35	0.043265	0.2998	0.382831
36	-0.082852	-0.574	0.284318
37	-0.006268	-0.0434	0.48277
38	-0.036347	-0.2518	0.401128
39	-0.110721	-0.7671	0.22339
40	-0.004263	-0.0295	0.48828
41	0.035755	0.2477	0.402706
42	0.039509	0.2737	0.392735
43	-0.042516	-0.2946	0.3848
44	-0.080964	-0.5609	0.288725
45	-0.030744	-0.213	0.416114
46	0.040006	0.2772	0.391421
47	-0.021539	-0.1492	0.441001
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259261701higyly2qq2ucmx8/17z2v1259261553.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259261701higyly2qq2ucmx8/17z2v1259261553.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259261701higyly2qq2ucmx8/2g5y91259261553.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259261701higyly2qq2ucmx8/2g5y91259261553.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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