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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: Mon, 07 Dec 2009 12:33:45 -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/07/t126021450718dgrc8tynkzgog.htm/, Retrieved Mon, 07 Dec 2009 20:35:09 +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/07/t126021450718dgrc8tynkzgog.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 «

17 18 23.8 25.5 25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.296153	2.0941	0.02067
2	-0.128739	-0.9103	0.183511
3	-0.507612	-3.5894	0.000377
4	-0.546792	-3.8664	0.00016
5	-0.156805	-1.1088	0.136415
6	0.198252	1.4019	0.083568
7	0.383979	2.7151	0.004535
8	0.349517	2.4715	0.008453
9	0.109197	0.7721	0.221834
10	-0.199322	-1.4094	0.08245
11	-0.206873	-1.4628	0.074888
12	-0.350121	-2.4757	0.008364
13	-0.106825	-0.7554	0.226787
14	0.143118	1.012	0.158206
15	0.274545	1.9413	0.028933
16	0.12268	0.8675	0.194912
17	0.083901	0.5933	0.277837
18	-0.022777	-0.1611	0.436348
19	-0.184719	-1.3062	0.098737
20	-0.118336	-0.8368	0.203355
21	-0.149821	-1.0594	0.147255
22	0.047953	0.3391	0.367984
23	0.10169	0.7191	0.237726
24	0.14299	1.0111	0.15842
25	0.095205	0.6732	0.25196
26	0.07227	0.511	0.305791
27	-0.169218	-1.1966	0.118562
28	-0.072067	-0.5096	0.306289
29	-0.084774	-0.5994	0.275791
30	-0.121949	-0.8623	0.196318
31	0.097581	0.69	0.246693
32	0.144174	1.0195	0.156446
33	0.185252	1.3099	0.098103
34	0.014136	0.1	0.46039
35	-0.133238	-0.9421	0.175328
36	-0.160196	-1.1328	0.131359
37	-0.063549	-0.4494	0.327558
38	0.030794	0.2177	0.414257
39	0.126322	0.8932	0.188007
40	0.099159	0.7012	0.243226
41	-0.018639	-0.1318	0.447837
42	-0.025873	-0.1829	0.42779
43	-0.047759	-0.3377	0.368498
44	-0.046766	-0.3307	0.371133
45	-0.048448	-0.3426	0.366674
46	0.009348	0.0661	0.47378
47	0.022863	0.1617	0.43611
48	0.044444	0.3143	0.377313
49	-0.024305	-0.1719	0.432119
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.296153	2.0941	0.02067
2	-0.237254	-1.6776	0.049829
3	-0.453197	-3.2046	0.001178
4	-0.42438	-3.0008	0.002096
5	-0.161172	-1.1397	0.12993
6	-0.138809	-0.9815	0.16553
7	-0.129637	-0.9167	0.181857
8	-0.007173	-0.0507	0.479875
9	0.071483	0.5055	0.307729
10	-0.017325	-0.1225	0.451494
11	0.213114	1.5069	0.069058
12	-0.172859	-1.2223	0.113663
13	-0.05389	-0.3811	0.352387
14	0.009544	0.0675	0.473231
15	0.00409	0.0289	0.488522
16	-0.347389	-2.4564	0.008775
17	0.03556	0.2515	0.401248
18	0.166713	1.1788	0.122021
19	-0.125005	-0.8839	0.190485
20	0.018233	0.1289	0.448965
21	0.023972	0.1695	0.433041
22	0.014858	0.1051	0.458375
23	-0.058217	-0.4117	0.341175
24	-0.029357	-0.2076	0.418198
25	-0.1173	-0.8294	0.2054
26	0.102986	0.7282	0.234937
27	-0.060504	-0.4278	0.335306
28	0.054529	0.3856	0.350723
29	-0.023281	-0.1646	0.434954
30	-0.054313	-0.384	0.351285
31	0.061413	0.4343	0.332986
32	0.063492	0.449	0.327701
33	0.003911	0.0277	0.489024
34	-0.05443	-0.3849	0.35098
35	-0.052979	-0.3746	0.354765
36	0.077375	0.5471	0.293363
37	-0.020948	-0.1481	0.44142
38	0.126291	0.893	0.188064
39	0.005864	0.0415	0.483546
40	0.007505	0.0531	0.478944
41	0.025792	0.1824	0.428013
42	0.071342	0.5045	0.308076
43	-0.068536	-0.4846	0.315031
44	-0.016904	-0.1195	0.452668
45	0.05458	0.3859	0.350588
46	-0.141244	-0.9987	0.161363
47	-0.031346	-0.2217	0.412744
48	0.003216	0.0227	0.490974
49	-0.13163	-0.9308	0.178223
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t126021450718dgrc8tynkzgog/1ptxb1260214423.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t126021450718dgrc8tynkzgog/1ptxb1260214423.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t126021450718dgrc8tynkzgog/2usa01260214423.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t126021450718dgrc8tynkzgog/2usa01260214423.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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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