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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: Tue, 23 Dec 2008 09:01:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/23/t1230048093xcrkxvjcj78l6zc.htm/, Retrieved Tue, 23 Dec 2008 17:01:34 +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/2008/Dec/23/t1230048093xcrkxvjcj78l6zc.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

0,2 0,8 1,2 4,5 0,4 5,9 6,5 12,8 4,2 -3,3 -12,5 -16,3 -10,5 -11,8 -11,4 -17,7 -17,3 -18,6 -17,9 -21,4 -19,4 -15,5 -7,7 -0,7 -1,6 1,4 0,7 9,5 1,4 4,1 6,6 18,4 16,9 9,2 -4,3 -5,9 -7,7 -5,4 -2,3 -4,8 2,3 -5,2 -10 -17,1 -14,4 -3,9 3,7 6,5 0,9 -4,1 -7 -12,2 -2,5 4,4 13,7 12,3 13,4 2,2 1,7 -7,2 -4,8 -2,9 -2,4 -2,5 -5,3 -7,1 -8 -8,9 -7,7 -1,1 4 9,6 10,9 13

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.814351	7.0053	0
2	0.561333	4.8288	4e-06
3	0.259687	2.2339	0.014255
4	0.122503	1.0538	0.147699
5	0.06302	0.5421	0.294683
6	0.066204	0.5695	0.285367
7	0.061807	0.5317	0.29827
8	0.001983	0.0171	0.493218
9	-0.129708	-1.1158	0.134061
10	-0.349727	-3.0085	0.001794
11	-0.53103	-4.5681	1e-05
12	-0.611281	-5.2584	1e-06
13	-0.507901	-4.3691	2e-05
14	-0.343366	-2.9537	0.002103
15	-0.165301	-1.422	0.079618
16	-0.092956	-0.7996	0.213241
17	-0.067377	-0.5796	0.281973
18	-0.091515	-0.7872	0.216828
19	-0.115808	-0.9962	0.161196
20	-0.095521	-0.8217	0.206943
21	-0.010107	-0.0869	0.465474
22	0.145421	1.251	0.107445
23	0.313785	2.6993	0.004303
24	0.394577	3.3943	0.000554
25	0.370327	3.1857	0.001057
26	0.262689	2.2597	0.013391
27	0.135745	1.1677	0.123333
28	0.048514	0.4173	0.338822
29	0.029587	0.2545	0.399901
30	0.040072	0.3447	0.365645
31	0.068393	0.5883	0.279049
32	0.03268	0.2811	0.3897
33	-0.02744	-0.2361	0.407023
34	-0.153459	-1.3201	0.095434
35	-0.243152	-2.0917	0.01995
36	-0.297456	-2.5588	0.006273
37	-0.262322	-2.2566	0.013494
38	-0.156973	-1.3503	0.090513
39	-0.057184	-0.4919	0.312117
40	0.026174	0.2252	0.41124
41	0.020166	0.1735	0.431376
42	-0.005637	-0.0485	0.480727
43	-0.046556	-0.4005	0.344974
44	-0.025501	-0.2194	0.413484
45	0.020129	0.1732	0.431499
46	0.091505	0.7872	0.216852
47	0.13131	1.1296	0.131153
48	0.149337	1.2846	0.101461

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.814351	7.0053	0
2	-0.302332	-2.6008	0.005613
3	-0.292223	-2.5138	0.007059
4	0.370644	3.1884	0.001049
5	-0.025325	-0.2179	0.414072
6	-0.142569	-1.2264	0.111964
7	0.078453	0.6749	0.250928
8	-0.186469	-1.6041	0.056479
9	-0.277587	-2.3879	0.009749
10	-0.327214	-2.8148	0.003125
11	-0.042595	-0.3664	0.357551
12	0.045634	0.3926	0.347888
13	0.128792	1.1079	0.135745
14	-0.049167	-0.423	0.336779
15	0.045044	0.3875	0.349757
16	-0.049266	-0.4238	0.336469
17	0.030424	0.2617	0.397134
18	0.002206	0.019	0.492455
19	-0.167744	-1.443	0.076622
20	0.009539	0.0821	0.46741
21	0.022659	0.1949	0.422994
22	-0.014627	-0.1258	0.450105
23	0.208854	1.7966	0.038237
24	-0.073408	-0.6315	0.264836
25	0.021578	0.1856	0.426626
26	0.041683	0.3586	0.36047
27	-0.16717	-1.4381	0.077318
28	-0.016672	-0.1434	0.443177
29	0.110112	0.9472	0.173306
30	-0.225628	-1.9409	0.028038
31	0.040914	0.352	0.362935
32	-0.112738	-0.9698	0.16765
33	0.088647	0.7626	0.224071
34	0.040977	0.3525	0.362734
35	-0.007491	-0.0644	0.474396
36	0.048494	0.4172	0.338885
37	0.015348	0.132	0.447659
38	0.045632	0.3925	0.347894
39	-0.027635	-0.2377	0.406377
40	-0.002907	-0.025	0.490057
41	-0.083886	-0.7216	0.236404
42	-0.017692	-0.1522	0.439724
43	0.01429	0.1229	0.451251
44	0.014106	0.1213	0.451873
45	0.051521	0.4432	0.329458
46	-0.164374	-1.414	0.080777
47	0.031112	0.2676	0.394861
48	0.041282	0.3551	0.361753

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230048093xcrkxvjcj78l6zc/1h5hy1230048063.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230048093xcrkxvjcj78l6zc/1h5hy1230048063.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230048093xcrkxvjcj78l6zc/2jvgb1230048063.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230048093xcrkxvjcj78l6zc/2jvgb1230048063.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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