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Workshop 8

*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, 24 Nov 2009 04:56:57 -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/24/t1259063890vmdj86yp8d9hzpi.htm/, Retrieved Tue, 24 Nov 2009 12:58:15 +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/24/t1259063890vmdj86yp8d9hzpi.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:

JSSHWWS8P4

Dataseries X:

» Textbox « » Textfile « » CSV «

11.1 10.9 10 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9 9 9 9.8 10 9.8 9.3 9 9 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8 7.9 7.6 7.1 6.8 6.5 6.9 8.2 8.7 8.3 7.9 7.5 7.8 8.3 8.4 8.2 7.7 7.2 7.3 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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.608777	4.1736	6.4e-05
2	-0.003587	-0.0246	0.490244
3	-0.493888	-3.3859	0.000721
4	-0.560965	-3.8458	0.00018
5	-0.255966	-1.7548	0.042904
6	0.168423	1.1547	0.127035
7	0.396675	2.7195	0.004567
8	0.398779	2.7339	0.004398
9	0.171065	1.1728	0.1234
10	-0.144548	-0.991	0.163388
11	-0.377808	-2.5901	0.006368
12	-0.44042	-3.0194	0.002043
13	-0.279159	-1.9138	0.030872
14	0.020948	0.1436	0.44321
15	0.193786	1.3285	0.095209
16	0.211479	1.4498	0.076874
17	0.102158	0.7004	0.243577
18	-0.084308	-0.578	0.283016
19	-0.184611	-1.2656	0.105942
20	-0.157104	-1.0771	0.143477
21	-0.081126	-0.5562	0.290367
22	0.028875	0.198	0.421967
23	0.064488	0.4421	0.330219
24	0.050435	0.3458	0.365532
25	0.052624	0.3608	0.359944
26	0.073047	0.5008	0.30943
27	0.020676	0.1417	0.443942
28	-0.044069	-0.3021	0.381947
29	-0.117632	-0.8064	0.212024
30	-0.110237	-0.7557	0.226786
31	0.018424	0.1263	0.450013
32	0.116335	0.7976	0.214571
33	0.14478	0.9926	0.163003
34	0.073208	0.5019	0.309045
35	-0.028915	-0.1982	0.421859
36	-0.054091	-0.3708	0.356214
37	-0.023968	-0.1643	0.435093
38	0.014718	0.1009	0.46003
39	0.049051	0.3363	0.369079
40	0.052492	0.3599	0.36028
41	0.018696	0.1282	0.449278
42	-0.004801	-0.0329	0.48694
43	-0.032708	-0.2242	0.411772
44	-0.040959	-0.2808	0.390048
45	-0.02321	-0.1591	0.437129
46	-0.005859	-0.0402	0.484066
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
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	0.608777	4.1736	6.4e-05
2	-0.594538	-4.0759	8.8e-05
3	-0.315703	-2.1644	0.017775
4	0.046181	0.3166	0.376473
5	0.07215	0.4946	0.311582
6	0.065653	0.4501	0.327356
7	-0.031486	-0.2159	0.415017
8	0.193524	1.3267	0.095503
9	0.001018	0.007	0.49723
10	-0.129694	-0.8891	0.18923
11	-0.116281	-0.7972	0.214677
12	-0.189568	-1.2996	0.100037
13	-0.064971	-0.4454	0.32903
14	-0.035155	-0.241	0.405297
15	-0.271571	-1.8618	0.034445
16	-0.018487	-0.1267	0.449845
17	0.077902	0.5341	0.297906
18	-0.102103	-0.7	0.243694
19	0.032477	0.2227	0.412386
20	0.067631	0.4637	0.322519
21	-0.059969	-0.4111	0.341425
22	-0.038034	-0.2607	0.397714
23	-0.184214	-1.2629	0.106426
24	-0.077055	-0.5283	0.299901
25	0.016588	0.1137	0.454971
26	0.014257	0.0977	0.461277
27	-0.234134	-1.6051	0.057581
28	-0.090359	-0.6195	0.2693
29	0.027597	0.1892	0.425376
30	-0.050653	-0.3473	0.364974
31	0.034723	0.2381	0.406438
32	-0.090346	-0.6194	0.269328
33	0.003475	0.0238	0.490548
34	-0.073448	-0.5035	0.30847
35	-0.038722	-0.2655	0.395907
36	0.021224	0.1455	0.442467
37	-0.041397	-0.2838	0.388903
38	0.037592	0.2577	0.398874
39	-0.067314	-0.4615	0.323292
40	-0.085165	-0.5839	0.281053
41	-0.022311	-0.153	0.439543
42	-0.052657	-0.361	0.359858
43	-0.068989	-0.473	0.319214
44	-0.02256	-0.1547	0.438875
45	-0.084182	-0.5771	0.283307
46	-0.050657	-0.3473	0.364962
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
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/Nov/24/t1259063890vmdj86yp8d9hzpi/11o1k1259063815.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063890vmdj86yp8d9hzpi/11o1k1259063815.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063890vmdj86yp8d9hzpi/2ff341259063815.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063890vmdj86yp8d9hzpi/2ff341259063815.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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