Home » date » 2009 » Dec » 27 »

Toon Nauwelaerts

*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: Sun, 27 Dec 2009 05:19:39 -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/27/t126191641965cost4iuf4xk6z.htm/, Retrieved Sun, 27 Dec 2009 13:20:21 +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/27/t126191641965cost4iuf4xk6z.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 «

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

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.006018	-0.0548	0.478203
2	-0.092802	-0.8455	0.200141
3	-0.386396	-3.5202	0.000352
4	-0.318172	-2.8987	0.002396
5	0.079724	0.7263	0.234843
6	0.159613	1.4541	0.074839
7	0.151164	1.3772	0.086082
8	0.064065	0.5837	0.280515
9	0.040523	0.3692	0.356466
10	-0.138079	-1.258	0.105967
11	0.062293	0.5675	0.285947
12	-0.214808	-1.957	0.026855
13	0.055504	0.5057	0.307217
14	0.036054	0.3285	0.371694
15	0.073951	0.6737	0.251179
16	0.05228	0.4763	0.317558
17	-0.15831	-1.4423	0.076494
18	0.129211	1.1772	0.121246
19	-0.11627	-1.0593	0.146276
20	0.136413	1.2428	0.108724
21	-0.065362	-0.5955	0.276572
22	-0.040582	-0.3697	0.356267
23	0.036194	0.3297	0.371212
24	-0.052356	-0.477	0.317313
25	0.063666	0.58	0.281735
26	0.068176	0.6211	0.268113
27	-0.000156	-0.0014	0.499434
28	-0.06242	-0.5687	0.285557
29	-0.026236	-0.239	0.405838
30	-0.21479	-1.9568	0.026865
31	0.056921	0.5186	0.302718
32	0.116068	1.0574	0.146692
33	0.182892	1.6662	0.049719
34	0.124564	1.1348	0.129856
35	-0.133772	-1.2187	0.113202
36	-0.149741	-1.3642	0.088095
37	-0.220767	-2.0113	0.02377
38	0.111754	1.0181	0.155788
39	0.063954	0.5827	0.280854
40	0.101799	0.9274	0.178195
41	0.116208	1.0587	0.146402
42	-0.072817	-0.6634	0.254457
43	-0.00615	-0.056	0.477725
44	-0.164272	-1.4966	0.069146
45	0.00712	0.0649	0.474217
46	0.026094	0.2377	0.406339
47	0.103132	0.9396	0.17508
48	-0.053643	-0.4887	0.313167
49	0.04802	0.4375	0.331449
50	-0.090147	-0.8213	0.20692
51	0.042	0.3826	0.351483
52	0.031469	0.2867	0.387528
53	-0.016173	-0.1473	0.441609
54	0.030434	0.2773	0.391133
55	-0.071286	-0.6494	0.258923
56	0.069676	0.6348	0.26366
57	-0.027689	-0.2523	0.400734
58	4.7e-05	4e-04	0.499828
59	-0.013124	-0.1196	0.452559
60	-0.011674	-0.1064	0.457778

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.006018	-0.0548	0.478203
2	-0.092841	-0.8458	0.200041
3	-0.390948	-3.5617	0.000307
4	-0.411924	-3.7528	0.000162
5	-0.111294	-1.0139	0.15678
6	-0.119776	-1.0912	0.139169
7	-0.190554	-1.736	0.043135
8	-0.105617	-0.9622	0.169369
9	0.10464	0.9533	0.171598
10	-0.065729	-0.5988	0.275463
11	0.162047	1.4763	0.071821
12	-0.112306	-1.0232	0.154604
13	0.0678	0.6177	0.269236
14	0.047392	0.4318	0.333516
15	0.040249	0.3667	0.357392
16	-0.042098	-0.3835	0.351155
17	-0.179255	-1.6331	0.053119
18	0.18965	1.7278	0.043872
19	-0.125131	-1.14	0.128783
20	0.051956	0.4733	0.318607
21	-0.014919	-0.1359	0.446106
22	-0.030485	-0.2777	0.390955
23	0.129848	1.183	0.120099
24	-0.111774	-1.0183	0.155746
25	0.069346	0.6318	0.264635
26	0.120028	1.0935	0.138668
27	0.042102	0.3836	0.351141
28	0.048917	0.4457	0.328503
29	-0.101272	-0.9226	0.179438
30	-0.11426	-1.041	0.15046
31	-0.204592	-1.8639	0.032934
32	0.013299	0.1212	0.451928
33	0.010406	0.0948	0.46235
34	-0.028868	-0.263	0.3966
35	0.161709	1.4732	0.072235
36	-0.01434	-0.1306	0.448186
37	-0.012759	-0.1162	0.453872
38	0.142588	1.299	0.098763
39	-0.019155	-0.1745	0.430945
40	-0.095768	-0.8725	0.19273
41	0.053072	0.4835	0.315004
42	-0.012668	-0.1154	0.454198
43	-0.054023	-0.4922	0.311948
44	-0.171717	-1.5644	0.060762
45	0.142467	1.2979	0.098952
46	-0.022476	-0.2048	0.419127
47	0.032734	0.2982	0.383141
48	-0.049911	-0.4547	0.325252
49	0.005765	0.0525	0.479118
50	0.079089	0.7205	0.236609
51	0.022685	0.2067	0.418388
52	-0.061148	-0.5571	0.289484
53	0.056934	0.5187	0.302677
54	-0.035498	-0.3234	0.373601
55	0.082468	0.7513	0.227294
56	-0.037066	-0.3377	0.368227
57	0.040564	0.3696	0.356327
58	-0.026539	-0.2418	0.404774
59	0.025699	0.2341	0.407732
60	0.010907	0.0994	0.460542

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t126191641965cost4iuf4xk6z/1dypw1261916375.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t126191641965cost4iuf4xk6z/1dypw1261916375.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t126191641965cost4iuf4xk6z/2xzuu1261916375.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t126191641965cost4iuf4xk6z/2xzuu1261916375.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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