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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 18 Dec 2009 04:41:43 -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/18/t1261136525twqjhdrkjo53lc2.htm/, Retrieved Fri, 18 Dec 2009 12:42:08 +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/18/t1261136525twqjhdrkjo53lc2.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 «

100.00 100.00 93.55 88.17 89.25 91.40 92.47 91.40 88.17 87.10 84.95 92.47 93.55 93.55 91.40 90.32 91.40 93.55 93.55 92.47 91.40 89.25 86.02 88.17 87.10 87.10 86.02 84.95 84.95 86.02 86.02 84.95 86.02 82.80 77.42 80.65 78.49 75.27 75.27 75.27 77.42 78.49 76.34 73.12 68.82 65.59 69.89 82.80 84.95 80.65 74.19 70.97 74.19 82.80 86.02 86.02 82.80 78.49 79.57 87.10 89.25

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	0.537847	3.7263	0.000256
2	-0.08553	-0.5926	0.278126
3	-0.485876	-3.3662	0.000754
4	-0.50964	-3.5309	0.000463
5	-0.152639	-1.0575	0.147785
6	0.222556	1.5419	0.064831
7	0.406781	2.8183	0.003496
8	0.281539	1.9506	0.028481
9	-0.031898	-0.221	0.413017
10	-0.186682	-1.2934	0.101036
11	-0.244558	-1.6943	0.04834
12	-0.245622	-1.7017	0.047639
13	-0.070217	-0.4865	0.314421
14	0.111648	0.7735	0.221503
15	0.139176	0.9642	0.169879
16	0.041246	0.2858	0.388145
17	-0.044554	-0.3087	0.379451
18	-0.083322	-0.5773	0.283227
19	-0.095095	-0.6588	0.256575
20	0.018178	0.1259	0.450152
21	0.111547	0.7728	0.221709
22	0.003272	0.0227	0.491004
23	-0.127139	-0.8808	0.191395
24	-0.154918	-1.0733	0.144251
25	-0.059428	-0.4117	0.341186
26	0.054031	0.3743	0.354902
27	0.072471	0.5021	0.308949
28	0.013443	0.0931	0.463091
29	-0.091472	-0.6337	0.26463
30	-0.151979	-1.0529	0.14882
31	-0.013022	-0.0902	0.464244
32	0.094233	0.6529	0.258479
33	0.104537	0.7243	0.236213
34	0.055254	0.3828	0.351774
35	-0.008353	-0.0579	0.477046
36	-0.019143	-0.1326	0.447521
37	-0.009955	-0.069	0.472649
38	0.05926	0.4106	0.34161
39	0.076359	0.529	0.299611
40	0.067755	0.4694	0.320446
41	0.041983	0.2909	0.386203
42	-0.000331	-0.0023	0.49909
43	-0.033415	-0.2315	0.408952
44	-0.066939	-0.4638	0.322456
45	-0.042107	-0.2917	0.385876
46	0.000627	0.0043	0.498276
47	9.2e-05	6e-04	0.499747
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	0.537847	3.7263	0.000256
2	-0.527365	-3.6537	0.000319
3	-0.257227	-1.7821	0.040528
4	-0.13586	-0.9413	0.17564
5	0.135442	0.9384	0.176377
6	0.010811	0.0749	0.470302
7	0.101826	0.7055	0.241964
8	-0.029703	-0.2058	0.418914
9	-0.037326	-0.2586	0.398524
10	0.162487	1.1257	0.132936
11	-0.14681	-1.0171	0.157095
12	-0.236373	-1.6376	0.054019
13	0.068142	0.4721	0.319497
14	0.009733	0.0674	0.473258
15	-0.187752	-1.3008	0.099772
16	-0.101787	-0.7052	0.242046
17	0.088478	0.613	0.271386
18	-0.021266	-0.1473	0.441742
19	-0.037494	-0.2598	0.398078
20	0.155097	1.0745	0.143976
21	-0.045456	-0.3149	0.37709
22	-0.220166	-1.5254	0.066866
23	0.003817	0.0264	0.489506
24	-0.063885	-0.4426	0.330017
25	-0.09467	-0.6559	0.257513
26	-0.03029	-0.2099	0.417336
27	-0.148847	-1.0312	0.153798
28	-0.204894	-1.4195	0.081101
29	0.045975	0.3185	0.375734
30	-0.019704	-0.1365	0.445994
31	-0.014861	-0.103	0.459212
32	-0.053143	-0.3682	0.357177
33	0.070737	0.4901	0.313155
34	-0.094963	-0.6579	0.256864
35	-0.011475	-0.0795	0.468483
36	0.075364	0.5221	0.301987
37	-0.081451	-0.5643	0.287587
38	0.016156	0.1119	0.455671
39	-0.051599	-0.3575	0.361146
40	0.079791	0.5528	0.291479
41	-0.089416	-0.6195	0.26926
42	-0.009319	-0.0646	0.474396
43	0.049164	0.3406	0.367438
44	-0.077362	-0.536	0.297223
45	-0.015592	-0.108	0.457212
46	-0.086949	-0.6024	0.274871
47	-0.113315	-0.7851	0.218136
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/Dec/18/t1261136525twqjhdrkjo53lc2/1ayjk1261136501.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136525twqjhdrkjo53lc2/1ayjk1261136501.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136525twqjhdrkjo53lc2/2544m1261136501.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136525twqjhdrkjo53lc2/2544m1261136501.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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