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Autocorrelation

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 16 Aug 2010 15:21:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/16/t12819720722i4bqj0ckd88u0v.htm/, Retrieved Mon, 16 Aug 2010 17:21:12 +0200

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/2010/Aug/16/t12819720722i4bqj0ckd88u0v.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

257 256 255 253 251 250 251 253 254 254 255 257 260 251 255 252 245 239 240 247 251 255 259 260 259 266 261 243 232 225 229 238 240 241 239 246 242 251 246 219 203 192 197 203 208 207 208 212 208 215 200 170 162 150 148 152 155 150 146 147 142 146 130 102 98 90 86 104 108 94 88 92 93 95 81 50 49 34 27 45 47 42 32

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.959886	8.745	0
2	0.917228	8.3563	0
3	0.875995	7.9807	0
4	0.834358	7.6014	0
5	0.79044	7.2012	0
6	0.749668	6.8298	0
7	0.711898	6.4857	0
8	0.674021	6.1406	0
9	0.649323	5.9156	0
10	0.629728	5.7371	0
11	0.608457	5.5433	0
12	0.580388	5.2876	0
13	0.538158	4.9028	2e-06
14	0.494553	4.5056	1.1e-05
15	0.454423	4.14	4.1e-05
16	0.413273	3.7651	0.000155
17	0.370343	3.374	0.000564
18	0.330787	3.0136	0.001711
19	0.292425	2.6641	0.004636
20	0.254357	2.3173	0.011475
21	0.227511	2.0727	0.02065
22	0.205867	1.8755	0.032118
23	0.180365	1.6432	0.052062
24	0.150731	1.3732	0.086691
25	0.11235	1.0236	0.154509
26	0.071098	0.6477	0.259471
27	0.032014	0.2917	0.385635
28	-0.004992	-0.0455	0.481917
29	-0.038421	-0.35	0.363602
30	-0.069207	-0.6305	0.265049
31	-0.097942	-0.8923	0.187408
32	-0.124763	-1.1366	0.12948
33	-0.139642	-1.2722	0.103427
34	-0.148788	-1.3555	0.089464
35	-0.16159	-1.4722	0.072381
36	-0.178014	-1.6218	0.054321
37	-0.200233	-1.8242	0.035859
38	-0.226357	-2.0622	0.021158
39	-0.251464	-2.2909	0.012251
40	-0.27292	-2.4864	0.007454
41	-0.291282	-2.6537	0.00477
42	-0.309433	-2.8191	0.00301
43	-0.325753	-2.9678	0.001959
44	-0.337179	-3.0718	0.001438
45	-0.338683	-3.0856	0.00138
46	-0.337849	-3.078	0.001412
47	-0.341256	-3.109	0.001286
48	-0.345786	-3.1503	0.001134
49	-0.35455	-3.2301	0.000887
50	-0.364968	-3.325	0.000659
51	-0.373498	-3.4027	0.000515
52	-0.377154	-3.436	0.000462
53	-0.381514	-3.4758	0.000406
54	-0.385298	-3.5102	0.000363
55	-0.386422	-3.5205	0.000351
56	-0.383976	-3.4982	0.000378
57	-0.375335	-3.4195	0.000488
58	-0.364164	-3.3177	0.000674
59	-0.355164	-3.2357	0.000872
60	-0.346713	-3.1587	0.001105

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959886	8.745	0
2	-0.052828	-0.4813	0.315789
3	-0.003087	-0.0281	0.488816
4	-0.028285	-0.2577	0.398644
5	-0.051138	-0.4659	0.321257
6	0.017313	0.1577	0.437527
7	0.011516	0.1049	0.458349
8	-0.024171	-0.2202	0.413125
9	0.147934	1.3477	0.090704
10	0.036356	0.3312	0.370657
11	-0.034219	-0.3118	0.378005
12	-0.098689	-0.8991	0.185601
13	-0.212935	-1.9399	0.027892
14	-0.035333	-0.3219	0.374169
15	0.032315	0.2944	0.384592
16	-0.029202	-0.266	0.395434
17	-0.010327	-0.0941	0.462636
18	0.019058	0.1736	0.431291
19	-0.034728	-0.3164	0.376252
20	-0.049319	-0.4493	0.327187
21	0.050786	0.4627	0.322401
22	0.012097	0.1102	0.456256
23	-0.040614	-0.37	0.356159
24	-0.044105	-0.4018	0.344425
25	-0.134733	-1.2275	0.111557
26	-0.063404	-0.5776	0.282536
27	-0.002141	-0.0195	0.492244
28	-0.001028	-0.0094	0.496274
29	0.064405	0.5868	0.279479
30	0.01792	0.1633	0.435356
31	-0.029748	-0.271	0.393527
32	-0.041579	-0.3788	0.3529
33	0.038394	0.3498	0.363692
34	0.013373	0.1218	0.451661
35	-0.023965	-0.2183	0.413855
36	-0.028448	-0.2592	0.398072
37	-0.070626	-0.6434	0.260857
38	-0.059249	-0.5398	0.295394
39	-0.019312	-0.1759	0.430384
40	0.002899	0.0264	0.489496
41	0.051522	0.4694	0.320012
42	0.005252	0.0479	0.480975
43	-0.029466	-0.2684	0.394512
44	-0.013604	-0.1239	0.450834
45	0.01079	0.0983	0.460966
46	-0.035139	-0.3201	0.374837
47	-0.039305	-0.3581	0.360594
48	0.006561	0.0598	0.47624
49	-0.032247	-0.2938	0.384829
50	-0.007504	-0.0684	0.472829
51	-0.006163	-0.0561	0.477681
52	0.016118	0.1468	0.441806
53	-0.003189	-0.029	0.488448
54	0.009056	0.0825	0.467222
55	-0.023862	-0.2174	0.414218
56	-0.022185	-0.2021	0.420162
57	-0.003591	-0.0327	0.486991
58	-0.007601	-0.0693	0.472478
59	-0.009158	-0.0834	0.466854
60	0.024838	0.2263	0.41077

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819720722i4bqj0ckd88u0v/1kl0s1281972108.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819720722i4bqj0ckd88u0v/1kl0s1281972108.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819720722i4bqj0ckd88u0v/2cczd1281972108.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819720722i4bqj0ckd88u0v/2cczd1281972108.ps (open in new window)

Parameters (Session):

par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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