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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: Sun, 15 Aug 2010 20:24:45 +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/15/t1281903858u1re30sf3ads7u8.htm/, Retrieved Sun, 15 Aug 2010 22:24:20 +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/15/t1281903858u1re30sf3ads7u8.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 «

244 243 242 240 260 259 244 234 235 235 236 238 240 233 233 233 247 251 233 226 233 233 227 225 223 212 206 202 223 221 212 205 204 200 195 193 196 180 174 164 192 189 181 167 166 164 167 164 161 141 134 111 147 144 142 140 143 137 140 130 129 112 101 74 104 103 100 98 99 91 92 94 93 76 64 32 62 69 69 68 68 59 66 73 70 57 48 22 64 74 67 61 61 52 54 69 69 53 50 22 69 78 74 63 67 59 60 80 77 58 54 32 78 86 84 78 72 64 62 72

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.969917	10.6249	0
2	0.943061	10.3307	0
3	0.920493	10.0835	0
4	0.908809	9.9555	0
5	0.894321	9.7968	0
6	0.880515	9.6456	0
7	0.860233	9.4234	0
8	0.839289	9.194	0
9	0.813213	8.9083	0
10	0.798138	8.7432	0
11	0.786855	8.6196	0
12	0.781427	8.5601	0
13	0.746759	8.1803	0
14	0.714667	7.8288	0
15	0.68579	7.5125	0
16	0.665851	7.294	0
17	0.641637	7.0288	0
18	0.618844	6.7791	0
19	0.592069	6.4858	0
20	0.563131	6.1688	0
21	0.528157	5.7857	0
22	0.503324	5.5136	0
23	0.483371	5.2951	0
24	0.470077	5.1494	1e-06
25	0.43326	4.7461	3e-06
26	0.398745	4.368	1.3e-05
27	0.367192	4.0224	5.1e-05
28	0.344336	3.772	0.000126
29	0.316734	3.4696	0.000362
30	0.292179	3.2007	0.000877
31	0.263925	2.8912	0.002279
32	0.233066	2.5531	0.005965
33	0.197122	2.1594	0.016406
34	0.170372	1.8663	0.032218
35	0.148892	1.631	0.052753
36	0.133793	1.4656	0.072682
37	0.099482	1.0898	0.138998
38	0.068888	0.7546	0.225975
39	0.039917	0.4373	0.331352
40	0.020466	0.2242	0.411494
41	-0.004961	-0.0543	0.478376
42	-0.027959	-0.3063	0.379963
43	-0.054045	-0.592	0.277471
44	-0.081771	-0.8958	0.186089
45	-0.11423	-1.2513	0.106624
46	-0.137975	-1.5114	0.066652
47	-0.157093	-1.7209	0.043926
48	-0.168596	-1.8469	0.033615

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.969917	10.6249	0
2	0.039162	0.429	0.334346
3	0.061509	0.6738	0.250868
4	0.180775	1.9803	0.024979
5	-0.026591	-0.2913	0.385665
6	0.02914	0.3192	0.37506
7	-0.087795	-0.9617	0.169055
8	-0.042907	-0.47	0.319595
9	-0.111505	-1.2215	0.112149
10	0.12928	1.4162	0.079655
11	0.062476	0.6844	0.247523
12	0.104099	1.1403	0.128206
13	-0.444567	-4.87	2e-06
14	0.02009	0.2201	0.413093
15	0.0148	0.1621	0.435738
16	0.008855	0.097	0.461444
17	-0.069942	-0.7662	0.222539
18	-0.018053	-0.1978	0.421782
19	0.001952	0.0214	0.491489
20	-0.065207	-0.7143	0.238212
21	-0.046972	-0.5146	0.303905
22	0.022901	0.2509	0.401174
23	0.038077	0.4171	0.338672
24	0.031532	0.3454	0.365195
25	-0.191613	-2.099	0.018956
26	0.008761	0.096	0.461851
27	0.008434	0.0924	0.463272
28	0.012861	0.1409	0.444097
29	-0.065391	-0.7163	0.237592
30	0.00389	0.0426	0.48304
31	-0.030722	-0.3365	0.368524
32	-0.048438	-0.5306	0.298335
33	-0.00213	-0.0233	0.490711
34	-0.006452	-0.0707	0.471887
35	0.019893	0.2179	0.413933
36	-0.001938	-0.0212	0.491548
37	-0.086259	-0.9449	0.1733
38	0.035919	0.3935	0.347334
39	-0.022529	-0.2468	0.402745
40	0.03657	0.4006	0.344714
41	-0.074612	-0.8173	0.20768
42	-0.033897	-0.3713	0.355526
43	-0.035479	-0.3887	0.349111
44	-0.017321	-0.1897	0.424917
45	-0.010731	-0.1176	0.453308
46	-0.01133	-0.1241	0.450716
47	-0.001029	-0.0113	0.495513
48	0.032803	0.3593	0.359987

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281903858u1re30sf3ads7u8/1b0ng1281903883.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281903858u1re30sf3ads7u8/1b0ng1281903883.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281903858u1re30sf3ads7u8/2g6xv1281903883.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281903858u1re30sf3ads7u8/2g6xv1281903883.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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