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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: Wed, 18 Aug 2010 00:15:20 +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/18/t1282090474h6o8fhf70lkgfz7.htm/, Retrieved Wed, 18 Aug 2010 02:14:37 +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/18/t1282090474h6o8fhf70lkgfz7.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 «

158 157 156 154 152 151 152 154 155 155 156 158 155 151 152 156 147 159 152 148 146 148 142 141 139 143 146 150 141 153 142 139 134 152 142 139 137 132 137 134 127 140 127 120 112 128 119 117 115 104 108 104 98 111 104 98 91 94 82 81 70 64 71 73 71 80 72 68 60 71 62 69 55 58 67 69 71 85 76 79 69 95 94 99

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	0.96421	8.8371	0
2	0.947771	8.6865	0
3	0.923373	8.4629	0
4	0.901348	8.261	0
5	0.872824	7.9996	0
6	0.850712	7.7969	0
7	0.820326	7.5184	0
8	0.790397	7.2441	0
9	0.749499	6.8693	0
10	0.712656	6.5316	0
11	0.66968	6.1377	0
12	0.641112	5.8759	0
13	0.583661	5.3493	0
14	0.543982	4.9857	2e-06
15	0.499743	4.5802	8e-06
16	0.4588	4.205	3.2e-05
17	0.415836	3.8112	0.000131
18	0.37492	3.4362	0.00046
19	0.330303	3.0273	0.001638
20	0.28925	2.651	0.004795
21	0.246638	2.2605	0.013189
22	0.202568	1.8566	0.033439
23	0.162147	1.4861	0.070498
24	0.134179	1.2298	0.111108
25	0.08905	0.8162	0.208359
26	0.057113	0.5234	0.301021
27	0.020209	0.1852	0.426752
28	-0.009555	-0.0876	0.465211
29	-0.042174	-0.3865	0.35004
30	-0.07401	-0.6783	0.249718
31	-0.10574	-0.9691	0.167634
32	-0.135106	-1.2383	0.109534
33	-0.160828	-1.474	0.072108
34	-0.192846	-1.7675	0.040391
35	-0.218835	-2.0057	0.024056
36	-0.231637	-2.123	0.018349
37	-0.261357	-2.3954	0.009413
38	-0.278326	-2.5509	0.006279
39	-0.302615	-2.7735	0.003415
40	-0.319375	-2.9271	0.0022
41	-0.338422	-3.1017	0.00131
42	-0.355611	-3.2592	0.000807
43	-0.369492	-3.3865	0.00054
44	-0.37852	-3.4692	0.000413
45	-0.38627	-3.5402	0.000327
46	-0.398583	-3.6531	0.000225
47	-0.408187	-3.7411	0.000167
48	-0.408857	-3.7472	0.000164

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.96421	8.8371	0
2	0.257049	2.3559	0.010404
3	-0.052124	-0.4777	0.317043
4	-0.01905	-0.1746	0.430909
5	-0.098747	-0.905	0.184019
6	0.035056	0.3213	0.374393
7	-0.089169	-0.8173	0.208049
8	-0.070404	-0.6453	0.260258
9	-0.182435	-1.672	0.049119
10	-0.053933	-0.4943	0.311191
11	-0.076046	-0.697	0.243871
12	0.160909	1.4748	0.072009
13	-0.354929	-3.253	0.000823
14	0.037009	0.3392	0.367655
15	0.045218	0.4144	0.339807
16	0.021589	0.1979	0.421815
17	0.03578	0.3279	0.371889
18	-0.088401	-0.8102	0.210055
19	-0.029428	-0.2697	0.394022
20	-0.003376	-0.0309	0.487696
21	0.065577	0.601	0.274721
22	-0.133996	-1.2281	0.111422
23	0.039706	0.3639	0.35842
24	0.080297	0.7359	0.231912
25	-0.069668	-0.6385	0.262437
26	0.006341	0.0581	0.476897
27	-0.074443	-0.6823	0.248469
28	0.068234	0.6254	0.266711
29	-0.03122	-0.2861	0.38774
30	-0.056293	-0.5159	0.303628
31	-0.054378	-0.4984	0.309759
32	-0.046247	-0.4239	0.336376
33	0.07004	0.6419	0.261334
34	-0.106954	-0.9803	0.164888
35	-0.009744	-0.0893	0.464527
36	0.099207	0.9092	0.182911
37	-0.080794	-0.7405	0.230533
38	0.020629	0.1891	0.425249
39	-0.085058	-0.7796	0.218919
40	0.004127	0.0378	0.484959
41	-0.005757	-0.0528	0.479022
42	-0.008591	-0.0787	0.468714
43	0.016475	0.151	0.440169
44	0.029446	0.2699	0.393957
45	0.002667	0.0244	0.490277
46	-0.024337	-0.2231	0.412018
47	-0.028123	-0.2577	0.398616
48	-0.023075	-0.2115	0.416512

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282090474h6o8fhf70lkgfz7/1vhmf1282090518.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282090474h6o8fhf70lkgfz7/1vhmf1282090518.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282090474h6o8fhf70lkgfz7/2vhmf1282090518.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282090474h6o8fhf70lkgfz7/2vhmf1282090518.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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