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*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: Tue, 21 Dec 2010 16:00:40 +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/Dec/21/t12929471101eoug79li916asu.htm/, Retrieved Tue, 21 Dec 2010 16:58:30 +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/2010/Dec/21/t12929471101eoug79li916asu.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 «

77.33 75.28 77.43 73.25 68.41 72.87 65.61 69.04 57.84 51.07 47.48 44.01 45.29 43.8 55.48 75.73 101.42 116.07 135.81 132.69 124.05 109.65 102.79 94.09 92.23 90.6 92.6 81.71 76.36 71.44 75.26 70.3 67.68 67.65 61.92 58.34 55.04 62.5 59.44 60.03 64.24 74.33 74.41 69.75 72.03 68.18 63.01 61.71 63.52

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.559267	3.8747	0.000162
2	0.418993	2.9029	0.002785
3	0.076478	0.5299	0.299328
4	-0.066637	-0.4617	0.323201
5	-0.303871	-2.1053	0.020263
6	-0.335604	-2.3251	0.01217
7	-0.222988	-1.5449	0.064469
8	-0.185052	-1.2821	0.102986
9	-0.196198	-1.3593	0.090202
10	-0.156375	-1.0834	0.142022
11	-0.026396	-0.1829	0.427833
12	-0.092226	-0.639	0.262943
13	-0.070913	-0.4913	0.312728
14	-0.048027	-0.3327	0.370389
15	0.005787	0.0401	0.484092
16	-0.064011	-0.4435	0.329704
17	-0.070198	-0.4863	0.314469
18	-0.061912	-0.4289	0.334943
19	0.008059	0.0558	0.477854
20	-0.078643	-0.5449	0.294189
21	0.028821	0.1997	0.421287
22	0.05543	0.384	0.351325
23	0.174164	1.2066	0.116742
24	0.124288	0.8611	0.196734
25	0.159304	1.1037	0.137615
26	0.121155	0.8394	0.202706
27	-0.005706	-0.0395	0.484315
28	-0.040946	-0.2837	0.388936
29	-0.091689	-0.6352	0.264144
30	-0.032073	-0.2222	0.412548
31	-0.083831	-0.5808	0.282047
32	-0.015458	-0.1071	0.457579
33	-0.033135	-0.2296	0.409702
34	0.01232	0.0854	0.466166
35	0.011496	0.0796	0.468425
36	0.001244	0.0086	0.49658
37	0.016541	0.1146	0.454621
38	-0.010214	-0.0708	0.471939
39	0.01684	0.1167	0.453803
40	-0.006969	-0.0483	0.480846
41	-0.004328	-0.03	0.488102
42	0.009885	0.0685	0.472841
43	0.006573	0.0455	0.481934
44	-0.003626	-0.0251	0.490031
45	-0.000655	-0.0045	0.4982
46	0.002227	0.0154	0.493878
47	-0.001193	-0.0083	0.496719
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.559267	3.8747	0.000162
2	0.154556	1.0708	0.144809
3	-0.310183	-2.149	0.018353
4	-0.097643	-0.6765	0.250988
5	-0.22183	-1.5369	0.065444
6	-0.072396	-0.5016	0.30913
7	0.203807	1.412	0.082197
8	-0.110455	-0.7653	0.223934
9	-0.273277	-1.8933	0.032176
10	-0.05297	-0.367	0.357621
11	0.150259	1.041	0.15154
12	-0.180549	-1.2509	0.108521
13	-0.096078	-0.6656	0.254412
14	-0.009631	-0.0667	0.473538
15	-0.088893	-0.6159	0.270445
16	-0.100123	-0.6937	0.245615
17	-0.051885	-0.3595	0.36041
18	-0.153824	-1.0657	0.14594
19	0.045085	0.3124	0.378061
20	-0.135597	-0.9394	0.176104
21	-0.012811	-0.0888	0.464823
22	-0.044025	-0.305	0.380837
23	0.10965	0.7597	0.225581
24	-0.054841	-0.38	0.352829
25	-0.090701	-0.6284	0.266362
26	-0.052675	-0.3649	0.358378
27	-0.167403	-1.1598	0.125933
28	0.089164	0.6177	0.26983
29	-0.001572	-0.0109	0.495676
30	-0.093547	-0.6481	0.260001
31	-0.048496	-0.336	0.369171
32	-0.01569	-0.1087	0.456945
33	-0.091932	-0.6369	0.263601
34	-0.00705	-0.0488	0.480624
35	0.116714	0.8086	0.211361
36	-0.193704	-1.342	0.092952
37	-0.061277	-0.4245	0.336535
38	0.041398	0.2868	0.387745
39	-0.012406	-0.086	0.46593
40	-0.032203	-0.2231	0.4122
41	-0.015048	-0.1043	0.4587
42	-0.056798	-0.3935	0.347844
43	-0.018516	-0.1283	0.449232
44	0.008845	0.0613	0.475696
45	-0.030471	-0.2111	0.416849
46	-0.06687	-0.4633	0.322627
47	-0.012375	-0.0857	0.466016
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929471101eoug79li916asu/139uh1292947236.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929471101eoug79li916asu/139uh1292947236.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929471101eoug79li916asu/239uh1292947236.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929471101eoug79li916asu/239uh1292947236.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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