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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 04:43:54 -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/t1261136658di9p2u4ejrrwjcc.htm/, Retrieved Fri, 18 Dec 2009 12:44:20 +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/t1261136658di9p2u4ejrrwjcc.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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.173982	1.1928	0.119475
2	-0.240384	-1.648	0.053013
3	-0.408461	-2.8003	0.003694
4	-0.41107	-2.8182	0.003522
5	-0.019212	-0.1317	0.447887
6	0.208075	1.4265	0.080168
7	0.336803	2.309	0.012694
8	0.199337	1.3666	0.089129
9	-0.173584	-1.19	0.120006
10	-0.108209	-0.7418	0.230936
11	-0.057658	-0.3953	0.347211
12	-0.18761	-1.2862	0.102339
13	-0.004132	-0.0283	0.48876
14	0.16654	1.1417	0.129673
15	0.130972	0.8979	0.186908
16	-0.015505	-0.1063	0.457899
17	-0.048984	-0.3358	0.36925
18	-0.029207	-0.2002	0.42108
19	-0.133413	-0.9146	0.182527
20	0.021068	0.1444	0.442888
21	0.217241	1.4893	0.07154
22	0.025392	0.1741	0.431275
23	-0.113932	-0.7811	0.219337
24	-0.13339	-0.9145	0.182567
25	-0.016571	-0.1136	0.455018
26	0.101381	0.695	0.245228
27	0.084788	0.5813	0.281916
28	0.050126	0.3436	0.366322
29	-0.049955	-0.3425	0.36676
30	-0.215845	-1.4798	0.072805
31	0.032395	0.2221	0.412603
32	0.107292	0.7356	0.232828
33	0.069266	0.4749	0.318543
34	0.015971	0.1095	0.456639
35	-0.060013	-0.4114	0.341314
36	-0.024966	-0.1712	0.432416
37	-0.068774	-0.4715	0.319736
38	0.059738	0.4095	0.342001
39	0.029718	0.2037	0.419719
40	0.022889	0.1569	0.437989
41	0.015973	0.1095	0.456634
42	-0.011412	-0.0782	0.468985
43	0	0	0.5
44	-0.064106	-0.4395	0.331162
45	-0.018413	-0.1262	0.450042
46	0.045863	0.3144	0.377297
47	NA	NA	NA
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	0.173982	1.1928	0.119475
2	-0.279102	-1.9134	0.030898
3	-0.342665	-2.3492	0.011534
4	-0.441436	-3.0263	0.002004
5	-0.221526	-1.5187	0.067768
6	-0.253178	-1.7357	0.044585
7	-0.092143	-0.6317	0.265322
8	-0.08329	-0.571	0.285357
9	-0.252071	-1.7281	0.045267
10	0.058603	0.4018	0.34484
11	0.12976	0.8896	0.189109
12	-0.190459	-1.3057	0.099002
13	-0.107629	-0.7379	0.232133
14	0.080947	0.5549	0.290782
15	-0.026605	-0.1824	0.428029
16	-0.200258	-1.3729	0.08815
17	-0.070324	-0.4821	0.31598
18	-0.055213	-0.3785	0.353374
19	-0.225791	-1.5479	0.064172
20	-0.01518	-0.1041	0.458778
21	0.144246	0.9889	0.163887
22	-0.092585	-0.6347	0.264342
23	-0.028393	-0.1947	0.423253
24	-0.002695	-0.0185	0.492669
25	-0.063471	-0.4351	0.332727
26	0.042322	0.2901	0.386491
27	0.068267	0.468	0.32097
28	-0.180583	-1.238	0.11093
29	-0.095477	-0.6546	0.257972
30	-0.091989	-0.6306	0.265663
31	-0.051736	-0.3547	0.362206
32	-0.161467	-1.107	0.136972
33	0.011226	0.077	0.469489
34	-0.07363	-0.5048	0.308036
35	-0.151723	-1.0402	0.151794
36	0.011046	0.0757	0.469979
37	-0.085466	-0.5859	0.280364
38	-0.015084	-0.1034	0.459038
39	-0.145321	-0.9963	0.16211
40	0.030928	0.212	0.4165
41	-0.049375	-0.3385	0.368247
42	-0.10213	-0.7002	0.243637
43	0.022937	0.1572	0.437862
44	-0.035114	-0.2407	0.405406
45	0.03292	0.2257	0.41121
46	0.048244	0.3307	0.371155
47	NA	NA	NA
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/t1261136658di9p2u4ejrrwjcc/19yul1261136632.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136658di9p2u4ejrrwjcc/19yul1261136632.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136658di9p2u4ejrrwjcc/2rwz21261136632.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136658di9p2u4ejrrwjcc/2rwz21261136632.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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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