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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: Mon, 15 Nov 2010 16:15:07 +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/Nov/15/t1289837634js7ax84m52abr7s.htm/, Retrieved Mon, 15 Nov 2010 17:13:55 +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/Nov/15/t1289837634js7ax84m52abr7s.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

101,02 101,15 101,51 101,75 101,8 101,8 101,8 101,82 101,99 102,25 102,34 102,35 102,35 102,39 102,49 102,67 102,68 102,7 102,71 102,72 102,83 102,92 103,04 103,08 103,09 103,11 103,18 103,18 103,22 103,25 103,25 103,25 103,47 103,57 103,66 103,7 103,7 103,75 103,85 104,02 104,13 104,17 104,18 104,2 104,5 104,78 104,88 104,89 104,9 104,95 105,24 105,35 105,44 105,46 105,47 105,48 105,75 106,1 106,19 106,23 106,24 106,25 106,35 106,48 106,52 106,55 106,55 106,56 106,89 107,09 107,24 107,28 107,3 107,31 107,47 107,35 107,31 107,32 107,32 107,34 107,53 107,72 107,75 107,79 107,81 107,9 107,8 107,86 107,8 107,74 107,75 107,83 107,8 107,81 107,86 107,83

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	0.971423	9.518	0
2	0.941975	9.2294	0
3	0.915213	8.9672	0
4	0.890197	8.7221	0
5	0.86474	8.4727	0
6	0.838584	8.2164	0
7	0.810608	7.9423	0
8	0.781002	7.6522	0
9	0.751856	7.3667	0
10	0.724967	7.1032	0
11	0.697483	6.8339	0
12	0.669089	6.5557	0
13	0.638856	6.2595	0
14	0.607652	5.9537	0
15	0.576829	5.6518	0
16	0.548427	5.3735	0
17	0.520766	5.1024	1e-06
18	0.492234	4.8229	3e-06
19	0.462459	4.5312	8e-06
20	0.431876	4.2315	2.7e-05
21	0.401381	3.9327	7.9e-05
22	0.370509	3.6302	0.000228
23	0.341065	3.3417	0.000594
24	0.310829	3.0455	0.001499
25	0.279214	2.7357	0.003707
26	0.247032	2.4204	0.008692
27	0.215933	2.1157	0.018479
28	0.185784	1.8203	0.035914
29	0.157526	1.5434	0.063008
30	0.128631	1.2603	0.105303
31	0.098497	0.9651	0.168468
32	0.067656	0.6629	0.254494
33	0.038637	0.3786	0.352922
34	0.011027	0.108	0.457095
35	-0.015706	-0.1539	0.43901
36	-0.043118	-0.4225	0.336815
37	-0.071708	-0.7026	0.242005
38	-0.100582	-0.9855	0.163428
39	-0.128398	-1.258	0.105714
40	-0.15268	-1.4959	0.068974
41	-0.174664	-1.7113	0.045123
42	-0.197077	-1.931	0.028219
43	-0.220432	-2.1598	0.01664
44	-0.244228	-2.3929	0.00933
45	-0.265105	-2.5975	0.005434
46	-0.28296	-2.7724	0.003342
47	-0.298439	-2.9241	0.002155
48	-0.314256	-3.0791	0.001354

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971423	9.518	0
2	-0.029951	-0.2935	0.384904
3	0.032787	0.3212	0.37436
4	0.015565	0.1525	0.439555
5	-0.019894	-0.1949	0.422933
6	-0.023114	-0.2265	0.41066
7	-0.046065	-0.4513	0.326378
8	-0.044921	-0.4401	0.330414
9	-0.011073	-0.1085	0.456915
10	0.019086	0.187	0.426027
11	-0.027869	-0.2731	0.392699
12	-0.027263	-0.2671	0.394973
13	-0.046968	-0.4602	0.323208
14	-0.035852	-0.3513	0.363075
15	-0.015925	-0.156	0.438166
16	0.018191	0.1782	0.429457
17	-0.007323	-0.0718	0.471474
18	-0.027616	-0.2706	0.393647
19	-0.033851	-0.3317	0.370429
20	-0.033932	-0.3325	0.37013
21	-0.023188	-0.2272	0.410378
22	-0.035493	-0.3478	0.364393
23	3.3e-05	3e-04	0.499871
24	-0.035421	-0.3471	0.364657
25	-0.04006	-0.3925	0.347777
26	-0.03196	-0.3131	0.377427
27	-0.010473	-0.1026	0.459242
28	-0.014399	-0.1411	0.444052
29	0.007096	0.0695	0.472359
30	-0.033389	-0.3271	0.372137
31	-0.039746	-0.3894	0.348912
32	-0.033961	-0.3328	0.370023
33	-0.000667	-0.0065	0.497398
34	-0.009611	-0.0942	0.462588
35	-0.013628	-0.1335	0.447027
36	-0.03523	-0.3452	0.365355
37	-0.044015	-0.4313	0.333624
38	-0.030595	-0.2998	0.382499
39	-0.01899	-0.1861	0.426392
40	0.023696	0.2322	0.40845
41	0.00843	0.0826	0.467173
42	-0.026362	-0.2583	0.398367
43	-0.0332	-0.3253	0.372832
44	-0.033551	-0.3287	0.371536
45	0.015921	0.156	0.438182
46	0.013608	0.1333	0.447104
47	0.011701	0.1146	0.454481
48	-0.024033	-0.2355	0.407171

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289837634js7ax84m52abr7s/1sx2h1289837703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289837634js7ax84m52abr7s/1sx2h1289837703.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289837634js7ax84m52abr7s/2sx2h1289837703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289837634js7ax84m52abr7s/2sx2h1289837703.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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