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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: Thu, 18 Nov 2010 20:18:02 +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/18/t1290111463fahqosewj60kh6h.htm/, Retrieved Thu, 18 Nov 2010 21:17:45 +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/18/t1290111463fahqosewj60kh6h.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 - Sofie Baert

Dataseries X:

» Textbox « » Textfile « » CSV «

6,59 6,59 6,59 6,59 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,79 6,79 6,79 6,81 6,80 6,80 6,85 6,85 6,85 6,85 6,85 6,85 6,86 6,86 6,88 6,88 6,88 6,91 6,91 6,91 6,91 6,99 6,99 6,99 7,02 7,02 7,05 7,05 7,05 7,05 7,10 7,10 7,10 7,10 7,12 7,13 7,18 7,24 7,24 7,24 7,27 7,27 7,27 7,27 7,30 7,30 7,57 7,76 7,94 7,94 7,96

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.912851	7.7458	0
2	0.816742	6.9303	0
3	0.712499	6.0458	0
4	0.6293	5.3398	1e-06
5	0.570758	4.843	4e-06
6	0.547172	4.6429	8e-06
7	0.520748	4.4187	1.7e-05
8	0.496568	4.2135	3.6e-05
9	0.471294	3.9991	7.6e-05
10	0.443066	3.7595	0.000172
11	0.410921	3.4868	0.000419
12	0.379197	3.2176	0.000969
13	0.34483	2.926	0.002295
14	0.30898	2.6218	0.005333
15	0.279451	2.3712	0.010204
16	0.255412	2.1672	0.016762
17	0.230004	1.9516	0.027435
18	0.204551	1.7357	0.04345
19	0.177302	1.5045	0.068419
20	0.149545	1.2689	0.104276
21	0.119941	1.0177	0.156107
22	0.101976	0.8653	0.194874
23	0.082138	0.697	0.244034
24	0.060621	0.5144	0.304279
25	0.038251	0.3246	0.373224
26	0.016455	0.1396	0.444674
27	-0.008035	-0.0682	0.472915
28	-0.028355	-0.2406	0.405274
29	-0.048844	-0.4145	0.339886
30	-0.070713	-0.6	0.275189
31	-0.084249	-0.7149	0.238498
32	-0.099022	-0.8402	0.20178
33	-0.114498	-0.9715	0.167264
34	-0.130127	-1.1042	0.136599
35	-0.143565	-1.2182	0.113564
36	-0.156516	-1.3281	0.094173
37	-0.170756	-1.4489	0.075852
38	-0.183699	-1.5587	0.061721
39	-0.195867	-1.662	0.050432
40	-0.206722	-1.7541	0.041834
41	-0.219921	-1.8661	0.033051
42	-0.23459	-1.9906	0.025163
43	-0.246307	-2.09	0.020076
44	-0.258636	-2.1946	0.015709
45	-0.271981	-2.3078	0.011943
46	-0.277822	-2.3574	0.010562
47	-0.289259	-2.4544	0.008264
48	-0.304862	-2.5868	0.005853

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.912851	7.7458	0
2	-0.099304	-0.8426	0.201114
3	-0.099671	-0.8457	0.200252
4	0.071957	0.6106	0.271702
5	0.089874	0.7626	0.224096
6	0.150142	1.274	0.10338
7	-0.057418	-0.4872	0.313796
8	0.000656	0.0056	0.497787
9	0.032236	0.2735	0.392614
10	0.002707	0.023	0.49087
11	-0.014114	-0.1198	0.452501
12	-0.020313	-0.1724	0.431818
13	-0.023748	-0.2015	0.420436
14	-0.025526	-0.2166	0.41457
15	0.014475	0.1228	0.451293
16	0.005511	0.0468	0.481417
17	-0.039301	-0.3335	0.369869
18	-0.025117	-0.2131	0.415916
19	-0.021308	-0.1808	0.428514
20	-0.00849	-0.072	0.471385
21	-0.032665	-0.2772	0.391221
22	0.03949	0.3351	0.369269
23	-0.034468	-0.2925	0.385385
24	-0.041133	-0.349	0.364045
25	-0.014646	-0.1243	0.450723
26	-0.009044	-0.0767	0.469521
27	-0.023486	-0.1993	0.421301
28	-0.014689	-0.1246	0.450579
29	-0.027131	-0.2302	0.409291
30	-0.030352	-0.2575	0.398747
31	0.031609	0.2682	0.39465
32	-0.035006	-0.297	0.383646
33	-0.028722	-0.2437	0.404073
34	-0.019708	-0.1672	0.43383
35	-0.004091	-0.0347	0.486204
36	0.000116	0.001	0.499608
37	-0.039668	-0.3366	0.368701
38	-0.017253	-0.1464	0.442009
39	-0.010841	-0.092	0.46348
40	-0.010514	-0.0892	0.464579
41	-0.039385	-0.3342	0.369602
42	-0.037677	-0.3197	0.37506
43	0.006	0.0509	0.479769
44	-0.032494	-0.2757	0.391777
45	-0.038143	-0.3237	0.37357
46	0.018713	0.1588	0.437141
47	-0.061241	-0.5196	0.302452
48	-0.055747	-0.473	0.318811

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/18/t1290111463fahqosewj60kh6h/1v4eb1290111479.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/18/t1290111463fahqosewj60kh6h/1v4eb1290111479.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/18/t1290111463fahqosewj60kh6h/2v4eb1290111479.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/18/t1290111463fahqosewj60kh6h/2v4eb1290111479.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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