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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, 16 Dec 2009 14:08:59 -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/16/t1260997861vznrzerxb1vtv3u.htm/, Retrieved Wed, 16 Dec 2009 22:11:04 +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/16/t1260997861vznrzerxb1vtv3u.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

0.96 1 1.05 1.03 1.07 1.12 1.1 1.06 1.11 1.08 1.07 1.02 1 1.04 1.02 1.07 1.12 1.08 1.02 1.01 1.04 0.98 0.95 0.94 0.94 0.96 0.97 1.03 1.01 0.99 1 1 1.02 1.01 0.99 0.98 1.01 1.03 1.03 1 0.96 0.97 0.98 1.02 1.04 1.01 1.01 1 1.01 1.02 1.03 1.06 1.12 1.12 1.13 1.13 1.13 1.17 1.14 1.08 1.07 1.12 1.14 1.21 1.2 1.23 1.29 1.31 1.37 1.35 1.26 1.26 1.28 1.28 1.27 1.35 1.37 1.37 1.4 1.4 1.28 1.23 1.23 1.25 1.21 1.22 1.29 1.32 1.36 1.36 1.37 1.32 1.33 1.36 1.42 1.39 1.42 1.4 1.42 1.44 1.49 1.54 1.55 1.47 1.47 1.35 1.2 1.12 1.11 1.15 1.17 1.2 1.24

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	0.95971	10.2019	0
2	0.904146	9.6112	0
3	0.85223	9.0593	0
4	0.799711	8.501	0
5	0.756047	8.0369	0
6	0.730948	7.7701	0
7	0.715869	7.6098	0
8	0.699989	7.441	0
9	0.687594	7.3092	0
10	0.680744	7.2364	0
11	0.662604	7.0436	0
12	0.623324	6.626	0
13	0.580884	6.1749	0
14	0.551207	5.8594	0
15	0.517562	5.5018	0
16	0.484311	5.1483	1e-06
17	0.46002	4.8901	2e-06
18	0.44139	4.692	4e-06
19	0.424701	4.5146	8e-06
20	0.41515	4.4131	1.2e-05
21	0.416651	4.4291	1.1e-05
22	0.411731	4.3768	1.3e-05
23	0.395633	4.2056	2.6e-05
24	0.373552	3.9709	6.3e-05
25	0.346802	3.6866	0.000175
26	0.306966	3.2631	0.000729
27	0.258023	2.7428	0.003543
28	0.214772	2.2831	0.012148
29	0.177582	1.8877	0.030814
30	0.144452	1.5355	0.063723
31	0.119623	1.2716	0.103062
32	0.099393	1.0566	0.146482
33	0.083387	0.8864	0.188637
34	0.05975	0.6351	0.263308
35	0.034214	0.3637	0.358382
36	0.003131	0.0333	0.486752
37	-0.037375	-0.3973	0.345948
38	-0.07843	-0.8337	0.203099
39	-0.114961	-1.2221	0.112115
40	-0.149238	-1.5864	0.057719
41	-0.177906	-1.8912	0.030582
42	-0.205034	-2.1795	0.015683
43	-0.22749	-2.4182	0.008596
44	-0.241984	-2.5723	0.005699
45	-0.25196	-2.6784	0.004251
46	-0.258826	-2.7514	0.003457
47	-0.268001	-2.8489	0.002607
48	-0.283082	-3.0092	0.001615

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95971	10.2019	0
2	-0.214007	-2.2749	0.012398
3	0.055742	0.5925	0.277336
4	-0.062148	-0.6606	0.255093
5	0.101723	1.0813	0.140927
6	0.171554	1.8236	0.035425
7	0.049966	0.5311	0.298181
8	-0.03617	-0.3845	0.350668
9	0.054671	0.5812	0.281146
10	0.080058	0.851	0.198276
11	-0.122882	-1.3063	0.09706
12	-0.217035	-2.3071	0.011435
13	0.010682	0.1135	0.454899
14	0.18272	1.9423	0.027292
15	-0.11331	-1.2045	0.115456
16	-0.069824	-0.7422	0.22974
17	-0.012668	-0.1347	0.44656
18	0.081258	0.8638	0.194769
19	0.056939	0.6053	0.273108
20	0.007363	0.0783	0.468875
21	0.078328	0.8326	0.203402
22	-0.023705	-0.252	0.400756
23	-0.01976	-0.2101	0.417003
24	-0.107463	-1.1423	0.127862
25	-0.079632	-0.8465	0.199532
26	-0.106915	-1.1365	0.129071
27	-0.089814	-0.9547	0.170874
28	-0.028097	-0.2987	0.38287
29	-0.015269	-0.1623	0.435676
30	-0.029581	-0.3145	0.376878
31	-0.042741	-0.4543	0.325226
32	-0.070105	-0.7452	0.228842
33	0.112495	1.1958	0.117132
34	-0.063331	-0.6732	0.251093
35	-0.028455	-0.3025	0.381421
36	-0.085425	-0.9081	0.182885
37	-0.025759	-0.2738	0.39236
38	0.052415	0.5572	0.289254
39	-0.070013	-0.7443	0.229135
40	-0.099194	-1.0544	0.146964
41	0.033088	0.3517	0.362848
42	-0.083342	-0.8859	0.188766
43	-0.015126	-0.1608	0.436273
44	0.019598	0.2083	0.417674
45	0.023086	0.2454	0.403292
46	0.067498	0.7175	0.237268
47	-0.067233	-0.7147	0.238135
48	0.003535	0.0376	0.485045

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997861vznrzerxb1vtv3u/13wg71260997738.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997861vznrzerxb1vtv3u/13wg71260997738.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997861vznrzerxb1vtv3u/2nwof1260997738.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997861vznrzerxb1vtv3u/2nwof1260997738.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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