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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: Sat, 20 Nov 2010 14:49:27 +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/20/t1290264470309x54f5zr41ib3.htm/, Retrieved Sat, 20 Nov 2010 15:47:50 +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/20/t1290264470309x54f5zr41ib3.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 «

96,1 96,5 96,9 97,8 98,9 100,2 101,2 101 101,6 102,4 103,7 103,7 104,6 104,5 104,5 105,6 106,1 107,6 107,7 108,3 108,1 108,1 108 108,2 108,9 109,8 109,9 109,8 110,9 111,1 112,2 112,7 114,6 114,2 114,7 114,7 116 116,3 116,4 116,6 118,1 117,2 108,3 109,5 110,5 110,6 111,2 111,1 111 112,4 112,5 112,4 111,8 111,6 112,9 112,8 113,7 113,8 114 113,8 113,9 114,4 114,4 114,5 113,8 114,3 115 115,4 115,3 114,9 114,3 114,5 115,5 115,8 115,8 116 114,9 114,1 114,1 113,5 115 114,7 115,4 116,1 116,6 117,2 118,2 118 117,7 118,5 117,5 118 117,7 116,3 115 115,7 113,6 114,8 114,9 117,3 117,3 117,7 120 119,6 119,2 117,3 117,5 119 112,5 118,9 118,4 119,4 120,6 118,6 122 122,6 120,6 117,4 116,4 122,2 121 122,4 124,9 126,1 124,5 123,2 126,4 123,9 116 126,6 125,9 126,6 116,7 126,4 129 128,7 128,4 129,2 133,3 128,9 132,7 127,7 131,8 133,9

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.906265	10.8752	0
2	0.852924	10.2351	0
3	0.813501	9.762	0
4	0.773856	9.2863	0
5	0.722782	8.6734	0
6	0.661722	7.9407	0
7	0.642425	7.7091	0
8	0.605488	7.2659	0
9	0.573408	6.8809	0
10	0.537208	6.4465	0
11	0.511451	6.1374	0
12	0.503435	6.0412	0
13	0.472017	5.6642	0
14	0.448098	5.3772	0
15	0.417264	5.0072	1e-06
16	0.406824	4.8819	1e-06
17	0.385068	4.6208	4e-06
18	0.357556	4.2907	1.6e-05
19	0.347551	4.1706	2.6e-05
20	0.331047	3.9726	5.6e-05
21	0.297887	3.5746	0.000239
22	0.275703	3.3084	0.000593
23	0.255134	3.0616	0.001314
24	0.242081	2.905	0.002126
25	0.208172	2.4981	0.006806
26	0.203772	2.4453	0.007841
27	0.199769	2.3972	0.008901
28	0.184405	2.2129	0.014241
29	0.164699	1.9764	0.025011
30	0.144737	1.7368	0.042277
31	0.145301	1.7436	0.041681
32	0.131181	1.5742	0.058822
33	0.128254	1.539	0.062994
34	0.128807	1.5457	0.062188
35	0.123374	1.4805	0.070463
36	0.133618	1.6034	0.055517
37	0.127552	1.5306	0.064028
38	0.129629	1.5555	0.061005
39	0.131799	1.5816	0.057969
40	0.130759	1.5691	0.059409
41	0.133025	1.5963	0.056306
42	0.131579	1.5789	0.058271
43	0.117415	1.409	0.080498
44	0.10531	1.2637	0.104186
45	0.096918	1.163	0.123373
46	0.093589	1.1231	0.131638
47	0.092278	1.1073	0.134998
48	0.093552	1.1226	0.131733

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.906265	10.8752	0
2	0.176895	2.1227	0.017743
3	0.09791	1.1749	0.120982
4	0.022148	0.2658	0.395395
5	-0.069047	-0.8286	0.204363
6	-0.109912	-1.3189	0.094641
7	0.166654	1.9998	0.023699
8	-0.034996	-0.42	0.337572
9	0.024717	0.2966	0.383598
10	-0.030589	-0.3671	0.357052
11	0.015427	0.1851	0.426695
12	0.0917	1.1004	0.136496
13	-0.050138	-0.6017	0.274176
14	-0.014707	-0.1765	0.430082
15	-0.055029	-0.6604	0.255042
16	0.065639	0.7877	0.216094
17	-0.018814	-0.2258	0.410849
18	-0.00779	-0.0935	0.462824
19	0.038507	0.4621	0.322359
20	-0.010867	-0.1304	0.448216
21	-0.132073	-1.5849	0.057594
22	0.055579	0.6669	0.252938
23	-0.027957	-0.3355	0.368874
24	0.029967	0.3596	0.359837
25	-0.083951	-1.0074	0.157714
26	0.119961	1.4395	0.076084
27	0.020124	0.2415	0.404759
28	-0.037042	-0.4445	0.328673
29	-0.056166	-0.674	0.250697
30	-0.022327	-0.2679	0.39457
31	0.044168	0.53	0.29846
32	-0.006287	-0.0754	0.469985
33	0.07559	0.9071	0.182939
34	0.035638	0.4277	0.334769
35	-0.034364	-0.4124	0.34034
36	0.045473	0.5457	0.293066
37	0.014742	0.1769	0.429918
38	-0.020446	-0.2453	0.403269
39	0.021304	0.2557	0.399292
40	-0.041155	-0.4939	0.311077
41	0.062725	0.7527	0.226428
42	0.016967	0.2036	0.419477
43	-0.130186	-1.5622	0.060214
44	-0.001829	-0.022	0.491259
45	0.003826	0.0459	0.481723
46	0.000934	0.0112	0.495539
47	0.059036	0.7084	0.239913
48	0.03677	0.4412	0.329851

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290264470309x54f5zr41ib3/1tbxs1290264563.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290264470309x54f5zr41ib3/1tbxs1290264563.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290264470309x54f5zr41ib3/2m3eu1290264563.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290264470309x54f5zr41ib3/2m3eu1290264563.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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