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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: Tue, 16 Nov 2010 14:45:03 +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/16/t1289918617sii70mk1m1pn8fl.htm/, Retrieved Tue, 16 Nov 2010 15:43:39 +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/16/t1289918617sii70mk1m1pn8fl.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 «

98,6 100,1 98,8 98,3 102,8 103,6 105,2 100,1 98,2 98,4 97,4 98,4 100,3 101,1 104,1 107,3 110,1 112,6 114,3 115,3 109,9 108,2 103,2 101,8 105,6 108,2 109,8 114,6 117,2 116,5 116,1 112,1 106,8 106,9 104,5 103 105,9 107,7 107,1 112,5 114,5 114,6 113,1 112,8 111,9 112 112,4 110 112,3 109,6 111,9 110,8 110,4 110,8 114 108,4 110,5 105,1 102,3 104,3 103,4 102,4 104,5 107,3 110,1 111,8 111,8 105,7 106 106,4 107,1 111,5 109,6 109,9 109,3 111,4 112,9 115,5 118,4 116,2 113,3 113,8 114,1 117,1 115,5 115,2 114,2 115,3 118,8 118 118,1 111,8 112 114,3 115 118,5 117,6 119,1 120,6 123,6 122,7 123,8 123,1 124,5 120,7 118,7 119 122,3 118,6 118,1 118,2 120,8 119,7 119,7 117,1 114,5 116,5 116,4 114,9 115,5

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.099827	1.089	0.139182
2	0.084318	0.9198	0.17977
3	-0.095272	-1.0393	0.150388
4	-0.211455	-2.3067	0.0114
5	-0.182368	-1.9894	0.024475
6	-0.075632	-0.825	0.205498
7	-0.240818	-2.627	0.004874
8	-0.183676	-2.0037	0.023688
9	0.025913	0.2827	0.388956
10	0.131948	1.4394	0.076334
11	0.12916	1.409	0.080726
12	0.33991	3.708	0.000159
13	0.129821	1.4162	0.079668
14	0.023385	0.2551	0.399543
15	0.026882	0.2932	0.384923
16	-0.276258	-3.0136	0.001578
17	-0.085808	-0.936	0.175572
18	-0.131398	-1.4334	0.077186
19	-0.127862	-1.3948	0.082835
20	-0.120418	-1.3136	0.095753
21	-0.057753	-0.63	0.264946
22	0.033602	0.3666	0.3573
23	0.21208	2.3135	0.011205
24	0.293139	3.1978	0.000887
25	0.114051	1.2442	0.107945
26	0.013856	0.1512	0.440056
27	-0.041812	-0.4561	0.324568
28	-0.151219	-1.6496	0.050831
29	0.03338	0.3641	0.358203
30	-0.131679	-1.4364	0.07675
31	-0.154173	-1.6818	0.047613
32	-0.068961	-0.7523	0.226684
33	-0.028877	-0.315	0.376654
34	0.030545	0.3332	0.369782
35	0.210452	2.2958	0.01172
36	0.128458	1.4013	0.081862
37	0.016199	0.1767	0.43002
38	0.060386	0.6587	0.255669
39	-0.031829	-0.3472	0.364522
40	-0.132669	-1.4472	0.075229
41	-0.108039	-1.1786	0.120462
42	-0.059215	-0.646	0.259775
43	-0.175852	-1.9183	0.028734
44	-0.044283	-0.4831	0.314965
45	0.040634	0.4433	0.329191
46	-0.058708	-0.6404	0.261562
47	0.18452	2.0129	0.023193
48	0.104749	1.1427	0.127734

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.099827	1.089	0.139182
2	0.075101	0.8193	0.207141
3	-0.1123	-1.225	0.111488
4	-0.203544	-2.2204	0.014143
5	-0.137412	-1.499	0.068262
6	-0.027196	-0.2967	0.383615
7	-0.265617	-2.8975	0.002239
8	-0.261633	-2.8541	0.002546
9	-0.016943	-0.1848	0.426841
10	0.065973	0.7197	0.236567
11	-0.062981	-0.687	0.246697
12	0.18969	2.0693	0.020343
13	0.103259	1.1264	0.131126
14	-0.016556	-0.1806	0.428491
15	0.04483	0.489	0.312857
16	-0.196045	-2.1386	0.017256
17	0.08712	0.9504	0.171927
18	-0.018553	-0.2024	0.419978
19	-0.066273	-0.7229	0.235565
20	-0.084606	-0.9229	0.178952
21	-0.130832	-1.4272	0.078069
22	-0.057123	-0.6231	0.267193
23	0.047428	0.5174	0.302928
24	0.093792	1.0231	0.154156
25	-0.019461	-0.2123	0.416121
26	-0.015688	-0.1711	0.432203
27	-0.036172	-0.3946	0.346928
28	-0.002563	-0.028	0.488872
29	0.150373	1.6404	0.051783
30	-0.052165	-0.5691	0.285197
31	-0.008504	-0.0928	0.463123
32	0.006893	0.0752	0.470093
33	0.020086	0.2191	0.413471
34	-0.063209	-0.6895	0.245917
35	0.061244	0.6681	0.252685
36	-0.003979	-0.0434	0.482726
37	-0.11717	-1.2782	0.101837
38	0.000644	0.007	0.497201
39	-0.004575	-0.0499	0.48014
40	-0.029088	-0.3173	0.375781
41	-0.199525	-2.1766	0.015744
42	0.023291	0.2541	0.399938
43	-0.076707	-0.8368	0.202198
44	-0.124033	-1.353	0.089305
45	0.090666	0.989	0.162323
46	-0.200668	-2.189	0.015273
47	0.017114	0.1867	0.426111
48	-0.119252	-1.3009	0.097905

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918617sii70mk1m1pn8fl/1pmp31289918702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918617sii70mk1m1pn8fl/1pmp31289918702.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918617sii70mk1m1pn8fl/2pmp31289918702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918617sii70mk1m1pn8fl/2pmp31289918702.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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