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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: Sun, 10 Jan 2010 06:48:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/10/t126313145379u8q1656ckzazy.htm/, Retrieved Sun, 10 Jan 2010 14:50:55 +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/Jan/10/t126313145379u8q1656ckzazy.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

104,28 104,33 104,46 104,46 104,5 104,61 104,66 104,66 105,03 105,32 105,52 105,67 105,71 105,81 106 106,02 106,19 106,22 106,34 106,42 106,84 107,23 107,42 107,63 107,69 107,81 107,92 108,06 108,21 108,44 108,55 108,66 109,23 109,7 109,94 110,13 110,39 110,46 110,67 110,89 110,98 111,12 111,33 111,43 111,87 112,22 112,47 112,64 112,84 113,03 113,09 113,27 113,44 113,51 113,66 113,62 114,01 114,55 114,77 114,87 115,11 115,09 115,24 115,27 115,41 115,59 115,6 115,68 116,2 116,55 116,73 117,04 117,12 117,28 117,48 117,66 117,92 118,12 118,17 118,39

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	0.966214	8.6421	0
2	0.931863	8.3348	0
3	0.896715	8.0205	0
4	0.860903	7.7002	0
5	0.825061	7.3796	0
6	0.789111	7.058	0
7	0.752798	6.7332	0
8	0.715843	6.4027	0
9	0.67938	6.0766	0
10	0.644238	5.7622	0
11	0.609415	5.4508	0
12	0.575199	5.1447	1e-06
13	0.541768	4.8457	3e-06
14	0.507558	4.5397	1e-05
15	0.472835	4.2292	3.1e-05
16	0.437752	3.9154	9.4e-05
17	0.40281	3.6028	0.000272
18	0.366915	3.2818	0.000765
19	0.33098	2.9604	0.002021
20	0.293974	2.6294	0.005127
21	0.258716	2.314	0.011616
22	0.224433	2.0074	0.024042
23	0.190808	1.7066	0.045885
24	0.159362	1.4254	0.078969
25	0.128505	1.1494	0.12691
26	0.096607	0.8641	0.195064
27	0.064779	0.5794	0.281973
28	0.032796	0.2933	0.385014
29	0.001211	0.0108	0.495693
30	-0.029471	-0.2636	0.396384
31	-0.060428	-0.5405	0.295181
32	-0.090993	-0.8139	0.209069
33	-0.119066	-1.065	0.145049
34	-0.145202	-1.2987	0.098884
35	-0.169969	-1.5202	0.066196
36	-0.193254	-1.7285	0.043877
37	-0.21444	-1.918	0.029339
38	-0.235842	-2.1094	0.019017
39	-0.256149	-2.2911	0.012295
40	-0.275613	-2.4652	0.007918
41	-0.295002	-2.6386	0.005002
42	-0.313408	-2.8032	0.003173
43	-0.33059	-2.9569	0.002042
44	-0.347725	-3.1101	0.001296
45	-0.362368	-3.2411	0.000868
46	-0.375136	-3.3553	0.000607
47	-0.386262	-3.4548	0.000442
48	-0.395026	-3.5332	0.000343

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.966214	8.6421	0
2	-0.02568	-0.2297	0.409461
3	-0.029714	-0.2658	0.39555
4	-0.028362	-0.2537	0.400197
5	-0.019423	-0.1737	0.431261
6	-0.021027	-0.1881	0.425648
7	-0.025468	-0.2278	0.410195
8	-0.030309	-0.2711	0.39351
9	-0.013836	-0.1238	0.450911
10	-0.001519	-0.0136	0.494597
11	-0.01682	-0.1504	0.440396
12	-0.013081	-0.117	0.453576
13	-0.010394	-0.093	0.463081
14	-0.033895	-0.3032	0.381274
15	-0.030775	-0.2753	0.391915
16	-0.029287	-0.262	0.397015
17	-0.022224	-0.1988	0.421472
18	-0.039116	-0.3499	0.363679
19	-0.026469	-0.2367	0.406728
20	-0.042807	-0.3829	0.351414
21	-0.000626	-0.0056	0.497772
22	-0.012549	-0.1122	0.455456
23	-0.018673	-0.167	0.433888
24	0.003911	0.035	0.48609
25	-0.019196	-0.1717	0.432056
26	-0.044945	-0.402	0.344378
27	-0.029517	-0.264	0.396226
28	-0.033408	-0.2988	0.38293
29	-0.02567	-0.2296	0.409493
30	-0.017913	-0.1602	0.436558
31	-0.03629	-0.3246	0.373172
32	-0.026444	-0.2365	0.406815
33	0.007239	0.0647	0.474268
34	-0.00292	-0.0261	0.489613
35	-0.012222	-0.1093	0.456612
36	-0.010615	-0.0949	0.462298
37	-0.001056	-0.0094	0.496244
38	-0.036442	-0.3259	0.372657
39	-0.016216	-0.145	0.442521
40	-0.021301	-0.1905	0.42469
41	-0.031371	-0.2806	0.389875
42	-0.016734	-0.1497	0.4407
43	-0.013596	-0.1216	0.451757
44	-0.029272	-0.2618	0.397067
45	0.009238	0.0826	0.467178
46	-0.002545	-0.0228	0.490949
47	-0.00652	-0.0583	0.476821
48	0.005346	0.0478	0.480993

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/10/t126313145379u8q1656ckzazy/1te7i1263131319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/10/t126313145379u8q1656ckzazy/1te7i1263131319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/10/t126313145379u8q1656ckzazy/24kfq1263131319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/10/t126313145379u8q1656ckzazy/24kfq1263131319.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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