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*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 29 Nov 2009 06:48:02 -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/Nov/29/t1259502573qr53urqcihmvzn5.htm/, Retrieved Sun, 29 Nov 2009 14:49:36 +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/Nov/29/t1259502573qr53urqcihmvzn5.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:

ws8r4l2

Dataseries X:

» Textbox « » Textfile « » CSV «

2.05 2.11 2.09 2.05 2.08 2.06 2.06 2.08 2.07 2.06 2.07 2.06 2.09 2.07 2.09 2.28 2.33 2.35 2.52 2.63 2.58 2.70 2.81 2.97 3.04 3.28 3.33 3.50 3.56 3.57 3.69 3.82 3.79 3.96 4.06 4.05 4.03 3.94 4.02 3.88 4.02 4.03 4.09 3.99 4.01 4.01 4.19 4.30 4.27 3.82 3.15 2.49 1.81 1.26 1.06 0.84 0.78 0.70 0.36 0.35

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.905058	5.4303	2e-06
2	0.798861	4.7932	1.4e-05
3	0.700359	4.2022	8.3e-05
4	0.600659	3.604	0.00047
5	0.502651	3.0159	0.002339
6	0.401363	2.4082	0.01064
7	0.302429	1.8146	0.038965
8	0.216922	1.3015	0.100672
9	0.152524	0.9151	0.183102
10	0.0922	0.5532	0.291772
11	0.062194	0.3732	0.355606
12	0.040406	0.2424	0.40491
13	0.02233	0.134	0.447083
14	-0.003146	-0.0189	0.492523
15	-0.035016	-0.2101	0.417388
16	-0.065398	-0.3924	0.348542
17	-0.105549	-0.6333	0.265273
18	-0.142794	-0.8568	0.198621
19	-0.180449	-1.0827	0.143071
20	-0.218482	-1.3109	0.099098
21	-0.26013	-1.5608	0.063662
22	-0.292632	-1.7558	0.043815
23	-0.332794	-1.9968	0.026727
24	-0.364512	-2.1871	0.017658
25	-0.395911	-2.3755	0.011486
26	-0.414979	-2.4899	0.008767
27	-0.415684	-2.4941	0.008679
28	-0.40683	-2.441	0.009848
29	-0.381734	-2.2904	0.013981
30	-0.343649	-2.0619	0.023247
31	-0.294122	-1.7647	0.043046
32	-0.246121	-1.4767	0.074222
33	-0.196263	-1.1776	0.123346
34	-0.137007	-0.822	0.208232
35	-0.064754	-0.3885	0.349959
36	NA	NA	NA
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.905058	5.4303	2e-06
2	-0.112066	-0.6724	0.252812
3	-0.012628	-0.0758	0.470011
4	-0.069717	-0.4183	0.339105
5	-0.049961	-0.2998	0.38304
6	-0.085783	-0.5147	0.304954
7	-0.05568	-0.3341	0.370128
8	-0.002932	-0.0176	0.493031
9	0.042096	0.2526	0.401016
10	-0.045415	-0.2725	0.393401
11	0.118064	0.7084	0.241635
12	-0.017128	-0.1028	0.459359
13	-0.008841	-0.053	0.478994
14	-0.089324	-0.5359	0.297647
15	-0.068159	-0.409	0.342499
16	-0.039528	-0.2372	0.406936
17	-0.098606	-0.5916	0.278896
18	-0.015984	-0.0959	0.462065
19	-0.027966	-0.1678	0.433842
20	-0.044107	-0.2646	0.396398
21	-0.055516	-0.3331	0.370497
22	-0.008814	-0.0529	0.479057
23	-0.113737	-0.6824	0.24967
24	-0.030161	-0.181	0.428705
25	-0.104971	-0.6298	0.266393
26	0.008998	0.054	0.478621
27	0.008538	0.0512	0.479713
28	0.007835	0.047	0.481381
29	0.050557	0.3033	0.381689
30	0.047518	0.2851	0.388597
31	0.031623	0.1897	0.425291
32	-0.013917	-0.0835	0.466958
33	-0.011032	-0.0662	0.473795
34	0.069847	0.4191	0.338822
35	0.0863	0.5178	0.303883
36	NA	NA	NA
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/29/t1259502573qr53urqcihmvzn5/1jwq81259502480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/29/t1259502573qr53urqcihmvzn5/1jwq81259502480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/29/t1259502573qr53urqcihmvzn5/2tyde1259502480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/29/t1259502573qr53urqcihmvzn5/2tyde1259502480.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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