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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: Fri, 27 Nov 2009 10:19:20 -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/27/t12593424067nrvq1c3fecnekc.htm/, Retrieved Fri, 27 Nov 2009 18:20:08 +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/27/t12593424067nrvq1c3fecnekc.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

100,6 104,3 120,4 107,5 102,9 125,6 107,5 108,8 128,4 121,1 119,5 128,7 108,7 105,5 119,8 111,3 110,6 120,1 97,5 107,7 127,3 117,2 119,8 116,2 111 112,4 130,6 109,1 118,8 123,9 101,6 112,8 128 129,6 125,8 119,5 115,7 113,6 129,7 112 116,8 127 112,1 114,2 121,1 131,6 125 120,4 117,7 117,5 120,6 127,5 112,3 124,5 115,2 104,7 130,9 129,2 113,5 125,6 107,6

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	0.006024	0.0471	0.481313
2	-0.153797	-1.2012	0.117159
3	0.309833	2.4199	0.00926
4	-0.187785	-1.4666	0.073804
5	-0.01319	-0.103	0.459145
6	0.406017	3.1711	0.001188
7	-0.109564	-0.8557	0.19775
8	-0.170037	-1.328	0.094558
9	0.133995	1.0465	0.149722
10	-0.184632	-1.442	0.077206
11	0.003596	0.0281	0.488843
12	0.553465	4.3227	2.9e-05
13	0.039527	0.3087	0.379295
14	-0.143647	-1.1219	0.133147
15	0.150533	1.1757	0.122141
16	-0.106585	-0.8325	0.2042
17	-0.038148	-0.2979	0.383377
18	0.312359	2.4396	0.008813
19	-0.060096	-0.4694	0.320242
20	-0.197992	-1.5464	0.063594
21	0.083735	0.654	0.257787
22	-0.172728	-1.349	0.091154
23	0.011809	0.0922	0.463408
24	0.312979	2.4444	0.008706
25	0.032005	0.25	0.401726
26	-0.199479	-1.558	0.062206
27	0.034046	0.2659	0.395604
28	-0.112262	-0.8768	0.192018
29	-0.156446	-1.2219	0.113226
30	0.157041	1.2265	0.112357
31	-0.02837	-0.2216	0.412692
32	-0.242495	-1.8939	0.031488
33	-0.033064	-0.2582	0.398546
34	-0.119326	-0.932	0.177513
35	-0.08386	-0.655	0.257476
36	0.175695	1.3722	0.08751

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.006024	0.0471	0.481313
2	-0.153839	-1.2015	0.117097
3	0.319399	2.4946	0.007667
4	-0.263589	-2.0587	0.021901
5	0.155965	1.2181	0.113934
6	0.255895	1.9986	0.025057
7	-0.046181	-0.3607	0.35979
8	-0.14865	-1.161	0.125084
9	-0.028611	-0.2235	0.411963
10	-0.089939	-0.7024	0.242537
11	0.088071	0.6879	0.247076
12	0.461552	3.6048	0.000315
13	0.153127	1.196	0.11817
14	-0.061105	-0.4772	0.317446
15	-0.143898	-1.1239	0.132734
16	-0.014765	-0.1153	0.454287
17	-0.077653	-0.6065	0.273221
18	0.012965	0.1013	0.459837
19	0.000288	0.0022	0.499107
20	-0.008967	-0.07	0.472198
21	0.051702	0.4038	0.343885
22	-0.051529	-0.4025	0.344379
23	0.103631	0.8094	0.210721
24	-0.121621	-0.9499	0.172959
25	0.076759	0.5995	0.275527
26	-0.242941	-1.8974	0.031253
27	0.025302	0.1976	0.422001
28	-0.163237	-1.2749	0.103586
29	-0.116913	-0.9131	0.182386
30	-0.126226	-0.9859	0.164048
31	0.067454	0.5268	0.300109
32	0.021005	0.1641	0.435114
33	-0.061477	-0.4802	0.316418
34	0.007268	0.0568	0.477459
35	-0.101377	-0.7918	0.215779
36	-0.046401	-0.3624	0.359152

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593424067nrvq1c3fecnekc/1b9ox1259342359.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593424067nrvq1c3fecnekc/1b9ox1259342359.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593424067nrvq1c3fecnekc/27sk81259342359.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593424067nrvq1c3fecnekc/27sk81259342359.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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