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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: Mon, 20 Dec 2010 21:43:16 +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/Dec/20/t1292881451j509a56tla2a52o.htm/, Retrieved Mon, 20 Dec 2010 22:44:15 +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/Dec/20/t1292881451j509a56tla2a52o.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

9.1 5.9 7.2 6.8 8 14.3 14.6 17.5 17.2 17.2 14.1 10.4 6.8 4.1 6.5 6.1 6.3 9.3 16.4 16.1 18 17.6 14 10.5 6.9 2.8 0.7 3.6 6.7 12.5 14.4 16.5 18.7 19.4 15.8 11.3 9.7 2.9 0.1 2.5 6.7 10.3 11.2 17.4 20.5 17 14.2 10.6 6.1

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.17913	1.0896	0.141467
2	-0.015148	-0.0921	0.463542
3	-0.006033	-0.0367	0.485463
4	0.105926	0.6443	0.26167
5	-0.046401	-0.2822	0.389665
6	-0.149734	-0.9108	0.184149
7	-0.006946	-0.0423	0.483262
8	-0.134874	-0.8204	0.208619
9	0.020422	0.1242	0.450906
10	-0.06538	-0.3977	0.346571
11	0.056834	0.3457	0.365761
12	-0.184943	-1.125	0.133924
13	0.009432	0.0574	0.477278
14	0.038002	0.2312	0.409232
15	0.152782	0.9293	0.179369
16	-0.02232	-0.1358	0.446371
17	-0.254369	-1.5473	0.065155
18	-0.075618	-0.46	0.324116
19	-0.154285	-0.9385	0.177042
20	-0.053192	-0.3236	0.374049
21	-0.046971	-0.2857	0.388346
22	0.079565	0.484	0.315627
23	-0.038419	-0.2337	0.408256
24	-0.061435	-0.3737	0.355383
25	0.054865	0.3337	0.370233
26	0.006954	0.0423	0.483245
27	-0.128901	-0.7841	0.218994
28	-0.002853	-0.0174	0.493124
29	0.096048	0.5842	0.281304
30	-0.022818	-0.1388	0.445181
31	0.055697	0.3388	0.368342
32	0.009526	0.0579	0.477053
33	0.030848	0.1876	0.426092
34	0.013982	0.085	0.466342
35	0.025606	0.1558	0.438536
36	0.035023	0.213	0.416234
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

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.17913	1.0896	0.141467
2	-0.048801	-0.2968	0.384122
3	0.005753	0.035	0.486137
4	0.109029	0.6632	0.255658
5	-0.090438	-0.5501	0.292774
6	-0.124413	-0.7568	0.226989
7	0.04699	0.2858	0.388301
8	-0.174806	-1.0633	0.147268
9	0.096556	0.5873	0.280275
10	-0.07262	-0.4417	0.330627
11	0.064235	0.3907	0.349121
12	-0.215836	-1.3129	0.098654
13	0.092258	0.5612	0.289028
14	-0.032215	-0.196	0.422859
15	0.189235	1.1511	0.128544
16	-0.126797	-0.7713	0.222721
17	-0.219305	-1.334	0.095182
18	-0.085949	-0.5228	0.302113
19	-0.145243	-0.8835	0.191341
20	-0.051383	-0.3125	0.378189
21	0.128653	0.7826	0.219431
22	-0.011309	-0.0688	0.472764
23	-0.029932	-0.1821	0.42826
24	-0.185981	-1.1313	0.132609
25	0.024633	0.1498	0.440854
26	-0.083377	-0.5072	0.307524
27	-0.0961	-0.5846	0.281197
28	0.083277	0.5066	0.307738
29	-0.093266	-0.5673	0.286964
30	-0.081241	-0.4942	0.312055
31	0.065758	0.4	0.345733
32	-0.011759	-0.0715	0.471682
33	0.044059	0.268	0.395094
34	0.007368	0.0448	0.482246
35	-0.083897	-0.5103	0.306428
36	-0.12425	-0.7558	0.227282
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

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/1sm6x1292881390.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/1sm6x1292881390.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/2kv5z1292881390.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/2kv5z1292881390.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/3vm4k1292881390.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292881451j509a56tla2a52o/3vm4k1292881390.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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