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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: Wed, 23 Dec 2009 04:39:04 -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/Dec/23/t1261568490b2q3qgkhzd2ckyj.htm/, Retrieved Wed, 23 Dec 2009 12:41:32 +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/Dec/23/t1261568490b2q3qgkhzd2ckyj.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:

paper, TRA, levensm1

Dataseries X:

» Textbox « » Textfile « » CSV «

1.1 1.2 1.1 1.2 1.4 1.5 1.5 1.8 1.6 1.5 1.4 1.4 1.4 1.4 1.5 1.4 1.1 1.1 0.9 0.9 0.9 0.9 1.1 1.3 1 1.1 1.4 1.4 1.3 1.4 1 1.8 1.5 1.5 1.4 1.6 1.6 1.6 1.4 1.7 1.8 1.9 2.2 2.1 2.4 2.6 2.8 2.7 2.6 2.9 2.8 2.2 2.2 2.2 2 2 1.7 1.4 1.3 1.4 1.3 2.5 2.4 2.4 2.1 1.7 1.4 1.2 1.1 0.8 0.5 0.6 0.4 0.4 0.3 0.6 0.7 0.8 0.9 0.7 0.6 0.6 0.6 0.5 0.8 0.9 1 1 1.2 1.3 1.3 1.3 1.3 1.4 1.7 1.8 1.4 1.5 1.7 1.6 1.7 1.8 1.7 2.2 2.7 3 2.8 2.7 2.7 2.5 2 1.8 1.4 1.5 1.6 1.3 1.1 0.8 1.1 1.3 1.5 1.8

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	0.918651	10.1468	0
2	0.831574	9.185	0
3	0.728231	8.0436	0
4	0.624435	6.8971	0
5	0.528078	5.8328	0
6	0.438575	4.8442	2e-06
7	0.346908	3.8317	0.000101
8	0.283608	3.1326	0.001085
9	0.228815	2.5273	0.006386
10	0.1832	2.0235	0.022603
11	0.138944	1.5347	0.063725
12	0.109405	1.2084	0.114613
13	0.097037	1.0718	0.14296
14	0.07856	0.8677	0.193625
15	0.04234	0.4677	0.320431
16	-0.004403	-0.0486	0.480645
17	-0.071987	-0.7951	0.214042
18	-0.148603	-1.6414	0.051648
19	-0.220715	-2.4379	0.008108
20	-0.301011	-3.3248	0.000585
21	-0.369673	-4.0832	4e-05
22	-0.428265	-4.7303	3e-06
23	-0.480924	-5.312	0
24	-0.518632	-5.7285	0
25	-0.549396	-6.0683	0
26	-0.551662	-6.0933	0
27	-0.550757	-6.0833	0
28	-0.553374	-6.1122	0
29	-0.549691	-6.0715	0
30	-0.526497	-5.8154	0
31	-0.526818	-5.8189	0
32	-0.495017	-5.4676	0
33	-0.477947	-5.2791	0
34	-0.453876	-5.0132	1e-06
35	-0.416037	-4.5953	5e-06
36	-0.366988	-4.0535	4.5e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.918651	10.1468	0
2	-0.079102	-0.8737	0.191995
3	-0.151233	-1.6704	0.048699
4	-0.057551	-0.6357	0.263089
5	-0.005361	-0.0592	0.476439
6	-0.020127	-0.2223	0.41222
7	-0.0889	-0.9819	0.164037
8	0.112993	1.248	0.107202
9	0.001323	0.0146	0.494184
10	-0.023684	-0.2616	0.397035
11	-0.053266	-0.5883	0.278694
12	0.058082	0.6415	0.261189
13	0.086875	0.9596	0.169586
14	-0.102852	-1.136	0.129083
15	-0.152602	-1.6855	0.04722
16	-0.078602	-0.8682	0.193498
17	-0.138759	-1.5326	0.063977
18	-0.13004	-1.4363	0.076733
19	-0.023059	-0.2547	0.399694
20	-0.09074	-1.0023	0.159102
21	-0.029208	-0.3226	0.373771
22	-0.064979	-0.7177	0.237153
23	-0.082887	-0.9155	0.180863
24	-0.022536	-0.2489	0.401923
25	-0.076692	-0.8471	0.199302
26	0.074737	0.8255	0.205351
27	-0.108521	-1.1987	0.116492
28	-0.150844	-1.6661	0.049127
29	-0.056189	-0.6206	0.268
30	0.101521	1.1213	0.132173
31	-0.207532	-2.2923	0.011802
32	0.132274	1.461	0.073292
33	-0.054526	-0.6023	0.274061
34	0.003644	0.0402	0.483982
35	0.025467	0.2813	0.389483
36	0.051422	0.568	0.285548

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/23/t1261568490b2q3qgkhzd2ckyj/1q97r1261568342.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/23/t1261568490b2q3qgkhzd2ckyj/1q97r1261568342.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/23/t1261568490b2q3qgkhzd2ckyj/2l4la1261568342.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/23/t1261568490b2q3qgkhzd2ckyj/2l4la1261568342.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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