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ACF ( d=0 , D=2 )

*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, 15 Dec 2010 10:28:46 +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/15/t1292408844tfjxg7u886f8yy3.htm/, Retrieved Wed, 15 Dec 2010 11:27:25 +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/15/t1292408844tfjxg7u886f8yy3.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 «

94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5 105.1 95.1 88.7

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.129108	0.7746	0.221804
2	0.278294	1.6698	0.05182
3	0.481882	2.8913	0.003234
4	0.040123	0.2407	0.405562
5	0.228949	1.3737	0.089016
6	0.07093	0.4256	0.336473
7	-0.111798	-0.6708	0.253318
8	0.065315	0.3919	0.348725
9	-0.197462	-1.1848	0.121935
10	-0.075358	-0.4521	0.326939
11	-0.064666	-0.388	0.350153
12	-0.222857	-1.3371	0.094782
13	-0.01889	-0.1133	0.455195
14	-0.068874	-0.4132	0.340939
15	-0.03539	-0.2123	0.416519
16	-0.114165	-0.685	0.248869
17	-0.062677	-0.3761	0.354538
18	-0.057582	-0.3455	0.365868
19	-0.106294	-0.6378	0.263832
20	-0.030809	-0.1849	0.427191
21	-0.120288	-0.7217	0.237563
22	-0.185506	-1.113	0.136534
23	0.03718	0.2231	0.412366
24	-0.202919	-1.2175	0.115665
25	-0.087758	-0.5265	0.300868
26	-0.037575	-0.2255	0.411451
27	-0.121766	-0.7306	0.234877
28	0.037127	0.2228	0.412489
29	-0.028213	-0.1693	0.433262
30	-0.030601	-0.1836	0.427675
31	0.029194	0.1752	0.430965
32	-0.006953	-0.0417	0.483478
33	0.027642	0.1659	0.4346
34	0.04793	0.2876	0.387659
35	0.014727	0.0884	0.465039
36	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.129108	0.7746	0.221804
2	0.26606	1.5964	0.059575
3	0.460928	2.7656	0.004454
4	-0.094276	-0.5657	0.287568
5	-0.006047	-0.0363	0.485629
6	-0.192021	-1.1521	0.128431
7	-0.201921	-1.2115	0.116793
8	-0.032479	-0.1949	0.423293
9	-0.118848	-0.7131	0.240194
10	0.088019	0.5281	0.30033
11	0.041991	0.2519	0.401257
12	-0.013373	-0.0802	0.468245
13	0.018173	0.109	0.45689
14	0.041163	0.247	0.403164
15	0.10576	0.6346	0.264863
16	-0.241696	-1.4502	0.077833
17	-0.097764	-0.5866	0.280571
18	-0.153283	-0.9197	0.181926
19	-0.007964	-0.0478	0.481077
20	0.077706	0.4662	0.321928
21	-0.012803	-0.0768	0.469597
22	-0.119114	-0.7147	0.239707
23	0.088329	0.53	0.299693
24	-0.07953	-0.4772	0.318058
25	-0.029719	-0.1783	0.429739
26	-0.064215	-0.3853	0.351144
27	0.048034	0.2882	0.387421
28	-1.7e-05	-1e-04	0.499959
29	0.014952	0.0897	0.464506
30	-0.023732	-0.1424	0.443782
31	-0.090897	-0.5454	0.294426
32	0.010474	0.0628	0.47512
33	-0.058542	-0.3513	0.363723
34	0.00027	0.0016	0.499358
35	0.066152	0.3969	0.346888
36	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292408844tfjxg7u886f8yy3/1yvhu1292408923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292408844tfjxg7u886f8yy3/1yvhu1292408923.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292408844tfjxg7u886f8yy3/2yvhu1292408923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292408844tfjxg7u886f8yy3/2yvhu1292408923.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; 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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