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workshop 8 ACF

*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 07:11:42 -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/t1259331216re965zevncm4ydd.htm/, Retrieved Fri, 27 Nov 2009 15:13:39 +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/t1259331216re965zevncm4ydd.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:

workshop 8 ACF

Dataseries X:

» Textbox « » Textfile « » CSV «

9,3 9,3 8,7 8,2 8,3 8,5 8,6 8,5 8,2 8,1 7,9 8,6 8,7 8,7 8,5 8,4 8,5 8,7 8,7 8,6 8,5 8,3 8 8,2 8,1 8,1 8 7,9 7,9 8 8 7,9 8 7,7 7,2 7,5 7,3 7 7 7 7,2 7,3 7,1 6,8 6,4 6,1 6,5 7,7 7,9 7,5 6,9 6,6 6,9 7,7 8 8 7,7 7,3 7,4 8,1 8,3

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	0.885217	6.1965	0
2	0.659121	4.6138	1.4e-05
3	0.441864	3.093	0.001634
4	0.321197	2.2484	0.014542
5	0.30123	2.1086	0.020057
6	0.314486	2.2014	0.016224
7	0.288014	2.0161	0.024645
8	0.191555	1.3409	0.093071
9	0.060328	0.4223	0.337327
10	-0.062716	-0.439	0.33129
11	-0.157418	-1.1019	0.137938
12	-0.227514	-1.5926	0.058841
13	-0.254385	-1.7807	0.040581
14	-0.256631	-1.7964	0.039297
15	-0.255284	-1.787	0.040063
16	-0.256687	-1.7968	0.039265
17	-0.267479	-1.8724	0.033566
18	-0.284634	-1.9924	0.025955
19	-0.290403	-2.0328	0.023754
20	-0.282613	-1.9783	0.026766
21	-0.275613	-1.9293	0.029748
22	-0.287648	-2.0135	0.024784
23	-0.300889	-2.1062	0.020165
24	-0.283693	-1.9859	0.02633
25	-0.245111	-1.7158	0.04626
26	-0.202696	-1.4189	0.081133
27	-0.167673	-1.1737	0.123092
28	-0.152314	-1.0662	0.14578
29	-0.140096	-0.9807	0.165785
30	-0.104044	-0.7283	0.234946
31	-0.040678	-0.2847	0.38852
32	0.021304	0.1491	0.441033
33	0.051819	0.3627	0.359182
34	0.056503	0.3955	0.347087
35	0.063068	0.4415	0.330405
36	0.088215	0.6175	0.269881

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.885217	6.1965	0
2	-0.575288	-4.027	9.8e-05
3	0.220984	1.5469	0.064163
4	0.25805	1.8063	0.038504
5	0.040139	0.281	0.389958
6	-0.139399	-0.9758	0.16698
7	-0.124343	-0.8704	0.194163
8	-0.093551	-0.6549	0.25781
9	0.016924	0.1185	0.453089
10	-0.122765	-0.8594	0.197165
11	-0.174162	-1.2191	0.114315
12	-0.105927	-0.7415	0.230969
13	0.227623	1.5934	0.058755
14	-0.103897	-0.7273	0.235258
15	-0.115967	-0.8118	0.210425
16	0.051448	0.3601	0.360147
17	0.022286	0.156	0.438336
18	-0.041435	-0.29	0.386503
19	0.008552	0.0599	0.476254
20	-0.14696	-1.0287	0.154332
21	-0.106048	-0.7423	0.230714
22	-0.087712	-0.614	0.271032
23	0.07773	0.5441	0.294418
24	0.034685	0.2428	0.404588
25	-0.160072	-1.1205	0.133981
26	-0.071238	-0.4987	0.310123
27	0.119048	0.8333	0.204349
28	0.013983	0.0979	0.461214
29	0.013855	0.097	0.461567
30	-0.01257	-0.088	0.46512
31	0.025895	0.1813	0.428454
32	-0.038268	-0.2679	0.39496
33	-0.067461	-0.4722	0.31943
34	-0.016802	-0.1176	0.453427
35	0.072927	0.5105	0.306001
36	0.016748	0.1172	0.453576

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259331216re965zevncm4ydd/1qecr1259331101.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259331216re965zevncm4ydd/1qecr1259331101.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259331216re965zevncm4ydd/2gjjx1259331101.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259331216re965zevncm4ydd/2gjjx1259331101.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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