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workshop 8

*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 01:53:19 -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/t12593121477lrf7jg820q19a2.htm/, Retrieved Fri, 27 Nov 2009 09:55:49 +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/t12593121477lrf7jg820q19a2.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 «

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

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.567758	3.8924	0.000156
2	-0.048973	-0.3357	0.36928
3	-0.49388	-3.3859	0.000721
4	-0.530444	-3.6365	0.000342
5	-0.226428	-1.5523	0.063648
6	0.132686	0.9097	0.183824
7	0.246599	1.6906	0.048768
8	0.212973	1.4601	0.075462
9	0.032069	0.2199	0.413468
10	-0.075326	-0.5164	0.303994
11	-0.054115	-0.371	0.356154
12	-0.054121	-0.371	0.35614
13	-0.057064	-0.3912	0.348705
14	0.016569	0.1136	0.455022
15	0.007751	0.0531	0.478925
16	0.047241	0.3239	0.373737
17	0.043776	0.3001	0.382708
18	-0.014919	-0.1023	0.459485
19	-0.09803	-0.6721	0.252419
20	-0.073881	-0.5065	0.307437
21	-0.049079	-0.3365	0.369008
22	0.000139	0.001	0.499622
23	-0.003066	-0.021	0.491661
24	0.005873	0.0403	0.484028
25	0.021078	0.1445	0.44286
26	0.021203	0.1454	0.442524
27	-0.067522	-0.4629	0.322784
28	-0.144626	-0.9915	0.163258
29	-0.154098	-1.0564	0.148084
30	-0.044037	-0.3019	0.38203
31	0.161141	1.1047	0.13745
32	0.295749	2.0276	0.024149
33	0.213291	1.4622	0.075164
34	-0.035246	-0.2416	0.405058
35	-0.30513	-2.0919	0.02094
36	-0.384911	-2.6388	0.005625

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.567758	3.8924	0.000156
2	-0.547955	-3.7566	0.000237
3	-0.294683	-2.0202	0.024539
4	-0.053076	-0.3639	0.358794
5	0.030311	0.2078	0.418142
6	-0.019409	-0.1331	0.447358
7	-0.172605	-1.1833	0.121316
8	0.124849	0.8559	0.198193
9	-0.092121	-0.6315	0.26537
10	0.07473	0.5123	0.305412
11	0.073423	0.5034	0.30853
12	-0.161102	-1.1045	0.137508
13	0.008119	0.0557	0.477924
14	0.151754	1.0404	0.151744
15	-0.144565	-0.9911	0.16336
16	0.079697	0.5464	0.293697
17	-0.037441	-0.2567	0.399271
18	-0.039542	-0.2711	0.393756
19	-0.119974	-0.8225	0.207472
20	0.12849	0.8809	0.191432
21	-0.111557	-0.7648	0.224107
22	-0.156389	-1.0722	0.144563
23	0.025786	0.1768	0.430221
24	0.027946	0.1916	0.424446
25	-0.087694	-0.6012	0.275297
26	-0.02356	-0.1615	0.436189
27	-0.179114	-1.2279	0.112792
28	-0.172938	-1.1856	0.12087
29	0.043648	0.2992	0.383039
30	0.004561	0.0313	0.487595
31	0.04756	0.3261	0.372916
32	0.029937	0.2052	0.419136
33	0.039121	0.2682	0.39486
34	-0.169143	-1.1596	0.126037
35	-0.075531	-0.5178	0.303509
36	-0.059967	-0.4111	0.341429

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593121477lrf7jg820q19a2/16axk1259311998.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593121477lrf7jg820q19a2/16axk1259311998.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593121477lrf7jg820q19a2/2cxnz1259311998.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593121477lrf7jg820q19a2/2cxnz1259311998.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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