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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: Thu, 10 Dec 2009 12:37:57 -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/10/t12604739086levmp63kapz94k.htm/, Retrieved Thu, 10 Dec 2009 20:38:30 +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/10/t12604739086levmp63kapz94k.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 «

7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8 8.1

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	0.412166	3.0567	0.001725
2	-0.16243	-1.2046	0.116756
3	-0.520192	-3.8579	0.000151
4	-0.417374	-3.0953	0.001545
5	0.066924	0.4963	0.310823
6	0.415364	3.0804	0.001612
7	0.304746	2.2601	0.013899
8	-0.071291	-0.5287	0.299567
9	-0.267366	-1.9828	0.026194
10	-0.283741	-2.1043	0.019969
11	0.007269	0.0539	0.478602
12	0.308295	2.2864	0.013053
13	0.137728	1.0214	0.155763
14	0.064596	0.4791	0.316898
15	-0.007628	-0.0566	0.477547
16	-0.098361	-0.7295	0.234407
17	-0.073384	-0.5442	0.29424
18	-0.011274	-0.0836	0.466836
19	-0.009931	-0.0737	0.470777
20	-0.009585	-0.0711	0.471796
21	0.053668	0.398	0.34608
22	-0.015598	-0.1157	0.454165
23	-0.059092	-0.4382	0.331464
24	-0.044688	-0.3314	0.370794
25	-0.147956	-1.0973	0.138653
26	0.027697	0.2054	0.419006
27	0.125683	0.9321	0.177681
28	0.104388	0.7742	0.221076
29	0.042911	0.3182	0.375754
30	-0.071367	-0.5293	0.299373
31	-0.148863	-1.104	0.137201
32	-0.160231	-1.1883	0.11991
33	-0.031377	-0.2327	0.40843
34	0.024994	0.1854	0.426815
35	0.080193	0.5947	0.277232
36	0.066043	0.4898	0.313116

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.412166	3.0567	0.001725
2	-0.400317	-2.9688	0.002211
3	-0.375055	-2.7815	0.003699
4	-0.117719	-0.873	0.193221
5	0.19568	1.4512	0.076202
6	0.121421	0.9005	0.185894
7	-0.121334	-0.8998	0.186066
8	-0.130838	-0.9703	0.168068
9	0.125937	0.934	0.177199
10	-0.074726	-0.5542	0.290851
11	0.019798	0.1468	0.441902
12	0.137356	1.0187	0.156412
13	-0.2465	-1.8281	0.036481
14	0.267854	1.9865	0.025987
15	0.241179	1.7886	0.039591
16	-0.158685	-1.1768	0.122164
17	-0.122793	-0.9107	0.183224
18	0.089835	0.6662	0.254023
19	0.071801	0.5325	0.298266
20	-0.129651	-0.9615	0.17025
21	-0.06074	-0.4505	0.327075
22	0.019833	0.1471	0.441801
23	-0.109951	-0.8154	0.209175
24	0.021507	0.1595	0.436929
25	-0.1069	-0.7928	0.215652
26	-0.009217	-0.0684	0.472876
27	-0.028432	-0.2109	0.41689
28	0.083347	0.6181	0.269525
29	0.041705	0.3093	0.379135
30	-0.162071	-1.2019	0.117266
31	0.003366	0.025	0.490086
32	-0.05919	-0.439	0.331203
33	-0.128786	-0.9551	0.171853
34	-0.008311	-0.0616	0.475537
35	-0.008821	-0.0654	0.47404
36	-0.035514	-0.2634	0.396622

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604739086levmp63kapz94k/18fwu1260473876.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604739086levmp63kapz94k/18fwu1260473876.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604739086levmp63kapz94k/2pejw1260473876.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604739086levmp63kapz94k/2pejw1260473876.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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