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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, 09 Dec 2009 10:46:40 -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/09/t1260380940clhla8f0icsix1n.htm/, Retrieved Wed, 09 Dec 2009 18:49:02 +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/09/t1260380940clhla8f0icsix1n.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 «

24 22 25 24 29 26 26 21 23 22 21 16 19 16 25 27 23 22 23 20 24 23 20 21 22 17 21 19 23 22 15 23 21 18 18 18 18 10 13 10 9 9 6 11 9 10 9 16 10 7 7 14 11 10 6 8 13 12 15 16 16

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	0.820001	6.4044	0
2	0.776581	6.0653	0
3	0.718636	5.6127	0
4	0.695823	5.4346	1e-06
5	0.625958	4.8889	4e-06
6	0.553387	4.3221	2.9e-05
7	0.482311	3.767	0.000187
8	0.466712	3.6451	0.000277
9	0.418899	3.2717	0.000881
10	0.391309	3.0562	0.001662
11	0.378387	2.9553	0.002217
12	0.387012	3.0227	0.00183
13	0.313835	2.4511	0.008561
14	0.292276	2.2827	0.012972
15	0.236645	1.8483	0.034707
16	0.177033	1.3827	0.085903
17	0.108129	0.8445	0.20084
18	0.044559	0.348	0.364514
19	-0.006031	-0.0471	0.481291
20	-0.042722	-0.3337	0.369887
21	-0.118889	-0.9286	0.178391
22	-0.155964	-1.2181	0.113935
23	-0.157422	-1.2295	0.111803
24	-0.163031	-1.2733	0.103869
25	-0.192743	-1.5054	0.068695
26	-0.20004	-1.5624	0.061688
27	-0.181225	-1.4154	0.081016
28	-0.204351	-1.596	0.057825
29	-0.208387	-1.6276	0.054387
30	-0.231413	-1.8074	0.037816
31	-0.243224	-1.8996	0.031105
32	-0.271897	-2.1236	0.018885
33	-0.314155	-2.4536	0.008507
34	-0.365514	-2.8548	0.002939
35	-0.368418	-2.8774	0.002759
36	-0.373542	-2.9175	0.002467

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.820001	6.4044	0
2	0.318011	2.4837	0.007882
3	0.080069	0.6254	0.267033
4	0.117551	0.9181	0.181091
5	-0.076318	-0.5961	0.276669
6	-0.120635	-0.9422	0.174906
7	-0.089393	-0.6982	0.243859
8	0.105038	0.8204	0.207598
9	0.008228	0.0643	0.474486
10	0.048027	0.3751	0.354444
11	0.107647	0.8407	0.201886
12	0.101996	0.7966	0.214383
13	-0.224102	-1.7503	0.042548
14	-0.05425	-0.4237	0.336635
15	-0.113183	-0.884	0.190088
16	-0.195868	-1.5298	0.065621
17	-0.090939	-0.7103	0.240126
18	-0.017344	-0.1355	0.446348
19	0.029032	0.2268	0.410688
20	0.035431	0.2767	0.391463
21	-0.073683	-0.5755	0.283542
22	-0.042055	-0.3285	0.371845
23	0.049199	0.3843	0.351063
24	0.004671	0.0365	0.485508
25	-0.033869	-0.2645	0.396134
26	0.002764	0.0216	0.491422
27	0.132238	1.0328	0.152884
28	-0.080902	-0.6319	0.264917
29	0.020294	0.1585	0.437292
30	0.005209	0.0407	0.48384
31	-0.07585	-0.5924	0.277884
32	-0.108983	-0.8512	0.198999
33	-0.064358	-0.5027	0.308508
34	-0.163891	-1.28	0.102691
35	-0.025828	-0.2017	0.420403
36	0.102072	0.7972	0.214211

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380940clhla8f0icsix1n/1rccn1260380799.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380940clhla8f0icsix1n/1rccn1260380799.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380940clhla8f0icsix1n/26h6z1260380799.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380940clhla8f0icsix1n/26h6z1260380799.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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