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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, 26 Nov 2009 13:12:06 -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/26/t1259266352ynk1ed25qs2mt4t.htm/, Retrieved Thu, 26 Nov 2009 21:12:34 +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/26/t1259266352ynk1ed25qs2mt4t.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 «

110.5 110.8 104.2 88.9 89.8 90 93.9 91.3 87.8 99.7 73.5 79.2 96.9 95.2 95.6 89.7 92.8 88 101.1 92.7 95.8 103.8 81.8 87.1 105.9 108.1 102.6 93.7 103.5 100.6 113.3 102.4 102.1 106.9 87.3 93.1 109.1 120.3 104.9 92.6 109.8 111.4 117.9 121.6 117.8 124.2 106.8 102.7 116.8 113.6 96.1 85 83.2 84.9 83 79.6 83.2 83.8 82.8 71.4

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	0.866061	6.0002	0
2	0.795019	5.5081	1e-06
3	0.654271	4.5329	1.9e-05
4	0.502812	3.4836	0.000533
5	0.36375	2.5201	0.007555
6	0.203171	1.4076	0.082845
7	0.088266	0.6115	0.27187
8	-0.036136	-0.2504	0.401688
9	-0.114223	-0.7914	0.216314
10	-0.155253	-1.0756	0.143736
11	-0.204154	-1.4144	0.081846
12	-0.194729	-1.3491	0.091814
13	-0.167046	-1.1573	0.126432
14	-0.127718	-0.8849	0.190322
15	-0.091069	-0.6309	0.265536
16	-0.082389	-0.5708	0.285397
17	-0.05492	-0.3805	0.352627
18	-0.065608	-0.4545	0.325744
19	-0.053912	-0.3735	0.355206
20	-0.067472	-0.4675	0.321142
21	-0.079177	-0.5486	0.292927
22	-0.114396	-0.7926	0.215968
23	-0.119645	-0.8289	0.205625
24	-0.162799	-1.1279	0.132483
25	-0.168936	-1.1704	0.123805
26	-0.180723	-1.2521	0.108303
27	-0.212064	-1.4692	0.074149
28	-0.222668	-1.5427	0.064737
29	-0.240309	-1.6649	0.051223
30	-0.239489	-1.6592	0.051796
31	-0.245211	-1.6989	0.047909
32	-0.23683	-1.6408	0.053687
33	-0.225103	-1.5596	0.062717
34	-0.213336	-1.478	0.072965
35	-0.159273	-1.1035	0.137661
36	-0.117818	-0.8163	0.20919

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.866061	6.0002	0
2	0.179875	1.2462	0.109368
3	-0.273702	-1.8963	0.031977
4	-0.244175	-1.6917	0.048594
5	-0.036034	-0.2497	0.401961
6	-0.123208	-0.8536	0.19878
7	0.032327	0.224	0.411866
8	-0.057973	-0.4016	0.344864
9	0.028199	0.1954	0.422964
10	0.115097	0.7974	0.214568
11	-0.093401	-0.6471	0.260324
12	0.042138	0.2919	0.385795
13	0.139208	0.9645	0.169825
14	-0.003282	-0.0227	0.490976
15	-0.106084	-0.735	0.232966
16	-0.172624	-1.196	0.118791
17	0.005284	0.0366	0.485475
18	-0.035027	-0.2427	0.404645
19	0.045426	0.3147	0.377169
20	-0.035873	-0.2485	0.402391
21	0.023066	0.1598	0.436853
22	-0.130842	-0.9065	0.184599
23	0.086358	0.5983	0.276224
24	-0.139596	-0.9672	0.169158
25	0.072442	0.5019	0.309018
26	0.016534	0.1145	0.454641
27	-0.219657	-1.5218	0.067307
28	-0.102294	-0.7087	0.240966
29	0.025531	0.1769	0.430171
30	0.021641	0.1499	0.440723
31	-0.003184	-0.0221	0.491246
32	-0.007622	-0.0528	0.479054
33	-0.071213	-0.4934	0.311998
34	-0.00544	-0.0377	0.485046
35	0.151799	1.0517	0.149103
36	0.008873	0.0615	0.475617

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266352ynk1ed25qs2mt4t/1xnz71259266325.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266352ynk1ed25qs2mt4t/1xnz71259266325.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266352ynk1ed25qs2mt4t/26q5l1259266325.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266352ynk1ed25qs2mt4t/26q5l1259266325.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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