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Method 1

*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 08:20:03 -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/t1259249045u00l76nwd1vpsnl.htm/, Retrieved Thu, 26 Nov 2009 16:24:07 +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/t1259249045u00l76nwd1vpsnl.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 «

108.5 112.3 116.6 115.5 120.1 132.9 128.1 129.3 132.5 131 124.9 120.8 122 122.1 127.4 135.2 137.3 135 136 138.4 134.7 138.4 133.9 133.6 141.2 151.8 155.4 156.6 161.6 160.7 156 159.5 168.7 169.9 169.9 185.9 190.8 195.8 211.9 227.1 251.3 256.7 251.9 251.2 270.3 267.2 243 229.9 187.2 178.2 175.2 192.4 187 184 194.1 212.7 217.5 200.5 205.9 196.5 206.3

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.306004	2.1201	0.019599
2	0.22039	1.5269	0.066674
3	0.094904	0.6575	0.256996
4	0.172329	1.1939	0.119186
5	0.141723	0.9819	0.165539
6	-0.020508	-0.1421	0.443804
7	-0.153093	-1.0607	0.147077
8	-0.359464	-2.4904	0.008136
9	-0.070456	-0.4881	0.313839
10	-0.174173	-1.2067	0.11673
11	-0.161466	-1.1187	0.134425
12	-0.408534	-2.8304	0.003385
13	-0.239234	-1.6575	0.051974
14	-0.120443	-0.8345	0.20408
15	-0.040328	-0.2794	0.39057
16	0.045176	0.313	0.377822
17	-0.043684	-0.3027	0.381732
18	-0.050775	-0.3518	0.363272
19	0.092447	0.6405	0.26245
20	0.166615	1.1543	0.127038
21	0.018353	0.1272	0.449674
22	-0.002722	-0.0189	0.492516
23	-0.024923	-0.1727	0.431819
24	-0.077317	-0.5357	0.29733
25	0.014967	0.1037	0.458921
26	0.065143	0.4513	0.326894
27	-0.059816	-0.4144	0.340206
28	0.005381	0.0373	0.485208
29	0.027894	0.1933	0.423787
30	0.039493	0.2736	0.392777
31	0.01673	0.1159	0.454104
32	0.005119	0.0355	0.485927
33	-0.006223	-0.0431	0.482895
34	-0.01366	-0.0946	0.462496
35	0.072225	0.5004	0.309543
36	0.065481	0.4537	0.326057

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.306004	2.1201	0.019599
2	0.139847	0.9689	0.16873
3	-0.006638	-0.046	0.481755
4	0.132892	0.9207	0.180905
5	0.060642	0.4201	0.33813
6	-0.135858	-0.9413	0.175645
7	-0.175979	-1.2192	0.11436
8	-0.33123	-2.2948	0.013079
9	0.134255	0.9301	0.178476
10	-0.083148	-0.5761	0.283631
11	-0.05452	-0.3777	0.35365
12	-0.272682	-1.8892	0.032457
13	-0.008854	-0.0613	0.475671
14	0.012023	0.0833	0.466981
15	-0.006678	-0.0463	0.481646
16	0.078031	0.5406	0.295636
17	0.046395	0.3214	0.37464
18	-0.183538	-1.2716	0.104823
19	0.050372	0.349	0.364313
20	-0.107351	-0.7437	0.230327
21	-0.097078	-0.6726	0.252221
22	-0.076829	-0.5323	0.298492
23	-0.057336	-0.3972	0.346477
24	-0.229265	-1.5884	0.059382
25	-0.024285	-0.1683	0.433545
26	0.072572	0.5028	0.308705
27	-0.020044	-0.1389	0.445068
28	0.097655	0.6766	0.250962
29	0.029509	0.2044	0.419436
30	-0.118073	-0.818	0.20869
31	-0.035688	-0.2473	0.402884
32	-0.104551	-0.7243	0.236184
33	-0.079908	-0.5536	0.291204
34	-0.061626	-0.427	0.33566
35	-0.017582	-0.1218	0.451779
36	-0.05101	-0.3534	0.362665

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259249045u00l76nwd1vpsnl/1fo301259248800.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259249045u00l76nwd1vpsnl/1fo301259248800.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259249045u00l76nwd1vpsnl/2iw411259248800.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259249045u00l76nwd1vpsnl/2iw411259248800.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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