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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 12:41:34 -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/t1259264584yp1vh4zi1fe3jws.htm/, Retrieved Thu, 26 Nov 2009 20:43:06 +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/t1259264584yp1vh4zi1fe3jws.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 «

115.6 111.9 107 107.1 100.6 99.2 108.4 103 99.8 115 90.8 95.9 114.4 108.2 112.6 109.1 105 105 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 104.1 105.3 115 124.1 116.8 107.5 115.6 116.2 116.3 119 111.9 118.6 106.9 103.2 118.6 118.7 102.8 100.6 94.9 94.5 102.9 95.3 92.5 102.7 91.5 89.5

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	-0.587493	-4.0277	0.000102
2	0.037867	0.2596	0.398152
3	0.378974	2.5981	0.00624
4	-0.352982	-2.4199	0.009722
5	0.097555	0.6688	0.253447
6	0.156668	1.0741	0.14414
7	-0.294751	-2.0207	0.024514
8	0.229261	1.5717	0.06136
9	-0.139567	-0.9568	0.171776
10	-0.024425	-0.1674	0.433868
11	0.146856	1.0068	0.159595
12	-0.17713	-1.2143	0.115341
13	0.061184	0.4195	0.338396
14	0.035361	0.2424	0.404755
15	-0.006887	-0.0472	0.481272
16	-0.067177	-0.4605	0.323625
17	0.080106	0.5492	0.29274
18	0.017112	0.1173	0.453555
19	-0.132471	-0.9082	0.18421
20	0.135896	0.9317	0.178138
21	0.042626	0.2922	0.385698
22	-0.31593	-2.1659	0.017712
23	0.41231	2.8267	0.003444
24	-0.243685	-1.6706	0.050722
25	-0.018048	-0.1237	0.451027
26	0.203413	1.3945	0.084858
27	-0.181775	-1.2462	0.109435
28	0.011664	0.08	0.468302
29	0.151025	1.0354	0.152896
30	-0.202688	-1.3896	0.085606
31	0.159215	1.0915	0.140303
32	-0.079328	-0.5438	0.29456
33	-0.056994	-0.3907	0.348881
34	0.134241	0.9203	0.181055
35	-0.150019	-1.0285	0.154495
36	0.013398	0.0919	0.463602

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.587493	-4.0277	0.000102
2	-0.469239	-3.2169	0.001174
3	0.266291	1.8256	0.037134
4	0.194523	1.3336	0.094384
5	-0.02075	-0.1423	0.443742
6	-0.009804	-0.0672	0.473348
7	-0.176653	-1.2111	0.115961
8	-0.008958	-0.0614	0.475644
9	-0.156336	-1.0718	0.144644
10	-0.076566	-0.5249	0.301057
11	0.088489	0.6066	0.273502
12	0.051099	0.3503	0.363832
13	-0.053231	-0.3649	0.358399
14	-0.165029	-1.1314	0.131818
15	0.156215	1.071	0.144829
16	-0.002087	-0.0143	0.494322
17	-0.06514	-0.4466	0.328615
18	0.042483	0.2913	0.386071
19	-0.066013	-0.4526	0.326472
20	-0.015341	-0.1052	0.458343
21	0.132777	0.9103	0.183662
22	-0.267241	-1.8321	0.036638
23	0.056783	0.3893	0.349411
24	0.076587	0.5251	0.301006
25	0.115587	0.7924	0.216048
26	-0.042758	-0.2931	0.385355
27	0.036616	0.251	0.401444
28	-0.05753	-0.3944	0.347532
29	-0.089211	-0.6116	0.271874
30	0.017612	0.1207	0.452204
31	0.040178	0.2754	0.392091
32	-0.004854	-0.0333	0.486797
33	-0.0444	-0.3044	0.381087
34	-0.080001	-0.5485	0.292987
35	-0.095404	-0.6541	0.258131
36	-0.101556	-0.6962	0.244857

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264584yp1vh4zi1fe3jws/1gy601259264492.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264584yp1vh4zi1fe3jws/1gy601259264492.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264584yp1vh4zi1fe3jws/2bqq41259264492.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264584yp1vh4zi1fe3jws/2bqq41259264492.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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