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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: Tue, 24 Nov 2009 05:54:58 -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/24/t1259067355g77nan4lv4x4vo9.htm/, Retrieved Tue, 24 Nov 2009 13:55:57 +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/24/t1259067355g77nan4lv4x4vo9.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 «

149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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	0.78768	6.1013	0
2	0.482187	3.735	0.00021
3	0.238128	1.8445	0.035022
4	0.123414	0.956	0.171463
5	0.099806	0.7731	0.221251
6	0.095929	0.7431	0.230171
7	0.090576	0.7016	0.242821
8	0.112325	0.8701	0.193867
9	0.225863	1.7495	0.042657
10	0.366944	2.8423	0.003056
11	0.536954	4.1592	5.2e-05
12	0.604123	4.6795	8e-06
13	0.401545	3.1104	0.001429
14	0.137511	1.0652	0.145537
15	-0.069677	-0.5397	0.295694
16	-0.160392	-1.2424	0.109464
17	-0.180628	-1.3991	0.08346
18	-0.187778	-1.4545	0.075507
19	-0.204116	-1.5811	0.05956
20	-0.196076	-1.5188	0.067033
21	-0.112975	-0.8751	0.192505
22	-0.011848	-0.0918	0.463591
23	0.113782	0.8814	0.190822
24	0.156145	1.2095	0.115609
25	0.013073	0.1013	0.459839
26	-0.162759	-1.2607	0.106144
27	-0.283114	-2.193	0.016098
28	-0.330943	-2.5635	0.006444
29	-0.332708	-2.5771	0.006219
30	-0.330255	-2.5581	0.006533
31	-0.329638	-2.5534	0.006614
32	-0.302825	-2.3457	0.011158
33	-0.213327	-1.6524	0.051836
34	-0.12364	-0.9577	0.171025
35	-0.028492	-0.2207	0.413037
36	0.015464	0.1198	0.452527

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.78768	6.1013	0
2	-0.364242	-2.8214	0.003237
3	0.020907	0.1619	0.435947
4	0.108519	0.8406	0.201958
5	0.029793	0.2308	0.409138
6	-0.027943	-0.2164	0.414686
7	0.028623	0.2217	0.412644
8	0.114429	0.8864	0.189481
9	0.278449	2.1569	0.017517
10	0.113831	0.8817	0.190719
11	0.342627	2.654	0.005084
12	0.020534	0.1591	0.437081
13	-0.522239	-4.0452	7.6e-05
14	0.067079	0.5196	0.30263
15	-0.100243	-0.7765	0.220258
16	-0.165914	-1.2852	0.101836
17	-0.068853	-0.5333	0.297887
18	-0.147469	-1.1423	0.128935
19	-0.084665	-0.6558	0.257225
20	-0.172882	-1.3391	0.092789
21	-0.102688	-0.7954	0.214753
22	0.032491	0.2517	0.401076
23	-0.030141	-0.2335	0.408095
24	0.044124	0.3418	0.366854
25	-0.020196	-0.1564	0.438106
26	0.11896	0.9215	0.18025
27	0.112473	0.8712	0.193555
28	-0.08828	-0.6838	0.248362
29	0.124467	0.9641	0.169429
30	0.019304	0.1495	0.44082
31	0.018706	0.1449	0.442639
32	0.014761	0.1143	0.454675
33	-0.021305	-0.165	0.434737
34	-0.01624	-0.1258	0.450156
35	-0.136014	-1.0536	0.148154
36	0.016924	0.1311	0.448071

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067355g77nan4lv4x4vo9/13lr01259067296.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067355g77nan4lv4x4vo9/13lr01259067296.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067355g77nan4lv4x4vo9/2v0if1259067296.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067355g77nan4lv4x4vo9/2v0if1259067296.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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