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autocorrelation

*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, 11 Dec 2008 10:20:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229016088dsxicibs4f8x1j0.htm/, Retrieved Thu, 11 Dec 2008 17:21:30 +0000

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/2008/Dec/11/t1229016088dsxicibs4f8x1j0.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

99.5 93.5 104.6 95.3 102.8 103.3 100.2 107.9 107.5 119.8 112 102.1 105.3 101.3 108.4 107.4 109.1 109.5 111.4 110.1 117 129.6 113.5 113.3 110.1 107.4 110.1 112.5 106 117.6 117.8 113.5 121.2 130.4 115.2 117.9 110.7 107.6 124.3 115.1 112.5 127.9 117.4 119.3 130.4 126 125.4 130.5 115.9 108.7 124 119.4 118.6 131.3 111.1 124.8 132.3 126.7 131.7 130.9 122.1 113.2 133.6 119.2 129.4 131.4 117.1 130.5 132.3 140.8 137.5 128.6 126.7 120.8 139.3 128.6 131.3 136.3 128.8 133.2 136.3 151.1 145 134.4

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	0.701961	6.4336	0
2	0.614695	5.6338	0
3	0.598541	5.4857	0
4	0.43451	3.9824	7.2e-05
5	0.49177	4.5071	1.1e-05
6	0.500581	4.5879	8e-06
7	0.400605	3.6716	0.000211
8	0.355458	3.2578	0.00081
9	0.433823	3.9761	7.4e-05
10	0.370498	3.3957	0.000524
11	0.465056	4.2623	2.6e-05
12	0.588586	5.3945	0
13	0.372154	3.4108	0.000499
14	0.34619	3.1729	0.001054
15	0.277169	2.5403	0.006458
16	0.152634	1.3989	0.08276
17	0.227018	2.0807	0.020256
18	0.213137	1.9534	0.027049
19	0.126905	1.1631	0.12404
20	0.118462	1.0857	0.140354
21	0.162319	1.4877	0.07029
22	0.147154	1.3487	0.090531
23	0.25101	2.3005	0.011948
24	0.281755	2.5823	0.005774
25	0.158884	1.4562	0.074533
26	0.147017	1.3474	0.090732
27	0.055489	0.5086	0.306197
28	-0.028338	-0.2597	0.397858
29	0.019401	0.1778	0.429651
30	-0.009566	-0.0877	0.465173
31	-0.041952	-0.3845	0.350792
32	-0.048579	-0.4452	0.328647
33	-0.064397	-0.5902	0.278318
34	-0.027418	-0.2513	0.401102
35	0.037424	0.343	0.36623
36	0.063187	0.5791	0.282031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.701961	6.4336	0
2	0.240406	2.2034	0.015153
3	0.213474	1.9565	0.026863
4	-0.178836	-1.6391	0.052471
5	0.266837	2.4456	0.008275
6	0.106478	0.9759	0.165962
7	-0.069186	-0.6341	0.26387
8	-0.145767	-1.336	0.092583
9	0.340986	3.1252	0.00122
10	-0.046893	-0.4298	0.334227
11	0.25847	2.3689	0.010067
12	0.194031	1.7783	0.039484
13	-0.348998	-3.1986	0.000974
14	-0.180804	-1.6571	0.050615
15	-0.118082	-1.0822	0.141122
16	-0.015626	-0.1432	0.443231
17	0.021023	0.1927	0.423839
18	0.02266	0.2077	0.417991
19	0.009654	0.0885	0.464854
20	-0.027221	-0.2495	0.401796
21	0.079449	0.7282	0.234269
22	0.119247	1.0929	0.138778
23	-0.012648	-0.1159	0.453998
24	-0.093097	-0.8532	0.197974
25	0.025764	0.2361	0.406954
26	-0.066895	-0.6131	0.270732
27	-0.074725	-0.6849	0.247656
28	-0.093882	-0.8604	0.195998
29	-0.005375	-0.0493	0.480413
30	-0.011619	-0.1065	0.457725
31	0.102247	0.9371	0.175695
32	-0.047994	-0.4399	0.330581
33	-0.10161	-0.9313	0.17719
34	0.056691	0.5196	0.302362
35	-0.024744	-0.2268	0.41057
36	0.082432	0.7555	0.22603

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229016088dsxicibs4f8x1j0/1cl0n1229016038.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229016088dsxicibs4f8x1j0/1cl0n1229016038.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229016088dsxicibs4f8x1j0/2rqx71229016038.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229016088dsxicibs4f8x1j0/2rqx71229016038.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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