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Workshop 8 ACF

*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: Mon, 29 Nov 2010 17:48:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t1291052824iey9lpal9wxgwl8.htm/, Retrieved Mon, 29 Nov 2010 18:47:04 +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/2010/Nov/29/t1291052824iey9lpal9wxgwl8.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

58608 46865 51378 46235 47206 45382 41227 33795 31295 42625 33625 21538 56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.386463	2.9935	0.002
2	0.151367	1.1725	0.122819
3	0.060957	0.4722	0.319258
4	-0.175153	-1.3567	0.089976
5	-0.263012	-2.0373	0.02302
6	-0.419162	-3.2468	0.000956
7	-0.329088	-2.5491	0.006687
8	-0.21567	-1.6706	0.050008
9	-0.057349	-0.4442	0.32924
10	0.006996	0.0542	0.478481
11	0.205671	1.5931	0.058194
12	0.706953	5.476	0
13	0.297203	2.3021	0.012407
14	0.121857	0.9439	0.174502
15	0.043034	0.3333	0.370019
16	-0.178412	-1.382	0.086052
17	-0.228253	-1.768	0.041069
18	-0.356357	-2.7603	0.003824
19	-0.297509	-2.3045	0.012336
20	-0.177617	-1.3758	0.086997
21	-0.115162	-0.892	0.187967
22	-0.067331	-0.5215	0.301954
23	0.115214	0.8924	0.187861
24	0.483622	3.7461	0.000203
25	0.211873	1.6412	0.052998
26	0.096329	0.7462	0.229243
27	0.001007	0.0078	0.496901
28	-0.130383	-1.0099	0.158289
29	-0.146713	-1.1364	0.130146
30	-0.275562	-2.1345	0.018449
31	-0.195594	-1.5151	0.067503
32	-0.085884	-0.6653	0.254219
33	-0.022774	-0.1764	0.430284
34	0.006754	0.0523	0.479226
35	0.100662	0.7797	0.219309
36	0.366443	2.8385	0.003089

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.386463	2.9935	0.002
2	0.002366	0.0183	0.49272
3	0.00198	0.0153	0.493909
4	-0.23472	-1.8181	0.037018
5	-0.147813	-1.145	0.128387
6	-0.31246	-2.4203	0.009276
7	-0.075135	-0.582	0.281375
8	-0.092957	-0.72	0.237147
9	0.045383	0.3515	0.363208
10	-0.120403	-0.9326	0.177373
11	0.13724	1.0631	0.146009
12	0.628184	4.8659	4e-06
13	-0.320532	-2.4828	0.007924
14	-0.117408	-0.9094	0.183379
15	-0.119305	-0.9241	0.17956
16	-0.040783	-0.3159	0.376586
17	-0.043686	-0.3384	0.368125
18	0.082801	0.6414	0.261861
19	0.01617	0.1253	0.45037
20	-0.018777	-0.1454	0.442423
21	-0.155402	-1.2037	0.116709
22	-0.047919	-0.3712	0.355906
23	0.000448	0.0035	0.49862
24	-0.08481	-0.6569	0.256866
25	-0.068528	-0.5308	0.298753
26	-0.020034	-0.1552	0.4386
27	-0.148622	-1.1512	0.127104
28	0.078794	0.6103	0.271972
29	0.014266	0.1105	0.456188
30	-0.063269	-0.4901	0.312933
31	0.014375	0.1113	0.455857
32	-0.03505	-0.2715	0.393469
33	0.138501	1.0728	0.143823
34	0.033403	0.2587	0.39836
35	-0.097521	-0.7554	0.226483
36	-0.02175	-0.1685	0.433389

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291052824iey9lpal9wxgwl8/1ism31291052921.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291052824iey9lpal9wxgwl8/1ism31291052921.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291052824iey9lpal9wxgwl8/2ism31291052921.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291052824iey9lpal9wxgwl8/2ism31291052921.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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