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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: Tue, 29 Dec 2009 01:06:59 -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/Dec/29/t1262074129lvr849qyq6r3zhd.htm/, Retrieved Tue, 29 Dec 2009 09:08:51 +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/Dec/29/t1262074129lvr849qyq6r3zhd.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 «

13.4 13.5 14.8 14.3 14.3 14 13.2 12.2 14.3 15.7 14.2 14.6 14.5 14.3 15.3 14.4 13.7 14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.266431	2.0638	0.021687
2	0.350379	2.714	0.004333
3	0.469478	3.6366	0.000288
4	0.137651	1.0662	0.145294
5	0.119596	0.9264	0.178978
6	0.178003	1.3788	0.086536
7	-0.123993	-0.9604	0.170342
8	0.025451	0.1971	0.422191
9	-0.009812	-0.076	0.469834
10	-0.229403	-1.7769	0.040323
11	-0.120402	-0.9326	0.177375
12	-0.213995	-1.6576	0.051309
13	-0.206915	-1.6028	0.05712
14	-0.040913	-0.3169	0.376204
15	-0.162193	-1.2563	0.106931
16	-0.129273	-1.0013	0.160341
17	0.095738	0.7416	0.230617
18	-0.022176	-0.1718	0.432097
19	-0.014065	-0.1089	0.456805
20	7.2e-05	6e-04	0.499777
21	0.047948	0.3714	0.355823
22	-0.128974	-0.999	0.160896
23	0.042538	0.3295	0.371465
24	-0.181668	-1.4072	0.082265
25	-0.187264	-1.4505	0.076058
26	-0.047563	-0.3684	0.356927
27	-0.21409	-1.6583	0.051235
28	-0.181903	-1.409	0.081996
29	-0.09562	-0.7407	0.230891
30	-0.217551	-1.6851	0.048578
31	-0.104966	-0.8131	0.209698
32	-0.057769	-0.4475	0.328071
33	-0.209774	-1.6249	0.054713
34	0.018629	0.1443	0.442873
35	0.095955	0.7433	0.230112
36	-0.011427	-0.0885	0.464881
37	0.1891	1.4648	0.074103
38	0.119908	0.9288	0.178355
39	0.088581	0.6861	0.247632
40	0.232543	1.8013	0.038343
41	0.066396	0.5143	0.304465
42	0.074182	0.5746	0.283852
43	0.14502	1.1233	0.132888
44	0.068093	0.5274	0.299916
45	0.039615	0.3069	0.380007
46	0.042922	0.3325	0.370346
47	-0.032757	-0.2537	0.400284
48	-0.031866	-0.2468	0.402941
49	-0.041099	-0.3184	0.375662
50	-0.093815	-0.7267	0.235121
51	-0.057882	-0.4484	0.327756
52	-0.048848	-0.3784	0.353243
53	-0.062099	-0.481	0.316128
54	-0.04864	-0.3768	0.353839
55	-0.045442	-0.352	0.363039
56	-0.026528	-0.2055	0.418945
57	-0.010165	-0.0787	0.468752
58	-0.003601	-0.0279	0.48892
59	0.000222	0.0017	0.499318
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.266431	2.0638	0.021687
2	0.300742	2.3295	0.011607
3	0.383524	2.9708	0.002134
4	-0.108485	-0.8403	0.202032
5	-0.173256	-1.342	0.09232
6	-0.006563	-0.0508	0.479814
7	-0.197164	-1.5272	0.06598
8	0.052844	0.4093	0.34188
9	0.035751	0.2769	0.391393
10	-0.139951	-1.0841	0.141338
11	-0.117233	-0.9081	0.183734
12	-0.16523	-1.2799	0.102759
13	0.078961	0.6116	0.271546
14	0.217739	1.6866	0.048437
15	0.032921	0.255	0.399797
16	-0.097013	-0.7515	0.227657
17	0.052339	0.4054	0.343308
18	0.068651	0.5318	0.298425
19	-0.034647	-0.2684	0.394665
20	-0.20189	-1.5638	0.061558
21	0.075227	0.5827	0.281137
22	-0.251844	-1.9508	0.027879
23	0.018726	0.1451	0.442578
24	-0.194417	-1.5059	0.068663
25	-0.111096	-0.8605	0.196457
26	0.11218	0.8689	0.19417
27	-0.06658	-0.5157	0.303971
28	0.087379	0.6768	0.250555
29	0.000368	0.0028	0.498868
30	-0.053992	-0.4182	0.33864
31	-0.016576	-0.1284	0.449131
32	-0.057988	-0.4492	0.327461
33	-0.021373	-0.1656	0.434531
34	-0.007441	-0.0576	0.477116
35	0.091552	0.7092	0.240486
36	0.029041	0.2249	0.411392
37	0.001976	0.0153	0.493921
38	-0.067313	-0.5214	0.302001
39	-0.00705	-0.0546	0.478315
40	0.003748	0.029	0.488468
41	0.061391	0.4755	0.318068
42	-0.042615	-0.3301	0.37124
43	0.006529	0.0506	0.479918
44	-0.029084	-0.2253	0.411261
45	-0.015872	-0.1229	0.451281
46	-0.040068	-0.3104	0.37868
47	0.003761	0.0291	0.488429
48	-0.007244	-0.0561	0.477721
49	-0.121706	-0.9427	0.1748
50	0.035596	0.2757	0.391852
51	0.030298	0.2347	0.407625
52	-0.029538	-0.2288	0.409902
53	-0.055467	-0.4296	0.334497
54	-0.095576	-0.7403	0.230993
55	-0.011919	-0.0923	0.463373
56	0.028864	0.2236	0.411923
57	0.001362	0.0106	0.495808
58	-0.081056	-0.6279	0.26624
59	0.079529	0.616	0.270102
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262074129lvr849qyq6r3zhd/1fziv1262074017.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262074129lvr849qyq6r3zhd/1fziv1262074017.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262074129lvr849qyq6r3zhd/2nr901262074017.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262074129lvr849qyq6r3zhd/2nr901262074017.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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