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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: Mon, 28 Dec 2009 05:35:39 -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/28/t12620037813f1bo82ywn09cbg.htm/, Retrieved Mon, 28 Dec 2009 13:36:24 +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/28/t12620037813f1bo82ywn09cbg.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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.744286	6.3155	0
2	0.657496	5.579	0
3	0.698467	5.9267	0
4	0.611673	5.1902	1e-06
5	0.607899	5.1582	1e-06
6	0.658671	5.589	0
7	0.531821	4.5127	1.2e-05
8	0.502764	4.2661	3e-05
9	0.533029	4.5229	1.2e-05
10	0.403917	3.4274	0.000506
11	0.454479	3.8564	0.000124
12	0.566687	4.8085	4e-06
13	0.392498	3.3305	0.000685
14	0.346869	2.9433	0.002184
15	0.351265	2.9806	0.001961
16	0.272087	2.3087	0.011916
17	0.295656	2.5087	0.007185
18	0.318683	2.7041	0.00427
19	0.214996	1.8243	0.036128
20	0.18485	1.5685	0.060574
21	0.182289	1.5468	0.063152
22	0.050599	0.4293	0.334478
23	0.109397	0.9283	0.178186
24	0.122051	1.0356	0.151919
25	-0.013604	-0.1154	0.454211
26	-0.063392	-0.5379	0.296153
27	-0.06721	-0.5703	0.285125
28	-0.130814	-1.11	0.135347
29	-0.106111	-0.9004	0.185459
30	-0.095292	-0.8086	0.21071
31	-0.160009	-1.3577	0.089396
32	-0.163193	-1.3847	0.085205
33	-0.201179	-1.7071	0.04606
34	-0.263021	-2.2318	0.01437
35	-0.203263	-1.7247	0.044432
36	-0.178757	-1.5168	0.066847
37	-0.251274	-2.1321	0.018204
38	-0.29236	-2.4808	0.007724
39	-0.29775	-2.5265	0.00686
40	-0.321558	-2.7285	0.003995
41	-0.306665	-2.6021	0.00562
42	-0.298041	-2.529	0.006816
43	-0.340368	-2.8881	0.002558
44	-0.329739	-2.7979	0.003297
45	-0.358635	-3.0431	0.001634
46	-0.394553	-3.3479	0.000649
47	-0.357494	-3.0334	0.001681
48	-0.307419	-2.6085	0.005525
49	-0.334535	-2.8386	0.002942
50	-0.358943	-3.0457	0.001621
51	-0.331838	-2.8157	0.003137
52	-0.326213	-2.768	0.003583
53	-0.284025	-2.41	0.009254
54	-0.257841	-2.1878	0.015964
55	-0.259683	-2.2035	0.01538
56	-0.253545	-2.1514	0.0174
57	-0.2537	-2.1527	0.017346
58	-0.248581	-2.1093	0.019199
59	-0.226034	-1.918	0.029541
60	-0.201194	-1.7072	0.046048

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.744286	6.3155	0
2	0.232119	1.9696	0.026366
3	0.355279	3.0146	0.001776
4	-0.036499	-0.3097	0.37884
5	0.16732	1.4198	0.079997
6	0.187553	1.5914	0.057946
7	-0.191795	-1.6274	0.054006
8	0.012501	0.1061	0.457908
9	0.034361	0.2916	0.385729
10	-0.203395	-1.7259	0.044331
11	0.214469	1.8198	0.036471
12	0.271788	2.3062	0.011991
13	-0.303719	-2.5771	0.006005
14	-0.086454	-0.7336	0.232791
15	-0.103103	-0.8749	0.192279
16	0.023612	0.2004	0.420882
17	0.012843	0.109	0.456762
18	-0.032932	-0.2794	0.390354
19	0.046436	0.394	0.347364
20	-0.138066	-1.1715	0.122625
21	-0.041329	-0.3507	0.363424
22	-0.099838	-0.8472	0.199858
23	0.063223	0.5365	0.296646
24	-0.145948	-1.2384	0.109794
25	-0.088447	-0.7505	0.2277
26	-0.127346	-1.0806	0.141748
27	0.058082	0.4928	0.311812
28	0.006285	0.0533	0.478808
29	-0.013529	-0.1148	0.454464
30	0.023141	0.1964	0.42244
31	0.047507	0.4031	0.344031
32	-0.023696	-0.2011	0.420606
33	-0.11723	-0.9947	0.161601
34	0.088656	0.7523	0.22717
35	-0.036112	-0.3064	0.380084
36	0.079049	0.6708	0.252261
37	-0.017808	-0.1511	0.440159
38	-0.064063	-0.5436	0.294201
39	-0.001279	-0.0109	0.495685
40	-0.031404	-0.2665	0.395319
41	-0.041888	-0.3554	0.361654
42	0.000291	0.0025	0.49902
43	-0.047237	-0.4008	0.344871
44	0.027452	0.2329	0.408236
45	0.030033	0.2548	0.399788
46	-0.082988	-0.7042	0.241797
47	0.013628	0.1156	0.45413
48	0.010902	0.0925	0.463276
49	0.035891	0.3045	0.380796
50	-0.049627	-0.4211	0.337469
51	0.067086	0.5692	0.285482
52	0.016577	0.1407	0.444265
53	0.049664	0.4214	0.337355
54	-0.01926	-0.1634	0.43532
55	0.027158	0.2304	0.409202
56	-0.022877	-0.1941	0.423317
57	-0.039553	-0.3356	0.369067
58	0.080999	0.6873	0.247051
59	-0.069062	-0.586	0.279849
60	-0.105631	-0.8963	0.186538

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620037813f1bo82ywn09cbg/1totp1262003735.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620037813f1bo82ywn09cbg/1totp1262003735.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620037813f1bo82ywn09cbg/2vh651262003735.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620037813f1bo82ywn09cbg/2vh651262003735.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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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