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Earthquakes/year magnitude >= 7.0 1900 - 1998

*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 03 May 2010 13:07:25 +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/May/03/t1272892198i5h13m7szlm5oev.htm/, Retrieved Mon, 03 May 2010 15:10:00 +0200

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/May/03/t1272892198i5h13m7szlm5oev.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

13 14 8 10 16 26 32 27 18 32 36 24 22 23 22 18 25 21 21 14 8 11 14 23 18 17 19 20 22 19 13 26 13 14 22 24 21 22 26 21 23 24 27 41 31 27 35 26 28 36 39 21 17 22 17 19 15 34 10 15 22 18 15 20 15 22 19 16 30 27 29 23 20 16 21 21 25 16 18 15 18 14 10 15 8 15 6 11 8 7 13 10 23 16 15 25 22 20 16

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	0.541733	5.3902	0
2	0.418884	4.1678	3.3e-05
3	0.397955	3.9596	7.1e-05
4	0.324047	3.2242	0.000856
5	0.237164	2.3598	0.010124
6	0.171794	1.7093	0.045261
7	0.190228	1.8927	0.030656
8	0.061202	0.609	0.271976
9	-0.048505	-0.4826	0.315214
10	-0.10673	-1.062	0.14542
11	-0.043271	-0.4305	0.333867
12	-0.072305	-0.7194	0.236787
13	-0.126124	-1.2549	0.106232
14	-0.144314	-1.4359	0.077091
15	-0.129653	-1.29	0.100023
16	-0.187901	-1.8696	0.032248
17	-0.098558	-0.9806	0.16458
18	-0.067436	-0.671	0.251897
19	0.027725	0.2759	0.391616
20	-0.03228	-0.3212	0.374374
21	-0.034463	-0.3429	0.366201
22	0.013843	0.1377	0.445365
23	-0.087323	-0.8688	0.193516
24	-0.049589	-0.4934	0.31141
25	0.039769	0.3957	0.346589
26	0.108795	1.0825	0.140831
27	0.035289	0.3511	0.363121
28	0.029498	0.2935	0.384876
29	-0.010111	-0.1006	0.460034
30	0.04794	0.477	0.317209
31	0.02474	0.2462	0.403033
32	0.075812	0.7543	0.226223
33	0.075394	0.7502	0.227468
34	0.037854	0.3766	0.353623
35	-0.03063	-0.3048	0.380591
36	-0.070847	-0.7049	0.241257
37	-0.040108	-0.3991	0.345349
38	-0.111095	-1.1054	0.135836
39	-0.098105	-0.9761	0.16569
40	-0.13255	-1.3189	0.09513
41	-0.219039	-2.1794	0.015837
42	-0.221483	-2.2037	0.014931
43	-0.209096	-2.0805	0.020032
44	-0.200894	-1.9989	0.024182
45	-0.212468	-2.114	0.018513
46	-0.235451	-2.3427	0.010573
47	-0.175829	-1.7495	0.041654
48	-0.231121	-2.2996	0.011785

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.541733	5.3902	0
2	0.177502	1.7661	0.040229
3	0.168286	1.6744	0.048601
4	0.036858	0.3667	0.357299
5	-0.028418	-0.2828	0.388978
6	-0.039018	-0.3882	0.349341
7	0.072425	0.7206	0.236422
8	-0.134489	-1.3382	0.091956
9	-0.138835	-1.3814	0.085134
10	-0.111345	-1.1079	0.1353
11	0.101962	1.0145	0.156406
12	0.009349	0.093	0.463039
13	-0.042787	-0.4257	0.335617
14	-0.075045	-0.7467	0.228512
15	0.010133	0.1008	0.459948
16	-0.07595	-0.7557	0.225814
17	0.14135	1.4064	0.081366
18	-0.01112	-0.1106	0.456062
19	0.143534	1.4281	0.078199
20	-0.101563	-1.0105	0.157351
21	0.009397	0.0935	0.462848
22	-0.015673	-0.1559	0.438199
23	-0.15387	-1.531	0.064481
24	-0.028139	-0.28	0.390039
25	0.134512	1.3384	0.09192
26	0.10686	1.0632	0.145128
27	-0.004211	-0.0419	0.483331
28	-0.034831	-0.3466	0.364827
29	-0.117545	-1.1696	0.122494
30	0.083384	0.8297	0.204365
31	-0.005067	-0.0504	0.479944
32	0.087165	0.8673	0.193943
33	-0.041281	-0.4107	0.341074
34	-0.001035	-0.0103	0.495904
35	-0.048352	-0.4811	0.315754
36	-0.08985	-0.894	0.186745
37	-0.065834	-0.655	0.256979
38	-0.12496	-1.2433	0.108339
39	-0.010127	-0.1008	0.459972
40	0.041995	0.4178	0.338484
41	-0.12493	-1.243	0.108394
42	0.059182	0.5889	0.278649
43	-0.057907	-0.5762	0.282905
44	-0.032982	-0.3282	0.37174
45	-0.0895	-0.8905	0.187675
46	-0.053524	-0.5326	0.297766
47	0.016935	0.1685	0.433265
48	-0.030449	-0.303	0.381275

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/03/t1272892198i5h13m7szlm5oev/1huk41272892044.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272892198i5h13m7szlm5oev/1huk41272892044.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272892198i5h13m7szlm5oev/2rl1p1272892044.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272892198i5h13m7szlm5oev/2rl1p1272892044.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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