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*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, 14 Dec 2010 19:12:26 +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/Dec/14/t1292353804nmp8jmx6fcb19fh.htm/, Retrieved Tue, 14 Dec 2010 20:10:04 +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/Dec/14/t1292353804nmp8jmx6fcb19fh.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 «

313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224 275902 271115 277509 279681

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.130396	0.9034	0.185411
2	0.097505	0.6755	0.251288
3	0.34719	2.4054	0.010029
4	0.155395	1.0766	0.143518
5	0.054126	0.375	0.354657
6	0.165951	1.1497	0.127973
7	0.020715	0.1435	0.443241
8	0.17954	1.2439	0.10979
9	-0.017193	-0.1191	0.452841
10	-0.066648	-0.4617	0.323174
11	0.237299	1.6441	0.05335
12	-0.084537	-0.5857	0.280413
13	-0.185509	-1.2852	0.102437
14	0.124535	0.8628	0.196268
15	0.075232	0.5212	0.302305
16	-0.04887	-0.3386	0.368202
17	-0.002517	-0.0174	0.49308
18	-0.068187	-0.4724	0.319388
19	-0.023789	-0.1648	0.434892
20	-0.096883	-0.6712	0.252648
21	-0.208442	-1.4441	0.077599
22	-0.01577	-0.1093	0.456727
23	-0.131757	-0.9128	0.182944
24	-0.177797	-1.2318	0.11201
25	-0.057913	-0.4012	0.345014
26	-0.119087	-0.8251	0.206709
27	-0.269587	-1.8678	0.033954
28	-0.090977	-0.6303	0.265741
29	-0.089692	-0.6214	0.268636
30	-0.112909	-0.7823	0.218952
31	-0.031535	-0.2185	0.41399
32	-0.044422	-0.3078	0.379796
33	-0.04583	-0.3175	0.376114
34	-0.003156	-0.0219	0.491323
35	-0.029417	-0.2038	0.419682
36	-0.043055	-0.2983	0.383382
37	-0.002296	-0.0159	0.493687
38	-0.031201	-0.2162	0.414886
39	-0.00127	-0.0088	0.496508
40	0.023654	0.1639	0.435258
41	-0.017175	-0.119	0.452889
42	-0.010819	-0.075	0.470281
43	0.015375	0.1065	0.457806
44	0.003828	0.0265	0.489475
45	-0.014159	-0.0981	0.461133
46	0.005685	0.0394	0.484372
47	0.005972	0.0414	0.483585
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.130396	0.9034	0.185411
2	0.081895	0.5674	0.286549
3	0.332689	2.3049	0.012769
4	0.087302	0.6048	0.274066
5	-0.014037	-0.0972	0.461467
6	0.041922	0.2904	0.386363
7	-0.086594	-0.5999	0.275684
8	0.173672	1.2032	0.117393
9	-0.130284	-0.9026	0.185614
10	-0.081825	-0.5669	0.286711
11	0.196567	1.3619	0.089801
12	-0.157732	-1.0928	0.139969
13	-0.126467	-0.8762	0.192646
14	0.037748	0.2615	0.397404
15	0.152052	1.0534	0.148705
16	0.052234	0.3619	0.359512
17	-0.091965	-0.6372	0.263526
18	-0.103089	-0.7142	0.239274
19	-0.076919	-0.5329	0.298276
20	-0.038735	-0.2684	0.394786
21	-0.128454	-0.89	0.188965
22	-0.039694	-0.275	0.392246
23	-0.052354	-0.3627	0.359203
24	0.050989	0.3533	0.36272
25	-0.04511	-0.3125	0.377996
26	-0.116848	-0.8095	0.211099
27	-0.154146	-1.068	0.145442
28	0.052068	0.3607	0.359939
29	0.093048	0.6447	0.261111
30	-0.047439	-0.3287	0.371918
31	0.036983	0.2562	0.399435
32	0.054634	0.3785	0.353358
33	-0.014803	-0.1026	0.459371
34	-0.010125	-0.0701	0.472183
35	0.014381	0.0996	0.460525
36	-0.029289	-0.2029	0.420027
37	0.019475	0.1349	0.446616
38	0.041569	0.288	0.387294
39	-0.087009	-0.6028	0.274734
40	-0.049435	-0.3425	0.366737
41	0.043353	0.3004	0.3826
42	0.024425	0.1692	0.433168
43	-0.019359	-0.1341	0.446934
44	-0.009293	-0.0644	0.474466
45	-0.046592	-0.3228	0.374125
46	-0.063021	-0.4366	0.332171
47	-0.034639	-0.24	0.405681
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292353804nmp8jmx6fcb19fh/11fvk1292353942.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292353804nmp8jmx6fcb19fh/11fvk1292353942.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292353804nmp8jmx6fcb19fh/21fvk1292353942.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292353804nmp8jmx6fcb19fh/21fvk1292353942.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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