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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: Wed, 09 Dec 2009 13:01:36 -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/09/t12603889512pddu3xu6j9123g.htm/, Retrieved Wed, 09 Dec 2009 21:02:33 +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/09/t12603889512pddu3xu6j9123g.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 «

595 591 612 595 597 589 584 573 567 569 621 629 628 593 588 566 557 590 580 574 573 573 620 626 620 561 527 510 514 549 532 526 511 499 555 565 542 517 506 502 516 508 493 490 469 478 528 534 518 528 533 536 537 524 536 587 597 581 564 558

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	0.863757	5.9843	0
2	0.666427	4.6171	1.5e-05
3	0.492743	3.4138	0.000655
4	0.384335	2.6628	0.005258
5	0.351234	2.4334	0.009365
6	0.289213	2.0037	0.025381
7	0.203361	1.4089	0.082651
8	0.11509	0.7974	0.214582
9	0.054529	0.3778	0.353626
10	0.0352	0.2439	0.404185
11	0.002827	0.0196	0.492229
12	-0.062096	-0.4302	0.334483
13	-0.136927	-0.9487	0.173773
14	-0.160091	-1.1091	0.136448
15	-0.137015	-0.9493	0.173619
16	-0.09573	-0.6632	0.255177
17	-0.091671	-0.6351	0.264185
18	-0.148678	-1.0301	0.154069
19	-0.224347	-1.5543	0.063338
20	-0.295237	-2.0455	0.023156
21	-0.346179	-2.3984	0.010201
22	-0.374428	-2.5941	0.006269
23	-0.403139	-2.793	0.003739
24	-0.394341	-2.7321	0.004391
25	-0.317958	-2.2029	0.016219
26	-0.249332	-1.7274	0.045261
27	-0.200068	-1.3861	0.086059
28	-0.181145	-1.255	0.107775
29	-0.200149	-1.3867	0.085974
30	-0.168217	-1.1654	0.124799
31	-0.10507	-0.7279	0.235092
32	-0.033458	-0.2318	0.408837
33	0.014815	0.1026	0.459338
34	0.032237	0.2233	0.412106
35	0.036514	0.253	0.400684
36	0.045869	0.3178	0.376011
37	0.059752	0.414	0.34037
38	0.050749	0.3516	0.363338
39	0.016262	0.1127	0.455382
40	-0.03105	-0.2151	0.415291
41	-0.049576	-0.3435	0.366371
42	-0.01166	-0.0808	0.467975
43	0.034397	0.2383	0.406327
44	0.068567	0.475	0.318454
45	0.055846	0.3869	0.350265
46	0.027218	0.1886	0.425611
47	0.01662	0.1151	0.454404
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	0.863757	5.9843	0
2	-0.31367	-2.1732	0.017367
3	0.03271	0.2266	0.41084
4	0.112321	0.7782	0.220139
5	0.145789	1.0101	0.158767
6	-0.256106	-1.7744	0.041173
7	-0.013758	-0.0953	0.462229
8	0.006101	0.0423	0.483229
9	0.043975	0.3047	0.380968
10	-0.025834	-0.179	0.429352
11	-0.126419	-0.8759	0.192735
12	-0.104147	-0.7216	0.237035
13	0.001193	0.0083	0.496721
14	0.158958	1.1013	0.13813
15	-0.044582	-0.3089	0.379378
16	-0.009677	-0.067	0.473411
17	-0.109072	-0.7557	0.226769
18	-0.095943	-0.6647	0.254708
19	-0.084721	-0.587	0.279988
20	-0.120311	-0.8335	0.204335
21	-0.133011	-0.9215	0.180691
22	-0.023802	-0.1649	0.434855
23	-0.038933	-0.2697	0.39426
24	0.106602	0.7386	0.231886
25	0.196314	1.3601	0.090076
26	-0.193528	-1.3408	0.093148
27	-0.018082	-0.1253	0.450414
28	0.05409	0.3747	0.354749
29	-0.089917	-0.623	0.268129
30	0.111742	0.7742	0.221312
31	-0.013885	-0.0962	0.461882
32	-0.04086	-0.2831	0.389164
33	-0.052164	-0.3614	0.359692
34	0.121691	0.8431	0.201677
35	-0.130592	-0.9048	0.185053
36	-0.005143	-0.0356	0.485863
37	0.024572	0.1702	0.43277
38	-0.0341	-0.2363	0.40712
39	-0.072315	-0.501	0.309325
40	-0.069917	-0.4844	0.315153
41	-0.039742	-0.2753	0.392119
42	0.036391	0.2521	0.40101
43	0.006273	0.0435	0.482756
44	-0.03305	-0.229	0.409931
45	-0.048589	-0.3366	0.36893
46	0.027346	0.1895	0.425265
47	-0.04237	-0.2935	0.385186
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/2009/Dec/09/t12603889512pddu3xu6j9123g/1mv2b1260388895.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t12603889512pddu3xu6j9123g/1mv2b1260388895.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t12603889512pddu3xu6j9123g/2e3hf1260388895.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t12603889512pddu3xu6j9123g/2e3hf1260388895.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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