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(Partial) Autocorrelation Function

*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: Sun, 21 Dec 2008 11:15:18 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229883765tukwhy5d370ofls.htm/, Retrieved Sun, 21 Dec 2008 19:22:45 +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/2008/Dec/21/t1229883765tukwhy5d370ofls.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

357 363 364 363 358 357 357 380 378 376 380 379 384 392 394 392 396 392 396 419 421 420 418 410 418 426 428 430 424 423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397

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	-0.007413	-0.0625	0.475185
2	0.080144	0.6753	0.250837
3	0.126137	1.0628	0.145726
4	0.004399	0.0371	0.485268
5	0.091455	0.7706	0.221746
6	0.042037	0.3542	0.362115
7	-0.03437	-0.2896	0.386479
8	0.163981	1.3817	0.085693
9	-0.025478	-0.2147	0.415316
10	-0.195745	-1.6494	0.051744
11	0.123335	1.0392	0.151109
12	-0.247977	-2.0895	0.020124
13	-0.071944	-0.6062	0.273154
14	0.12432	1.0475	0.149202
15	0.031388	0.2645	0.396089
16	0.041724	0.3516	0.363099
17	-0.066024	-0.5563	0.289868
18	0.053562	0.4513	0.326566
19	0.077074	0.6494	0.259077
20	-0.003528	-0.0297	0.488183
21	-0.048004	-0.4045	0.343536
22	-0.001975	-0.0166	0.493386
23	0.064773	0.5458	0.293461
24	-0.165297	-1.3928	0.08401
25	-0.103372	-0.871	0.193338
26	-0.173424	-1.4613	0.074173
27	0.016454	0.1386	0.445061
28	-0.120764	-1.0176	0.156167
29	0.029747	0.2506	0.401405
30	-0.112873	-0.9511	0.172393
31	-0.091287	-0.7692	0.222163
32	-0.099358	-0.8372	0.202643
33	-0.059026	-0.4974	0.310235
34	0.001336	0.0113	0.495524
35	0.044981	0.379	0.352902
36	-0.016821	-0.1417	0.443845
37	-0.029738	-0.2506	0.401432
38	0.106469	0.8971	0.186342
39	-0.146294	-1.2327	0.110878
40	0.029462	0.2483	0.402327
41	0.001771	0.0149	0.494068
42	-0.112996	-0.9521	0.172132
43	0.076508	0.6447	0.26061
44	-0.026431	-0.2227	0.412201
45	-0.093653	-0.7891	0.216331
46	0.031691	0.267	0.395108
47	-0.091495	-0.771	0.221646
48	-0.010046	-0.0846	0.46639
49	0.062701	0.5283	0.299459
50	-0.103806	-0.8747	0.192347
51	0.07411	0.6245	0.267162
52	0.02436	0.2053	0.418977
53	-0.085392	-0.7195	0.23709
54	0.116895	0.985	0.163991
55	-0.058128	-0.4898	0.312894
56	0.006628	0.0558	0.47781
57	0.048674	0.4101	0.341472
58	0.036258	0.3055	0.380435
59	0.006182	0.0521	0.4793
60	0.012807	0.1079	0.457183

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.007413	-0.0625	0.475185
2	0.080094	0.6749	0.250971
3	0.128106	1.0794	0.142022
4	0.001037	0.0087	0.496525
5	0.072724	0.6128	0.270988
6	0.029052	0.2448	0.403661
7	-0.047667	-0.4016	0.344575
8	0.141435	1.1917	0.118664
9	-0.025264	-0.2129	0.416015
10	-0.227136	-1.9139	0.029833
11	0.092453	0.779	0.219278
12	-0.226435	-1.908	0.030219
13	-0.074542	-0.6281	0.265975
14	0.167539	1.4117	0.081202
15	0.139646	1.1767	0.121628
16	0.014287	0.1204	0.452259
17	-0.078774	-0.6638	0.254497
18	0.143114	1.2059	0.11593
19	0.002948	0.0248	0.490126
20	-0.004221	-0.0356	0.485864
21	-0.012276	-0.1034	0.458951
22	-0.201031	-1.6939	0.047332
23	0.066315	0.5588	0.289034
24	-0.199213	-1.6786	0.048813
25	-0.140195	-1.1813	0.120712
26	-0.154162	-1.299	0.099074
27	0.126792	1.0684	0.144487
28	-0.007745	-0.0653	0.474073
29	0.051355	0.4327	0.333262
30	0.005257	0.0443	0.482396
31	-0.06193	-0.5218	0.301707
32	-0.068618	-0.5782	0.282484
33	0.01035	0.0872	0.465374
34	-0.11482	-0.9675	0.168291
35	0.112003	0.9438	0.174248
36	-0.08763	-0.7384	0.231358
37	-0.130413	-1.0989	0.137767
38	0.029653	0.2499	0.401708
39	-0.038413	-0.3237	0.37357
40	0.103415	0.8714	0.193239
41	0.013835	0.1166	0.453763
42	-0.136078	-1.1466	0.127695
43	0.027758	0.2339	0.40787
44	0.019377	0.1633	0.435383
45	-0.035765	-0.3014	0.382009
46	-0.091108	-0.7677	0.222608
47	0.022245	0.1874	0.425924
48	0.006412	0.054	0.478533
49	-0.078115	-0.6582	0.256267
50	-0.049457	-0.4167	0.339066
51	0.047441	0.3997	0.345274
52	-0.064649	-0.5447	0.293819
53	0.0482	0.4061	0.34293
54	-0.032245	-0.2717	0.39332
55	-0.070216	-0.5916	0.277982
56	-0.035462	-0.2988	0.38298
57	-0.018995	-0.1601	0.436645
58	-0.013178	-0.111	0.45595
59	-0.016958	-0.1429	0.443391
60	0.064277	0.5416	0.294891

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229883765tukwhy5d370ofls/1ac3n1229883313.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229883765tukwhy5d370ofls/1ac3n1229883313.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229883765tukwhy5d370ofls/2ius01229883313.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229883765tukwhy5d370ofls/2ius01229883313.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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