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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, 23 Dec 2008 10:04:06 -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/23/t1230051897pich2s5iul6gmsx.htm/, Retrieved Tue, 23 Dec 2008 18:04:59 +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/23/t1230051897pich2s5iul6gmsx.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 «

513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.910391	7.8315	0
2	0.780211	6.7116	0
3	0.673363	5.7925	0
4	0.611032	5.2563	1e-06
5	0.579025	4.981	2e-06
6	0.540994	4.6538	7e-06
7	0.475794	4.0929	5.4e-05
8	0.400045	3.4413	0.000478
9	0.376503	3.2388	0.000899
10	0.400982	3.4494	0.000466
11	0.45619	3.9243	9.7e-05
12	0.479102	4.1214	4.9e-05
13	0.383895	3.3024	0.000739
14	0.261718	2.2514	0.013665
15	0.159268	1.3701	0.087403
16	0.102137	0.8786	0.191226
17	0.074522	0.6411	0.261731
18	0.041601	0.3579	0.36073
19	-0.012624	-0.1086	0.456907
20	-0.07276	-0.6259	0.266651
21	-0.090084	-0.7749	0.220425
22	-0.06888	-0.5925	0.277652
23	-0.019767	-0.17	0.43272
24	0.003085	0.0265	0.489451
25	-0.066756	-0.5743	0.283769
26	-0.160907	-1.3842	0.085233
27	-0.236005	-2.0302	0.022966
28	-0.270945	-2.3308	0.011247
29	-0.28487	-2.4505	0.008314
30	-0.303436	-2.6103	0.005473
31	-0.335162	-2.8832	0.002576
32	-0.370529	-3.1874	0.001052
33	-0.37173	-3.1977	0.001019
34	-0.343276	-2.953	0.002108
35	-0.290826	-2.5018	0.007284
36	-0.251574	-2.1641	0.016841
37	-0.281275	-2.4196	0.008997
38	-0.328157	-2.8229	0.003055
39	-0.359698	-3.0942	0.001392
40	-0.358562	-3.0845	0.001433
41	-0.346396	-2.9798	0.00195
42	-0.338702	-2.9136	0.002361
43	-0.345226	-2.9697	0.002008
44	-0.357024	-3.0712	0.001491
45	-0.339689	-2.9221	0.002304
46	-0.300623	-2.5861	0.005837
47	-0.241366	-2.0763	0.020669
48	-0.192481	-1.6558	0.051

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.910391	7.8315	0
2	-0.283906	-2.4422	0.008492
3	0.126271	1.0862	0.140452
4	0.139017	1.1959	0.117783
5	0.06181	0.5317	0.298261
6	-0.073836	-0.6352	0.26364
7	-0.107784	-0.9272	0.178421
8	-0.01049	-0.0902	0.464172
9	0.283508	2.4388	0.008567
10	0.101264	0.8711	0.193258
11	0.154537	1.3294	0.093904
12	-0.132742	-1.1419	0.12859
13	-0.598544	-5.1489	1e-06
14	0.103325	0.8888	0.188487
15	-0.080224	-0.6901	0.24614
16	0.029349	0.2525	0.400689
17	0.122006	1.0495	0.148673
18	-0.072599	-0.6245	0.267102
19	0.119858	1.0311	0.152935
20	0.001185	0.0102	0.495946
21	-0.164311	-1.4135	0.080858
22	0.009781	0.0841	0.466587
23	-0.081939	-0.7049	0.241553
24	0.010655	0.0917	0.463611
25	-0.110937	-0.9543	0.171516
26	-0.052188	-0.4489	0.327394
27	0.083268	0.7163	0.238032
28	-0.059327	-0.5104	0.305662
29	-0.037454	-0.3222	0.374107
30	-0.011761	-0.1012	0.459845
31	-0.001207	-0.0104	0.49587
32	0.022428	0.1929	0.42377
33	-0.090044	-0.7746	0.220525
34	-0.056667	-0.4875	0.313684
35	0.005002	0.043	0.482896
36	0.085056	0.7317	0.233339
37	-0.03021	-0.2599	0.39784
38	0.024367	0.2096	0.417274
39	0.009258	0.0796	0.468368
40	-0.023989	-0.2064	0.418538
41	-0.042346	-0.3643	0.358345
42	-0.046128	-0.3968	0.346326
43	-0.075965	-0.6535	0.257737
44	0.046053	0.3962	0.346561
45	0.016371	0.1408	0.444193
46	0.009958	0.0857	0.465983
47	0.038798	0.3338	0.369754
48	-0.028101	-0.2417	0.404826

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230051897pich2s5iul6gmsx/1roj91230051843.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230051897pich2s5iul6gmsx/1roj91230051843.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230051897pich2s5iul6gmsx/2hjtv1230051843.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230051897pich2s5iul6gmsx/2hjtv1230051843.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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