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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 21 Dec 2009 04:11:40 -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/21/t126139397896lem463qm5e19y.htm/, Retrieved Mon, 21 Dec 2009 12:13:01 +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/21/t126139397896lem463qm5e19y.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 «

581 597 587 536 524 537 536 533 528 516 502 506 518 534 528 478 469 490 493 508 517 514 510 527 542 565 555 499 511 526 532 549 561 557 566 588 620 626 620 573 573 574 580 590 593 597 595 612 628 629 621 569 567 573 584 589 591 595 594 611

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.883901	6.8467	0
2	0.725321	5.6183	0
3	0.618768	4.793	6e-06
4	0.579675	4.4901	1.6e-05
5	0.578538	4.4813	1.7e-05
6	0.559992	4.3377	2.8e-05
7	0.502656	3.8936	0.000125
8	0.43153	3.3426	0.000717
9	0.404232	3.1312	0.001345
10	0.406606	3.1496	0.001275
11	0.450853	3.4923	0.000453
12	0.445896	3.4539	0.00051
13	0.300799	2.33	0.011595
14	0.135831	1.0521	0.148476
15	0.020281	0.1571	0.437849
16	-0.033614	-0.2604	0.397735
17	-0.051395	-0.3981	0.345985
18	-0.077041	-0.5968	0.276457
19	-0.130142	-1.0081	0.158733
20	-0.194485	-1.5065	0.068596
21	-0.215158	-1.6666	0.050403
22	-0.210757	-1.6325	0.053904
23	-0.175981	-1.3631	0.088966
24	-0.180891	-1.4012	0.083157
25	-0.274266	-2.1245	0.018881
26	-0.371466	-2.8774	0.002773
27	-0.417412	-3.2333	0.000995
28	-0.422466	-3.2724	0.000886
29	-0.403309	-3.124	0.001373
30	-0.385484	-2.9859	0.002044
31	-0.385394	-2.9852	0.002048
32	-0.386584	-2.9945	0.001995
33	-0.345731	-2.678	0.00477
34	-0.300622	-2.3286	0.011633
35	-0.250162	-1.9377	0.028682
36	-0.220699	-1.7095	0.046261
37	-0.248771	-1.927	0.029361
38	-0.27652	-2.1419	0.018135
39	-0.281885	-2.1835	0.016461
40	-0.260302	-2.0163	0.024127
41	-0.227201	-1.7599	0.041762
42	-0.192566	-1.4916	0.07052
43	-0.169734	-1.3148	0.096798
44	-0.141589	-1.0967	0.138568
45	-0.101865	-0.789	0.216598
46	-0.075948	-0.5883	0.279271
47	-0.048807	-0.3781	0.353362
48	-0.029935	-0.2319	0.408713
49	-0.036144	-0.28	0.390231
50	-0.043482	-0.3368	0.368718
51	-0.042719	-0.3309	0.370935
52	-0.028655	-0.222	0.41255
53	-0.013918	-0.1078	0.457253
54	-0.001622	-0.0126	0.495008
55	0.006731	0.0521	0.479297
56	0.022291	0.1727	0.431748
57	0.038802	0.3006	0.382395
58	0.029488	0.2284	0.410051
59	0.01253	0.0971	0.461501
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.883901	6.8467	0
2	-0.25585	-1.9818	0.026044
3	0.194584	1.5072	0.068498
4	0.164019	1.2705	0.104408
5	0.107952	0.8362	0.203183
6	-0.044879	-0.3476	0.364668
7	-0.067603	-0.5236	0.301226
8	-0.012474	-0.0966	0.461674
9	0.153103	1.1859	0.120163
10	-0.004024	-0.0312	0.487619
11	0.233189	1.8063	0.037946
12	-0.228974	-1.7736	0.0406
13	-0.53727	-4.1617	5.1e-05
14	0.019734	0.1529	0.439511
15	-0.114769	-0.889	0.188778
16	-0.122636	-0.9499	0.172979
17	0.021289	0.1649	0.434786
18	-0.035743	-0.2769	0.391417
19	0.049574	0.384	0.35117
20	-0.101421	-0.7856	0.217596
21	0.091406	0.708	0.240835
22	0.020405	0.1581	0.437472
23	-0.026231	-0.2032	0.41984
24	0.051295	0.3973	0.346267
25	-0.034227	-0.2651	0.395911
26	0.018635	0.1443	0.442855
27	0.067924	0.5261	0.300367
28	-0.154161	-1.1941	0.118564
29	0.063804	0.4942	0.311477
30	-0.036699	-0.2843	0.388591
31	0.024177	0.1873	0.42604
32	0.044563	0.3452	0.365582
33	0.062838	0.4867	0.314107
34	-0.068674	-0.5319	0.298363
35	-0.03654	-0.283	0.389061
36	0.100828	0.781	0.218934
37	-0.019235	-0.149	0.441031
38	-0.067906	-0.526	0.300414
39	-0.069525	-0.5385	0.296098
40	0.008067	0.0625	0.47519
41	-0.057167	-0.4428	0.329747
42	-0.073676	-0.5707	0.28517
43	0.058798	0.4554	0.325215
44	0.00307	0.0238	0.490552
45	-0.203101	-1.5732	0.060464
46	0.032053	0.2483	0.402384
47	0.01373	0.1064	0.457828
48	-0.01979	-0.1533	0.43934
49	0.061023	0.4727	0.319078
50	-0.007603	-0.0589	0.476617
51	0.075179	0.5823	0.281263
52	-0.016787	-0.13	0.44849
53	-0.042647	-0.3303	0.371147
54	0.010441	0.0809	0.467904
55	-0.056162	-0.435	0.332552
56	-0.003009	-0.0233	0.49074
57	-0.023802	-0.1844	0.427172
58	-0.080201	-0.6212	0.268399
59	-0.039742	-0.3078	0.379635
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t126139397896lem463qm5e19y/1a4bk1261393897.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126139397896lem463qm5e19y/1a4bk1261393897.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126139397896lem463qm5e19y/26zu41261393897.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126139397896lem463qm5e19y/26zu41261393897.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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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