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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: Mon, 27 Dec 2010 20:46:03 +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/27/t1293482642trhj6ju6a1x2pcz.htm/, Retrieved Mon, 27 Dec 2010 21:44:02 +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/27/t1293482642trhj6ju6a1x2pcz.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 «

493 481 462 457 442 439 488 521 501 485 464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601 604 586 564 549

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	0.280757	3.2011	0.00086
2	-0.236878	-2.7008	0.003919
3	-0.336759	-3.8396	9.6e-05
4	-0.278954	-3.1806	0.000919
5	0.067378	0.7682	0.221874
6	0.230625	2.6295	0.004791
7	0.083704	0.9544	0.170832
8	-0.236097	-2.6919	0.00402
9	-0.28868	-3.2915	0.000642
10	-0.222441	-2.5362	0.006195
11	0.262006	2.9873	0.001682
12	0.813488	9.2752	0
13	0.198156	2.2593	0.012764
14	-0.205678	-2.3451	0.010268
15	-0.310527	-3.5406	0.000277
16	-0.260502	-2.9702	0.001773
17	0.056164	0.6404	0.26153
18	0.179805	2.0501	0.021183
19	0.039799	0.4538	0.325372
20	-0.246409	-2.8095	0.002864
21	-0.276909	-3.1573	0.00099
22	-0.183175	-2.0885	0.019351
23	0.263854	3.0084	0.001577
24	0.694782	7.9217	0
25	0.122772	1.3998	0.081974
26	-0.223577	-2.5492	0.00598
27	-0.283217	-3.2292	0.000786
28	-0.227942	-2.5989	0.005216
29	0.055572	0.6336	0.26372
30	0.145106	1.6545	0.050223
31	0.01808	0.2061	0.418501
32	-0.238897	-2.7238	0.00367
33	-0.246861	-2.8147	0.002822
34	-0.143229	-1.6331	0.052437
35	0.252247	2.8761	0.002354
36	0.622736	7.1003	0
37	0.107126	1.2214	0.112068
38	-0.193067	-2.2013	0.01474
39	-0.270024	-3.0787	0.001268
40	-0.19188	-2.1878	0.015237
41	0.05486	0.6255	0.26637
42	0.133246	1.5192	0.065565
43	0.018702	0.2132	0.415738
44	-0.219273	-2.5001	0.00683
45	-0.213355	-2.4326	0.008175
46	-0.099642	-1.1361	0.129003
47	0.210571	2.4009	0.008886
48	0.528261	6.0231	0
49	0.099221	1.1313	0.130008
50	-0.166798	-1.9018	0.029706
51	-0.231622	-2.6409	0.004641
52	-0.152466	-1.7384	0.042255
53	0.03505	0.3996	0.345041
54	0.108855	1.2411	0.108396
55	0.008075	0.0921	0.463391
56	-0.188005	-2.1436	0.016964
57	-0.149104	-1.7	0.045757
58	-0.077783	-0.8869	0.188394
59	0.203025	2.3148	0.011094
60	0.464668	5.298	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.280757	3.2011	0.00086
2	-0.342717	-3.9076	7.5e-05
3	-0.186034	-2.1211	0.017906
4	-0.236752	-2.6994	0.003935
5	0.093008	1.0605	0.145453
6	0.006297	0.0718	0.471437
7	-0.069952	-0.7976	0.213286
8	-0.281009	-3.204	0.000853
9	-0.127089	-1.449	0.074867
10	-0.294907	-3.3625	0.000508
11	0.257716	2.9384	0.001952
12	0.676995	7.7189	0
13	-0.245716	-2.8016	0.002931
14	0.163829	1.8679	0.032011
15	0.052709	0.601	0.274452
16	0.04385	0.5	0.30897
17	-0.034195	-0.3899	0.348631
18	-0.120737	-1.3766	0.085498
19	-0.093521	-1.0663	0.144132
20	-0.156023	-1.7789	0.038794
21	-0.114217	-1.3023	0.097563
22	-0.01318	-0.1503	0.440392
23	-0.075202	-0.8574	0.19639
24	0.057073	0.6507	0.258183
25	-0.125017	-1.4254	0.078217
26	-0.075194	-0.8573	0.196415
27	0.083336	0.9502	0.171893
28	-0.05902	-0.6729	0.251093
29	-0.024618	-0.2807	0.389696
30	-0.056726	-0.6468	0.25946
31	0.000987	0.0113	0.495521
32	-0.015926	-0.1816	0.428098
33	-0.020264	-0.231	0.40882
34	-0.015645	-0.1784	0.42935
35	-0.069538	-0.7929	0.214653
36	0.088171	1.0053	0.158309
37	0.048838	0.5568	0.289298
38	0.026108	0.2977	0.383211
39	-0.064661	-0.7373	0.231149
40	0.093266	1.0634	0.144786
41	-0.06567	-0.7487	0.22768
42	0.043153	0.492	0.311769
43	-0.030296	-0.3454	0.365166
44	-0.023062	-0.2629	0.396504
45	-0.049352	-0.5627	0.287303
46	0.012684	0.1446	0.442618
47	-0.199232	-2.2716	0.012377
48	-0.023248	-0.2651	0.395687
49	-0.035443	-0.4041	0.343398
50	-0.096255	-1.0975	0.137232
51	-0.029732	-0.339	0.367579
52	-0.025839	-0.2946	0.384382
53	-0.061597	-0.7023	0.24187
54	-0.021901	-0.2497	0.401605
55	-0.045103	-0.5143	0.303972
56	0.066067	0.7533	0.226323
57	0.036803	0.4196	0.337727
58	-0.074396	-0.8482	0.19893
59	0.177583	2.0248	0.02247
60	-0.053094	-0.6054	0.272996

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/1dpxh1293482759.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/1dpxh1293482759.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/2ogf21293482759.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/2ogf21293482759.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/3ogf21293482759.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293482642trhj6ju6a1x2pcz/3ogf21293482759.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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