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PaperTimDamen

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 31 Jan 2011 10:42:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac.htm/, Retrieved Mon, 31 Jan 2011 11:40:11 +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/2011/Jan/31/t12964703872dehm4m10t36pac.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

349 336 331 327 323 322 385 405 412 411 410 415 414 411 408 410 411 416 479 498 502 498 499 506 510 509 502 495 490 490 553 570 573 572 575 580 580 574 563 556 546 545 605 628 631 626 614 606 602 589 574 558 552 546 607 636 631 623 618 605 619 596 570 546 528 506 555 568 564 553 541 542 540 521 505 491 482 478 523 531 532 540 525 533 531 508 495 482 470 466 515 518 516 511 500 498 494 476 458 443 430 424 476 481 470 460 451 450 444 429 421 400 389 384 432 446 431 423 416 416 413 399 386 374 365 365 418 428 424 421 417 423 423 419 406 398 390 391 444 460 455 456 452 459 461 451 443 439 430 436 488 506 502 501 501 515 521 520 512 509 505 511 570 592 594 586 586 592 594 594 586 586 572 572 563 563 555 555 554 554 601 601 622 622 617 617 606 606 595 595 599 599 600 600 592 592 575 575 567 567 555 555 555 555 608 etc...

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' @ www.wessa.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.959754	21.2884	0
2	0.905836	20.0924	0
3	0.849051	18.8329	0
4	0.801148	17.7703	0
5	0.766859	17.0098	0
6	0.73339	16.2674	0
7	0.70983	15.7448	0
8	0.688748	15.2772	0
9	0.682133	15.1304	0
10	0.684046	15.1729	0
11	0.691235	15.3323	0
12	0.687781	15.2557	0
13	0.645231	14.3119	0
14	0.592879	13.1507	0
15	0.545826	12.107	0
16	0.508655	11.2825	0
17	0.484402	10.7446	0
18	0.461311	10.2324	0
19	0.44554	9.8826	0
20	0.432848	9.601	0
21	0.433381	9.6128	0
22	0.442292	9.8105	0
23	0.451172	10.0075	0
24	0.451299	10.0103	0
25	0.402558	8.9292	0
26	0.345948	7.6735	0
27	0.288302	6.3949	0
28	0.239117	5.3039	0
29	0.201715	4.4742	5e-06
30	0.165482	3.6706	0.000134
31	0.138133	3.0639	0.001152
32	0.114885	2.5483	0.005564
33	0.105724	2.3451	0.00971
34	0.10546	2.3392	0.009862
35	0.111635	2.4762	0.006807
36	0.110365	2.448	0.007357
37	0.080039	1.7753	0.038229
38	0.042941	0.9525	0.170659
39	0.01062	0.2356	0.406934
40	-0.014407	-0.3196	0.374721
41	-0.029539	-0.6552	0.256319
42	-0.044194	-0.9803	0.163715
43	-0.053881	-1.1951	0.116305
44	-0.059293	-1.3152	0.094529
45	-0.05301	-1.1758	0.12012
46	-0.038503	-0.854	0.196747
47	-0.025254	-0.5601	0.287816
48	-0.019297	-0.428	0.334408
49	-0.05187	-1.1505	0.12524
50	-0.090622	-2.0101	0.022483
51	-0.130276	-2.8897	0.002013
52	-0.164602	-3.651	0.000145
53	-0.189519	-4.2037	1.6e-05
54	-0.214291	-4.7532	1e-06
55	-0.233004	-5.1683	0
56	-0.246986	-5.4784	0
57	-0.248833	-5.5194	0
58	-0.243768	-5.407	0
59	-0.232074	-5.1476	0
60	-0.225885	-5.0104	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959754	21.2884	0
2	-0.193891	-4.3007	1e-05
3	-0.036957	-0.8197	0.206379
4	0.093617	2.0765	0.019182
5	0.115143	2.554	0.005475
6	-0.06915	-1.5338	0.06286
7	0.11944	2.6493	0.004162
8	0.00939	0.2083	0.417552
9	0.183814	4.0772	2.7e-05
10	0.063709	1.4131	0.079125
11	0.081301	1.8034	0.035972
12	-0.138191	-3.0652	0.001147
13	-0.426844	-9.4679	0
14	0.01169	0.2593	0.397759
15	0.169186	3.7527	9.8e-05
16	0.004771	0.1058	0.457879
17	0.048342	1.0723	0.142061
18	-0.008145	-0.1807	0.428349
19	0.047956	1.0637	0.143988
20	-0.000647	-0.0143	0.49428
21	0.083893	1.8608	0.031682
22	0.012537	0.2781	0.390535
23	-0.059155	-1.3121	0.095045
24	-0.005122	-0.1136	0.454794
25	-0.44914	-9.9624	0
26	0.070337	1.5601	0.059684
27	-0.028099	-0.6233	0.266698
28	-0.029753	-0.6599	0.254798
29	-0.009661	-0.2143	0.415201
30	0.025087	0.5564	0.289079
31	-0.012435	-0.2758	0.3914
32	0.007184	0.1594	0.436727
33	-0.009506	-0.2109	0.416541
34	0.025697	0.57	0.284476
35	0.037057	0.822	0.205751
36	0.012339	0.2737	0.392215
37	0.032346	0.7175	0.23671
38	0.005371	0.1191	0.452612
39	0.029912	0.6635	0.253669
40	-0.030516	-0.6769	0.249401
41	0.000998	0.0221	0.491172
42	0.002038	0.0452	0.481984
43	-0.010138	-0.2249	0.411087
44	0.013954	0.3095	0.378532
45	0.015373	0.341	0.366626
46	0.003941	0.0874	0.465188
47	-0.074905	-1.6615	0.048629
48	-0.007976	-0.1769	0.429827
49	-0.151544	-3.3614	0.000418
50	0.012764	0.2831	0.388604
51	-0.020503	-0.4548	0.324732
52	-0.032741	-0.7262	0.234025
53	-0.010867	-0.241	0.404814
54	0.004627	0.1026	0.459147
55	-0.050403	-1.118	0.132059
56	0.006177	0.137	0.445537
57	-0.033442	-0.7418	0.229285
58	-0.028821	-0.6393	0.261467
59	0.053246	1.181	0.119077
60	0.019023	0.4219	0.336626

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/1x8xt1296470552.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/1x8xt1296470552.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/2fn6z1296470552.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/2fn6z1296470552.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/3y4cc1296470552.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/31/t12964703872dehm4m10t36pac/3y4cc1296470552.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 (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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