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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 20:48:39 +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/t12934828106i5zf9ufnwejyqb.htm/, Retrieved Mon, 27 Dec 2010 21:46:53 +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/t12934828106i5zf9ufnwejyqb.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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.149471	1.6237	0.053557
2	0.121119	1.3157	0.095415
3	0.117175	1.2729	0.102787
4	0.13845	1.504	0.067633
5	0.155861	1.6931	0.046539
6	0.126528	1.3744	0.085954
7	0.053025	0.576	0.282857
8	0.104631	1.1366	0.129008
9	0.137417	1.4927	0.069089
10	-0.067768	-0.7362	0.23155
11	-0.02047	-0.2224	0.412209
12	-0.21729	-2.3604	0.009948
13	-0.019437	-0.2111	0.416572
14	0.163309	1.774	0.039322
15	-0.03159	-0.3432	0.366046
16	-0.054637	-0.5935	0.276987
17	-0.091638	-0.9954	0.160778
18	-0.035458	-0.3852	0.350402
19	0.004036	0.0438	0.482553
20	-0.065276	-0.7091	0.239836
21	-0.098315	-1.068	0.143856
22	-0.03425	-0.3721	0.35526
23	0.023833	0.2589	0.398084
24	-0.185555	-2.0156	0.023054
25	-0.15169	-1.6478	0.05103
26	-0.23953	-2.602	0.005228
27	-0.077117	-0.8377	0.201944
28	-0.107374	-1.1664	0.122906
29	-0.017656	-0.1918	0.424117
30	-0.126347	-1.3725	0.086259
31	-0.079856	-0.8675	0.193726
32	-0.023965	-0.2603	0.397532
33	-0.042536	-0.4621	0.322445
34	-0.046672	-0.507	0.306555
35	0.005067	0.055	0.478098
36	0.036934	0.4012	0.344496
37	0.067185	0.7298	0.233473
38	0.07547	0.8198	0.206989
39	-0.085701	-0.931	0.176889
40	-0.039459	-0.4286	0.334486
41	0.017894	0.1944	0.423108
42	0.028747	0.3123	0.377693
43	0.028454	0.3091	0.378898
44	-0.034706	-0.377	0.353423
45	-0.080107	-0.8702	0.192983
46	-0.025506	-0.2771	0.391108
47	-0.111732	-1.2137	0.11364
48	-0.045965	-0.4993	0.309245
49	-0.050659	-0.5503	0.291578
50	0.013225	0.1437	0.443008
51	7.4e-05	8e-04	0.499679
52	0.01983	0.2154	0.414911
53	-0.064302	-0.6985	0.243119
54	0.043445	0.4719	0.318924
55	-0.041263	-0.4482	0.327403
56	-0.001268	-0.0138	0.494516
57	0.041953	0.4557	0.324713
58	-0.027763	-0.3016	0.381751
59	-0.017924	-0.1947	0.422978
60	0.016939	0.184	0.427164

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.149471	1.6237	0.053557
2	0.101034	1.0975	0.137326
3	0.088665	0.9631	0.168722
4	0.103855	1.1281	0.130773
5	0.111328	1.2093	0.114476
6	0.069144	0.7511	0.227044
7	-0.011802	-0.1282	0.449104
8	0.053747	0.5838	0.280222
9	0.08156	0.886	0.188719
10	-0.149247	-1.6212	0.053818
11	-0.056902	-0.6181	0.268846
12	-0.259991	-2.8242	0.002783
13	0.001204	0.0131	0.494796
14	0.213566	2.3199	0.011032
15	-0.016482	-0.179	0.429105
16	-0.005462	-0.0593	0.476393
17	-0.070838	-0.7695	0.221568
18	0.003634	0.0395	0.484288
19	0.047849	0.5198	0.302096
20	-0.050633	-0.55	0.291675
21	-0.028471	-0.3093	0.378828
22	-0.091181	-0.9905	0.161983
23	0.010103	0.1097	0.4564
24	-0.204193	-2.2181	0.014231
25	-0.103545	-1.1248	0.131481
26	-0.081605	-0.8865	0.188588
27	-0.009936	-0.1079	0.457116
28	-0.072565	-0.7883	0.216062
29	0.104866	1.1391	0.128476
30	-0.007984	-0.0867	0.465516
31	0.066563	0.7231	0.235536
32	0.056339	0.612	0.270859
33	0.02472	0.2685	0.39438
34	-0.017239	-0.1873	0.425889
35	0.077377	0.8405	0.201155
36	-0.066326	-0.7205	0.236325
37	-0.031878	-0.3463	0.364872
38	0.011009	0.1196	0.452505
39	-0.116451	-1.265	0.104184
40	-0.082687	-0.8982	0.185452
41	0.000127	0.0014	0.499451
42	0.005273	0.0573	0.477209
43	0.012861	0.1397	0.444565
44	-0.001845	-0.02	0.492024
45	-0.078021	-0.8475	0.199211
46	-0.058417	-0.6346	0.263468
47	-0.067869	-0.7372	0.231219
48	-0.008075	-0.0877	0.465127
49	-0.056584	-0.6147	0.269981
50	0.021315	0.2315	0.408648
51	-0.071867	-0.7807	0.218277
52	-0.061239	-0.6652	0.253602
53	0.02325	0.2526	0.400522
54	0.090606	0.9842	0.163506
55	-0.041923	-0.4554	0.324828
56	-0.021351	-0.2319	0.408497
57	-0.010077	-0.1095	0.456509
58	-0.06994	-0.7597	0.224462
59	-0.024524	-0.2664	0.395198
60	0.025557	0.2776	0.390894

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/16puy1293482917.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/16puy1293482917.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/2hztj1293482917.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/2hztj1293482917.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/3hztj1293482917.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934828106i5zf9ufnwejyqb/3hztj1293482917.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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