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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: Wed, 22 Dec 2010 12:38:16 +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/22/t1293021361frw21wxaxbyjo6p.htm/, Retrieved Wed, 22 Dec 2010 13:36:01 +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/2010/Dec/22/t1293021361frw21wxaxbyjo6p.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 «

377 370 358 357 349 348 369 381 368 361 351 351 358 354 347 345 343 340 362 370 373 371 354 357 363 364 363 358 357 357 380 378 376 380 379 384 392 394 392 396 392 396 419 421 420 418 410 418 426 428 430 424 423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441 439 454 460 457 451 444 437 443 471 469 454 444 436

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	0.969755	11.0994	0
2	0.926384	10.6029	0
3	0.892894	10.2196	0
4	0.870381	9.962	0
5	0.857	9.8088	0
6	0.836927	9.5791	0
7	0.801025	9.1682	0
8	0.756621	8.6599	0
9	0.717023	8.2067	0
10	0.686898	7.8619	0
11	0.668993	7.657	0
12	0.642638	7.3553	0
13	0.585146	6.6973	0
14	0.522018	5.9748	0
15	0.467864	5.3549	0
16	0.423764	4.8502	2e-06
17	0.390545	4.47	8e-06
18	0.35239	4.0333	4.6e-05
19	0.304092	3.4805	0.00034
20	0.250963	2.8724	0.002377
21	0.209294	2.3955	0.009007
22	0.180986	2.0715	0.020138
23	0.161864	1.8526	0.033094
24	0.135228	1.5478	0.062047
25	0.085495	0.9785	0.164805
26	0.036658	0.4196	0.337745
27	0.001178	0.0135	0.494633
28	-0.025279	-0.2893	0.386394
29	-0.040668	-0.4655	0.321185
30	-0.059729	-0.6836	0.247708
31	-0.085132	-0.9744	0.165833
32	-0.115365	-1.3204	0.0945
33	-0.134832	-1.5432	0.062595
34	-0.142129	-1.6267	0.053097
35	-0.141526	-1.6198	0.053835
36	-0.147462	-1.6878	0.046916
37	-0.173764	-1.9888	0.024402
38	-0.200755	-2.2977	0.011581
39	-0.218745	-2.5037	0.00676
40	-0.22626	-2.5897	0.005347
41	-0.225252	-2.5781	0.00552
42	-0.226723	-2.595	0.005269
43	-0.234784	-2.6872	0.00407
44	-0.246787	-2.8246	0.002737
45	-0.248529	-2.8445	0.002581
46	-0.241477	-2.7638	0.003268
47	-0.231746	-2.6525	0.004489
48	-0.225074	-2.5761	0.005551

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.969755	11.0994	0
2	-0.23568	-2.6975	0.003953
3	0.201786	2.3095	0.011239
4	0.085325	0.9766	0.165287
5	0.11895	1.3614	0.087855
6	-0.150645	-1.7242	0.043514
7	-0.176596	-2.0212	0.022647
8	-0.086009	-0.9844	0.163362
9	0.034159	0.391	0.34823
10	0.014264	0.1633	0.435281
11	0.133558	1.5286	0.064382
12	-0.204938	-2.3456	0.010248
13	-0.424754	-4.8615	2e-06
14	0.091757	1.0502	0.147779
15	0.005531	0.0633	0.474809
16	-0.049311	-0.5644	0.286728
17	0.026761	0.3063	0.379934
18	-0.067312	-0.7704	0.221218
19	0.042763	0.4894	0.312672
20	-0.018961	-0.217	0.414264
21	0.191843	2.1957	0.014936
22	0.007806	0.0893	0.464471
23	-0.046659	-0.534	0.29711
24	-0.043907	-0.5025	0.308068
25	-0.136847	-1.5663	0.059848
26	0.113305	1.2968	0.098485
27	0.065198	0.7462	0.228434
28	-0.112521	-1.2879	0.100033
29	0.066163	0.7573	0.225125
30	-0.033691	-0.3856	0.350205
31	0.126194	1.4444	0.075514
32	-0.105671	-1.2095	0.114333
33	0.05215	0.5969	0.275807
34	-0.039828	-0.4559	0.324625
35	0.0026	0.0298	0.488151
36	-0.013617	-0.1558	0.438196
37	-0.096039	-1.0992	0.136844
38	-0.056719	-0.6492	0.258681
39	-0.031786	-0.3638	0.358295
40	0.042316	0.4843	0.314481
41	-0.016144	-0.1848	0.426845
42	0.030757	0.352	0.36269
43	0.012083	0.1383	0.445109
44	-0.012404	-0.142	0.443659
45	0.078741	0.9012	0.18456
46	-0.062309	-0.7132	0.238509
47	-0.006769	-0.0775	0.469184
48	0.048711	0.5575	0.289059

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021361frw21wxaxbyjo6p/1h3xc1293021492.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021361frw21wxaxbyjo6p/1h3xc1293021492.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021361frw21wxaxbyjo6p/2auxx1293021492.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293021361frw21wxaxbyjo6p/2auxx1293021492.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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