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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 12:51:29 +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/t1293022170uyfkend1h1zgr91.htm/, Retrieved Wed, 22 Dec 2010 13:49:32 +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/t1293022170uyfkend1h1zgr91.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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.212075	2.418	0.008495
2	-0.262478	-2.9927	0.001655
3	-0.254006	-2.8961	0.002217
4	-0.218074	-2.4864	0.007085
5	0.179425	2.0458	0.021399
6	0.397001	4.5265	7e-06
7	0.194147	2.2136	0.0143
8	-0.160209	-1.8267	0.035022
9	-0.228065	-2.6003	0.005195
10	-0.287598	-3.2791	0.000668
11	0.172953	1.972	0.025368
12	0.662662	7.5555	0
13	0.087574	0.9985	0.159946
14	-0.216489	-2.4684	0.007436
15	-0.235944	-2.6902	0.004039
16	-0.219951	-2.5078	0.006689
17	0.127397	1.4525	0.07438
18	0.295305	3.367	5e-04
19	0.109256	1.2457	0.107556
20	-0.212353	-2.4212	0.008425
21	-0.264065	-3.0108	0.001566
22	-0.236254	-2.6937	0.003999
23	0.175728	2.0036	0.023595
24	0.497146	5.6683	0
25	-0.015788	-0.18	0.428712
26	-0.275798	-3.1446	0.001031
27	-0.222462	-2.5365	0.006191
28	-0.223687	-2.5504	0.005959
29	0.116146	1.3243	0.093868
30	0.21869	2.4934	0.006953
31	0.061748	0.704	0.241336
32	-0.22208	-2.5321	0.006264
33	-0.241632	-2.755	0.003356
34	-0.172759	-1.9698	0.025496
35	0.15093	1.7209	0.043827
36	0.437673	4.9902	1e-06
37	0.003311	0.0378	0.484972
38	-0.197792	-2.2552	0.012897
39	-0.225148	-2.5671	0.005694
40	-0.178368	-2.0337	0.022008
41	0.112369	1.2812	0.101202
42	0.193541	2.2067	0.014545
43	0.067631	0.7711	0.221019
44	-0.212078	-2.4181	0.008495
45	-0.203668	-2.3222	0.010889
46	-0.096582	-1.1012	0.136422
47	0.0916	1.0444	0.14912
48	0.339946	3.876	8.4e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.212075	2.418	0.008495
2	-0.321933	-3.6706	0.000176
3	-0.131006	-1.4937	0.06884
4	-0.243244	-2.7734	0.003182
5	0.210664	2.4019	0.008861
6	0.207953	2.371	0.009603
7	0.14088	1.6063	0.05532
8	-0.087977	-1.0031	0.158839
9	0.033472	0.3816	0.351676
10	-0.277717	-3.1665	0.000961
11	0.263314	3.0022	0.001607
12	0.448167	5.1099	1e-06
13	-0.206537	-2.3549	0.010013
14	0.007214	0.0823	0.467287
15	0.008378	0.0955	0.462022
16	-0.030291	-0.3454	0.365188
17	-0.048693	-0.5552	0.289862
18	-0.098251	-1.1202	0.13234
19	-0.053835	-0.6138	0.270205
20	-0.187878	-2.1421	0.017023
21	-0.049732	-0.567	0.285836
22	0.023747	0.2708	0.393503
23	0.010143	0.1156	0.454055
24	0.069077	0.7876	0.216183
25	-0.104709	-1.1939	0.117352
26	-0.117255	-1.3369	0.091792
27	0.085432	0.9741	0.165915
28	-0.144042	-1.6423	0.05147
29	0.020693	0.2359	0.406927
30	-0.180691	-2.0602	0.020687
31	0.053511	0.6101	0.271423
32	-0.089979	-1.0259	0.153418
33	0.066774	0.7613	0.223917
34	-0.02085	-0.2377	0.406234
35	-0.024484	-0.2792	0.390284
36	0.103259	1.1773	0.120606
37	0.107369	1.2242	0.111547
38	0.029218	0.3331	0.369786
39	-0.063242	-0.7211	0.236081
40	0.040745	0.4646	0.321512
41	-0.07483	-0.8532	0.197561
42	-0.04122	-0.47	0.31958
43	-0.037244	-0.4246	0.3359
44	-0.095845	-1.0928	0.138252
45	-0.057283	-0.6531	0.257413
46	0.020182	0.2301	0.409186
47	-0.184727	-2.1062	0.018554
48	0.023284	0.2655	0.395529

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293022170uyfkend1h1zgr91/1pzzl1293022286.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293022170uyfkend1h1zgr91/1pzzl1293022286.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293022170uyfkend1h1zgr91/2pzzl1293022286.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293022170uyfkend1h1zgr91/2pzzl1293022286.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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 (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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