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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: Fri, 10 Dec 2010 21:12:45 +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/10/t1292015425qx1hs57jj48ypu3.htm/, Retrieved Fri, 10 Dec 2010 22:10:27 +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/10/t1292015425qx1hs57jj48ypu3.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 «

493 514 522 490 484 506 501 462 465 454 464 427 460 473 465 422 415 413 420 363 376 380 384 346 389 407 393 346 348 353 364 305 307 312 312 286 324 336 327 302 299 311 315 264 278 278 287 279 324 354 354 360 363 385 412 370 389 395 417 404

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	-0.146445	-1.1249	0.132601
2	-0.20074	-1.5419	0.06422
3	-0.14458	-1.1105	0.135636
4	0.577601	4.4366	2e-05
5	-0.140411	-1.0785	0.142597
6	-0.228807	-1.7575	0.04201
7	-0.169942	-1.3054	0.098421
8	0.51931	3.9889	9.3e-05
9	-0.185866	-1.4277	0.07933
10	-0.192448	-1.4782	0.072334
11	-0.120587	-0.9262	0.179046
12	0.713165	5.4779	0
13	-0.160559	-1.2333	0.111181
14	-0.224069	-1.7211	0.045236
15	-0.140098	-1.0761	0.14313
16	0.43806	3.3648	0.000676
17	-0.145921	-1.1208	0.133449
18	-0.213688	-1.6414	0.05302
19	-0.144307	-1.1084	0.136084
20	0.36508	2.8042	0.003409
21	-0.180812	-1.3888	0.085051
22	-0.182396	-1.401	0.083224
23	-0.06327	-0.486	0.314388
24	0.472401	3.6286	0.000298
25	-0.13659	-1.0492	0.14919
26	-0.166934	-1.2822	0.102387
27	-0.10689	-0.821	0.207465
28	0.295154	2.2671	0.013531
29	-0.078726	-0.6047	0.273848
30	-0.172912	-1.3282	0.09462
31	-0.112286	-0.8625	0.195956
32	0.198045	1.5212	0.066774
33	-0.121412	-0.9326	0.177418
34	-0.079758	-0.6126	0.271237
35	-0.078374	-0.602	0.274738
36	0.248917	1.912	0.03037
37	-0.089217	-0.6853	0.247924
38	-0.106318	-0.8166	0.208708
39	-0.065227	-0.501	0.309111
40	0.127741	0.9812	0.165251
41	-0.050948	-0.3913	0.348479
42	-0.103487	-0.7949	0.214928
43	-0.052459	-0.4029	0.344223
44	0.094958	0.7294	0.234326
45	-0.064509	-0.4955	0.311043
46	-0.007674	-0.0589	0.476596
47	-0.037632	-0.2891	0.386775
48	0.091051	0.6994	0.243533

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.146445	-1.1249	0.132601
2	-0.227056	-1.744	0.043179
3	-0.230473	-1.7703	0.040922
4	0.519353	3.9892	9.3e-05
5	-0.062647	-0.4812	0.316077
6	-0.132809	-1.0201	0.155916
7	-0.135489	-1.0407	0.151128
8	0.224286	1.7228	0.045084
9	-0.140827	-1.0817	0.14189
10	-0.030282	-0.2326	0.408439
11	0.004731	0.0363	0.485569
12	0.527672	4.0531	7.5e-05
13	0.006887	0.0529	0.478994
14	-0.085489	-0.6567	0.256979
15	-0.088973	-0.6834	0.24851
16	-0.272156	-2.0905	0.020447
17	-0.058972	-0.453	0.326114
18	0.026264	0.2017	0.420409
19	0.088345	0.6786	0.250025
20	-0.08691	-0.6676	0.253505
21	-0.019818	-0.1522	0.439766
22	-0.074348	-0.5711	0.285057
23	0.00377	0.029	0.488497
24	-0.036452	-0.28	0.39023
25	0.040819	0.3135	0.37749
26	0.118181	0.9078	0.183847
27	-0.045368	-0.3485	0.36436
28	-0.095023	-0.7299	0.234173
29	0.039181	0.301	0.382254
30	-0.053808	-0.4133	0.34044
31	-0.049034	-0.3766	0.353899
32	-0.089254	-0.6856	0.247834
33	-0.011	-0.0845	0.466474
34	0.139959	1.075	0.143366
35	-0.100332	-0.7707	0.22199
36	-0.108464	-0.8331	0.204065
37	-0.074087	-0.5691	0.285734
38	-0.109268	-0.8393	0.202342
39	0.058484	0.4492	0.327458
40	-0.007302	-0.0561	0.47773
41	-0.049319	-0.3788	0.353088
42	-0.046122	-0.3543	0.3622
43	0.066652	0.512	0.305293
44	0.059402	0.4563	0.324934
45	0.020953	0.1609	0.436345
46	-0.022679	-0.1742	0.431152
47	-0.02611	-0.2006	0.420869
48	-0.074516	-0.5724	0.284623

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015425qx1hs57jj48ypu3/1juw91292015563.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015425qx1hs57jj48ypu3/1juw91292015563.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015425qx1hs57jj48ypu3/2juw91292015563.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015425qx1hs57jj48ypu3/2juw91292015563.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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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