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Paper: Partial Autocorrelation function

*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: Sun, 19 Dec 2010 15:09:48 +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/19/t12927712795zsk7ht2i495edo.htm/, Retrieved Sun, 19 Dec 2010 16:07:59 +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/19/t12927712795zsk7ht2i495edo.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 «

608 651 691 627 634 731 475 337 803 722 590 724 627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 706 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1.006 789 734 906 532 387 991 841 892 782

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	0.00645	0.0591	0.476499
2	-0.313518	-2.8734	0.00257
3	-0.032151	-0.2947	0.384487
4	0.035553	0.3259	0.372674
5	0.023162	0.2123	0.416199
6	-0.080053	-0.7337	0.232587
7	0.027981	0.2565	0.399115
8	0.013342	0.1223	0.451485
9	-0.020582	-0.1886	0.425417
10	-0.239003	-2.1905	0.01563
11	0.043104	0.3951	0.346901
12	0.568224	5.2079	1e-06
13	0.036471	0.3343	0.369508
14	-0.265988	-2.4378	0.008443
15	0.052432	0.4805	0.316043
16	-0.03146	-0.2883	0.386902
17	-0.134948	-1.2368	0.1098
18	-0.008828	-0.0809	0.467851
19	0.061372	0.5625	0.287643
20	0.100958	0.9253	0.178731
21	-0.012612	-0.1156	0.454126
22	-0.242418	-2.2218	0.014493
23	9.2e-05	8e-04	0.499664
24	0.402513	3.6891	0.000199
25	0.039398	0.3611	0.359471
26	-0.245986	-2.2545	0.013383
27	-0.024576	-0.2252	0.411167
28	-0.052509	-0.4812	0.315795
29	-0.12431	-1.1393	0.128904
30	-0.015959	-0.1463	0.442032
31	0.083874	0.7687	0.222109
32	0.070652	0.6475	0.259526
33	-0.006242	-0.0572	0.477259
34	-0.192886	-1.7678	0.04036
35	0.0095	0.0871	0.465411
36	0.33946	3.1112	0.001273
37	0.025024	0.2293	0.409578
38	-0.257834	-2.3631	0.010217
39	-0.030442	-0.279	0.390462
40	-0.009488	-0.087	0.465457
41	-0.079854	-0.7319	0.233141
42	-0.012988	-0.119	0.452765
43	0.100934	0.9251	0.178787
44	0.076141	0.6978	0.243602
45	-0.008908	-0.0816	0.467564
46	-0.130978	-1.2004	0.116673
47	-0.01984	-0.1818	0.428076
48	0.243287	2.2298	0.014215

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.00645	0.0591	0.476499
2	-0.313573	-2.8739	0.002567
3	-0.030469	-0.2793	0.390369
4	-0.069399	-0.6361	0.263235
5	0.003765	0.0345	0.486277
6	-0.101285	-0.9283	0.177957
7	0.039744	0.3643	0.358289
8	-0.046552	-0.4267	0.335362
9	-0.002467	-0.0226	0.491008
10	-0.284639	-2.6088	0.005377
11	0.050498	0.4628	0.322345
12	0.476038	4.363	1.8e-05
13	0.089868	0.8236	0.206235
14	-0.005814	-0.0533	0.478814
15	0.168086	1.5405	0.063594
16	-0.142286	-1.3041	0.097886
17	-0.180945	-1.6584	0.050484
18	0.002246	0.0206	0.491811
19	-0.016507	-0.1513	0.440057
20	0.11531	1.0568	0.14681
21	0.100982	0.9255	0.178675
22	-0.075214	-0.6894	0.246251
23	-0.053121	-0.4869	0.313811
24	0.036582	0.3353	0.369124
25	-0.047048	-0.4312	0.333713
26	-0.07806	-0.7154	0.238162
27	-0.122459	-1.1224	0.132455
28	-0.067153	-0.6155	0.269955
29	0.001065	0.0098	0.496116
30	-0.072711	-0.6664	0.253488
31	0.012486	0.1144	0.454583
32	-0.038493	-0.3528	0.362563
33	-0.062016	-0.5684	0.285645
34	-0.046196	-0.4234	0.336546
35	0.01265	0.1159	0.453989
36	0.080516	0.7379	0.231302
37	0.083828	0.7683	0.222233
38	-0.076805	-0.7039	0.241713
39	-0.034231	-0.3137	0.377251
40	-0.026894	-0.2465	0.402954
41	0.031716	0.2907	0.386006
42	0.026519	0.243	0.40428
43	0.0866	0.7937	0.214803
44	-0.000315	-0.0029	0.498853
45	0.02636	0.2416	0.404841
46	0.017464	0.1601	0.436608
47	-0.033715	-0.309	0.379042
48	-0.032315	-0.2962	0.383916

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/15pwf1292771384.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/15pwf1292771384.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/25pwf1292771384.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/25pwf1292771384.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/35pwf1292771384.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927712795zsk7ht2i495edo/35pwf1292771384.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 (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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