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ACF Arma

*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, 29 Dec 2010 15:14:42 +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/29/t1293635579vkiuvszshyxmx3c.htm/, Retrieved Wed, 29 Dec 2010 16:13:02 +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/29/t1293635579vkiuvszshyxmx3c.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 «

5745 4549 5074 3602 2732 2589 2148 2330 2752 3241 4517 6550 6778 6240 5570 3558 3299 2447 2380 2378 2947 3651 4816 6436 7090 4682 4198 3860 3056 2563 2568 2472 2821 4015 4686 5418 5649 4572 4695 3766 2900 2528 2549 2478 2828 4139 5390 5621 5291 5272 4677 3520 2842 2723 2581 2429 2606 3787 4630 5505 5577 4911 4701 3557 2921 2734 2636 2433 2640 3794 4745 5698 5909 5119 5200 3876 3104 2251 2386 2794 2967 3392 4741 5909 5901 4962 4751 3909 3130 2860 2568 2540 2894 4216 4530 5144 6206 5645 4601 3645 3140 2264 2557 2431 2747 4587 4512 5313 6011 5328 5014 3630 3102 2739 2877 2659 2957 3785 4785 5757 5458 5427 5018 3498 3204 2763 2589 2591 2805 3278 4615 5524 6167 5380 5377 3603 2774 2470 2407 2512 2451 3134 4210 4859 5022 4584 4267 3022 2777 2428 2389 2496 2820 3854 4748 5666 5293 4905 4920 3854 2659 2491 2455 2472 3030 3987 4453 5417

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.27448	3.4283	0.000389
2	0.051925	0.6485	0.258793
3	0.186883	2.3342	0.010431
4	0.108966	1.361	0.087741
5	0.031464	0.393	0.347435
6	0.044793	0.5595	0.288322
7	0.009766	0.122	0.451537
8	0.007293	0.0911	0.46377
9	0.069411	0.8669	0.193654
10	0.013289	0.166	0.434193
11	-0.040112	-0.501	0.308537
12	-0.371644	-4.6418	4e-06
13	-0.163663	-2.0442	0.02131
14	-0.053723	-0.671	0.251606
15	-0.14692	-1.835	0.034203
16	-0.038233	-0.4775	0.316826
17	0.038884	0.4857	0.313944
18	-0.017748	-0.2217	0.412431
19	-0.022887	-0.2859	0.387684
20	0.054525	0.681	0.248435
21	-0.025775	-0.3219	0.373968
22	-0.047824	-0.5973	0.275578
23	-0.069395	-0.8667	0.193709
24	-0.061284	-0.7654	0.222585
25	0.048275	0.603	0.273707
26	0.054142	0.6762	0.249948
27	-0.057644	-0.72	0.23631
28	-0.143039	-1.7866	0.037976
29	-0.047187	-0.5894	0.278236
30	-0.002666	-0.0333	0.486742
31	-0.084819	-1.0594	0.145529
32	-0.125596	-1.5687	0.059373
33	-0.056909	-0.7108	0.239136
34	0.021794	0.2722	0.392909
35	-0.000888	-0.0111	0.495583
36	-0.029283	-0.3657	0.357525
37	-0.014295	-0.1785	0.429265
38	-0.035869	-0.448	0.327388
39	0.053308	0.6658	0.253255
40	0.093271	1.1649	0.122909
41	0.060877	0.7604	0.224095
42	0.070706	0.8831	0.189265
43	0.12637	1.5784	0.058255
44	0.050849	0.6351	0.263146
45	0.112171	1.401	0.081598
46	0.093529	1.1682	0.122258
47	-0.082988	-1.0365	0.150781
48	-0.054452	-0.6801	0.248721

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.27448	3.4283	0.000389
2	-0.025322	-0.3163	0.376111
3	0.193946	2.4224	0.008282
4	0.007161	0.0894	0.464424
5	0.003722	0.0465	0.481492
6	0.008204	0.1025	0.459259
7	-0.027927	-0.3488	0.363853
8	0.008734	0.1091	0.456636
9	0.062464	0.7802	0.218236
10	-0.023353	-0.2917	0.38546
11	-0.037122	-0.4637	0.321771
12	-0.422322	-5.2748	0
13	0.047929	0.5986	0.275145
14	-0.046617	-0.5822	0.28062
15	0.014255	0.1781	0.429457
16	0.097814	1.2217	0.111833
17	0.049906	0.6233	0.266991
18	0.003048	0.0381	0.484842
19	-0.032788	-0.4095	0.341359
20	0.055611	0.6946	0.244174
21	0.027362	0.3418	0.366497
22	-0.04078	-0.5093	0.305618
23	-0.069957	-0.8738	0.191795
24	-0.232674	-2.9061	0.002096
25	0.078806	0.9843	0.163249
26	0.014219	0.1776	0.429635
27	-0.11142	-1.3916	0.083007
28	-0.107752	-1.3458	0.090157
29	0.027189	0.3396	0.367312
30	0.048917	0.611	0.271054
31	-0.058295	-0.7281	0.233822
32	0.004097	0.0512	0.479629
33	0.019293	0.241	0.404947
34	0.022624	0.2826	0.388941
35	-0.034789	-0.4345	0.332256
36	-0.142612	-1.7812	0.038411
37	0.082368	1.0288	0.152589
38	-0.024072	-0.3007	0.382037
39	0.026847	0.3353	0.368917
40	-0.028922	-0.3612	0.359206
41	0.081394	1.0166	0.155456
42	0.073208	0.9144	0.180966
43	-0.007899	-0.0987	0.460767
44	-0.042674	-0.533	0.297396
45	0.14343	1.7914	0.037581
46	0.002862	0.0357	0.485764
47	-0.21095	-2.6348	0.004634
48	-0.154269	-1.9268	0.02791

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/1txxg1293635680.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/1txxg1293635680.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/2ram71293635680.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/2ram71293635680.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/3fgw31293635680.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635579vkiuvszshyxmx3c/3fgw31293635680.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = -0.8 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = -0.8 ; par3 = 0 ; 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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