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ACF - D=1 d=0 (ASO)

*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: Tue, 21 Dec 2010 18:37:03 +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/21/t129295650680dnf5v253it0cy.htm/, Retrieved Tue, 21 Dec 2010 19:35:09 +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/21/t129295650680dnf5v253it0cy.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 «

4940 3924 3927 4535 3446 3016 4934 2743 3242 6662 3262 3381 7144 3803 3684 6759 3386 3066 5538 2940 3215 7023 3443 3712 7475 4137 3491 7019 3908 3402 5604 3222 3636 7123 4368 4092 8377 4595 4188 6988 4218 3655 6211 3622 3841 8510 4627 4582 8967 4928 4809 7917 4790 4065 7290 4670 3561 5149 6880 6981 8454 4960 4670 7638 4560 3980 6825 3939 4079 8117 5121 5167 7960 4670 4397 7191 4293 3747 6425 3709 3840 7642 4821 4865

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	0.038754	0.3288	0.371616
2	-0.276967	-2.3501	0.010755
3	0.163899	1.3907	0.084296
4	0.168626	1.4308	0.078401
5	0.080713	0.6849	0.247812
6	0.076472	0.6489	0.259239
7	0.111465	0.9458	0.173703
8	0.063939	0.5425	0.294562
9	0.073049	0.6198	0.268659
10	0.274774	2.3315	0.011264
11	0.092042	0.781	0.21868
12	-0.361597	-3.0683	0.001517
13	0.084972	0.721	0.236619
14	0.16944	1.4377	0.07742
15	0.023879	0.2026	0.420001
16	0.007006	0.0595	0.476379
17	0.024395	0.207	0.418298
18	0.034576	0.2934	0.385036
19	-0.037349	-0.3169	0.376112
20	-0.049349	-0.4187	0.338325
21	-0.019517	-0.1656	0.434466
22	-0.017802	-0.1511	0.440179
23	-0.046089	-0.3911	0.348446
24	0.048484	0.4114	0.341002
25	-0.059617	-0.5059	0.307248
26	-0.029038	-0.2464	0.40304
27	-0.012385	-0.1051	0.458298
28	-0.094668	-0.8033	0.212226
29	-0.105192	-0.8926	0.187526
30	-6.9e-05	-6e-04	0.499767
31	0.008917	0.0757	0.469949
32	-0.059379	-0.5038	0.307954
33	0.002615	0.0222	0.491178
34	-0.044687	-0.3792	0.352835
35	-0.007954	-0.0675	0.473188
36	-0.038029	-0.3227	0.373933
37	-0.010933	-0.0928	0.463171
38	-0.040316	-0.3421	0.36664
39	-0.033285	-0.2824	0.38921
40	0.046317	0.393	0.347737
41	-0.001845	-0.0157	0.493776
42	-0.150451	-1.2766	0.102919
43	0.066429	0.5637	0.287366
44	0.058658	0.4977	0.310095
45	-0.185346	-1.5727	0.060085
46	0.038567	0.3273	0.372212
47	0.04591	0.3896	0.349007
48	-0.046321	-0.393	0.347722

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.038754	0.3288	0.371616
2	-0.278887	-2.3664	0.010327
3	0.204634	1.7364	0.043388
4	0.071595	0.6075	0.272713
5	0.183389	1.5561	0.062034
6	0.105095	0.8918	0.187747
7	0.149016	1.2644	0.105075
8	0.053072	0.4503	0.326913
9	0.090632	0.769	0.222192
10	0.271689	2.3054	0.012016
11	0.074534	0.6324	0.264551
12	-0.357592	-3.0343	0.001677
13	0.004458	0.0378	0.484964
14	-0.239776	-2.0346	0.022789
15	0.069278	0.5878	0.279237
16	-0.071035	-0.6028	0.274283
17	0.073772	0.626	0.266655
18	-0.010109	-0.0858	0.46594
19	-0.00874	-0.0742	0.470544
20	-0.098596	-0.8366	0.20279
21	-0.026634	-0.226	0.410922
22	0.101	0.857	0.19714
23	-0.014917	-0.1266	0.449815
24	-0.078287	-0.6643	0.254314
25	-0.071152	-0.6037	0.273956
26	-0.054782	-0.4648	0.321724
27	0.034919	0.2963	0.383927
28	-0.078418	-0.6654	0.25396
29	-0.033141	-0.2812	0.389678
30	0.041396	0.3513	0.363212
31	0.001178	0.01	0.496026
32	-0.032301	-0.2741	0.392404
33	0.07905	0.6708	0.252258
34	0.047019	0.399	0.345548
35	0.110678	0.9391	0.175401
36	-0.008309	-0.0705	0.471992
37	0.031801	0.2698	0.394026
38	-0.022921	-0.1945	0.42317
39	0.031891	0.2706	0.393734
40	-0.03231	-0.2742	0.392373
41	-0.073812	-0.6263	0.266545
42	-0.193483	-1.6418	0.0525
43	0.102064	0.866	0.194671
44	-0.118851	-1.0085	0.158299
45	-0.085663	-0.7269	0.234831
46	0.044319	0.3761	0.353988
47	0.048252	0.4094	0.34172
48	-0.002853	-0.0242	0.490375

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/1yj401292956621.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/1yj401292956621.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/2qsl31292956621.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/2qsl31292956621.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/31jk51292956621.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t129295650680dnf5v253it0cy/31jk51292956621.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; 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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