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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, 24 Dec 2010 15:17:57 +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/24/t1293203745n5ym6uzmf9955cl.htm/, Retrieved Fri, 24 Dec 2010 16:15:45 +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/24/t1293203745n5ym6uzmf9955cl.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 «

1.35 1.91 1.31 1.19 1.3 1.14 1.1 1.02 1.11 1.18 1.24 1.36 1.29 1.73 1.41 1.15 1.31 1.15 1.08 1.1 1.14 1.24 1.33 1.49 1.38 1.96 1.36 1.24 1.35 1.23 1.09 1.08 1.33 1.35 1.38 1.5 1.47 2.09 1.52 1.29 1.52 1.27 1.35 1.29 1.41 1.39 1.45 1.53 1.45 2.11 1.53 1.38 1.54 1.35 1.29 1.33 1.47 1.47 1.54 1.59 1.5 2 1.51 1.4 1.62 1.44 1.29 1.28 1.4 1.39 1.46 1.49

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.312919	2.4239	0.009194
2	0.303151	2.3482	0.011089
3	0.115592	0.8954	0.187083
4	0.156506	1.2123	0.115077
5	0.161429	1.2504	0.108
6	0.048415	0.375	0.354484
7	0.075678	0.5862	0.279971
8	0.087958	0.6813	0.249146
9	0.086535	0.6703	0.25262
10	-0.018118	-0.1403	0.44443
11	-0.013059	-0.1012	0.459882
12	-0.245834	-1.9042	0.03084
13	0.163434	1.266	0.105211
14	0.030455	0.2359	0.407155
15	0.144774	1.1214	0.133289
16	-0.040222	-0.3116	0.378229
17	0.079715	0.6175	0.26963
18	0.098481	0.7628	0.224276
19	-0.006072	-0.047	0.481322
20	-0.046221	-0.358	0.360791
21	0.00958	0.0742	0.470547
22	-0.003363	-0.026	0.489653
23	-0.067507	-0.5229	0.301484
24	-0.163863	-1.2693	0.104622
25	-0.316914	-2.4548	0.008506
26	-0.143381	-1.1106	0.135581
27	-0.297808	-2.3068	0.012267
28	-0.176331	-1.3659	0.088541
29	-0.353526	-2.7384	0.004058
30	-0.235212	-1.8219	0.036724
31	-0.165841	-1.2846	0.101935
32	-0.038826	-0.3007	0.382323
33	-0.058658	-0.4544	0.325602
34	-0.069138	-0.5355	0.297128
35	0.017067	0.1322	0.447633
36	-0.047696	-0.3695	0.356545
37	-0.036092	-0.2796	0.390386
38	-0.117749	-0.9121	0.182688
39	-0.040005	-0.3099	0.378864
40	-0.010595	-0.0821	0.467433
41	0.035865	0.2778	0.391057
42	-0.030062	-0.2329	0.408331
43	-0.045364	-0.3514	0.363264
44	-0.08233	-0.6377	0.26304
45	-0.084272	-0.6528	0.258199
46	-0.103105	-0.7986	0.213823
47	-0.086138	-0.6672	0.253594
48	0.022039	0.1707	0.432511

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.312919	2.4239	0.009194
2	0.22751	1.7623	0.041557
3	-0.033762	-0.2615	0.397293
4	0.078179	0.6056	0.273542
5	0.104278	0.8077	0.211217
6	-0.077878	-0.6032	0.274311
7	0.022349	0.1731	0.431571
8	0.077776	0.6024	0.274573
9	0.009455	0.0732	0.470929
10	-0.104371	-0.8085	0.211012
11	-0.006019	-0.0466	0.481483
12	-0.275793	-2.1363	0.018372
13	0.351007	2.7189	0.004276
14	0.031132	0.2411	0.405132
15	0.03299	0.2555	0.399589
16	-0.110226	-0.8538	0.198304
17	0.143947	1.115	0.134646
18	-0.017793	-0.1378	0.445419
19	-0.06405	-0.4961	0.310809
20	-0.072402	-0.5608	0.288502
21	0.107206	0.8304	0.204798
22	-0.147026	-1.1389	0.129644
23	-0.074644	-0.5782	0.282649
24	-0.269859	-2.0903	0.020417
25	-0.021052	-0.1631	0.435507
26	-0.019523	-0.1512	0.440154
27	-0.126955	-0.9834	0.164683
28	-0.186882	-1.4476	0.076469
29	-0.064996	-0.5035	0.308243
30	-0.044856	-0.3475	0.364732
31	-0.006557	-0.0508	0.47983
32	0.12912	1.0002	0.160625
33	0.1522	1.1789	0.121538
34	-0.060849	-0.4713	0.319556
35	0.077965	0.6039	0.274088
36	-0.210984	-1.6343	0.053719
37	0.017068	0.1322	0.447631
38	0.052104	0.4036	0.343972
39	-0.064433	-0.4991	0.309768
40	0.031093	0.2408	0.405249
41	0.001808	0.014	0.494437
42	0.075217	0.5826	0.281163
43	-0.043866	-0.3398	0.367604
44	0.086771	0.6721	0.252041
45	-0.032026	-0.2481	0.402463
46	-0.059534	-0.4612	0.323179
47	0.006817	0.0528	0.47903
48	0.008726	0.0676	0.473168

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/1oh861293203873.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/1oh861293203873.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/2k9r71293203874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/2k9r71293203874.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/3k9r71293203874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203745n5ym6uzmf9955cl/3k9r71293203874.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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