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TUM (d=1)

*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, 26 Dec 2010 11:31:02 +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/26/t1293362944mne35gqsae8n13e.htm/, Retrieved Sun, 26 Dec 2010 12:29:05 +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/26/t1293362944mne35gqsae8n13e.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 «

10 10 10 10 10 9.94 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 10.06 9.94 9.94 9.94 9.94 9.94 9.94 10.06 10.06 9.94 10.06 10.06 10.06 10.18 10.28 10.28 10.18 10.28 10.28 10.28 10.18 10.28 10.28 10.18 10.18 10.18 10.28 10.28 10.18 10.18 10.18 10.18 10.18 10.18 10.28 10.28 10.28 10.18 10.18 10.18 10.28 10.18 10.18 10.28 10.18 10.18 10.18 10.28 10.28 10.28 10.28 10.28 10.28 10.18 10.18 10.18 10.18 10.18 10.18 10.18 10.18 10.18 10.28 10.28 10.28 10.28 10.28 10.28 10.28 10.28 10.18 10.28 10.28 10.28 10.28 10.18 10.28 10.28 10.28 10.18 10.18 10.28 10.28 10.28 10.28 10.28 10.28 10.28 10.18 10.28 10.28 10.28 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.34 10.34 10.34 10.42 10.42 10.42 10.42 10.34 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.42 10.34 10.34 10.34 10.3 etc...

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	-0.210985	-3.9415	4.9e-05
2	-0.129439	-2.4181	0.008056
3	-0.05129	-0.9582	0.169318
4	-0.035156	-0.6568	0.255882
5	0.064593	1.2067	0.114183
6	-0.097305	-1.8178	0.034975
7	0.084767	1.5836	0.057098
8	0.019631	0.3667	0.357017
9	0.00039	0.0073	0.497094
10	-0.128459	-2.3998	0.008464
11	-0.057128	-1.0672	0.143303
12	0.038861	0.726	0.234169
13	-0.014382	-0.2687	0.394169
14	0.070846	1.3235	0.093266
15	-0.009015	-0.1684	0.43318
16	0.013349	0.2494	0.401605
17	-0.079537	-1.4859	0.069107
18	-0.035369	-0.6608	0.254604
19	0.097431	1.8202	0.034795
20	-0.047074	-0.8794	0.18989
21	0.081217	1.5173	0.065054
22	-0.056128	-1.0486	0.147555
23	-0.053586	-1.0011	0.158745
24	0.066472	1.2418	0.107572
25	-0.062377	-1.1653	0.122347
26	0.063426	1.1849	0.118432
27	-0.031443	-0.5874	0.278659
28	-0.042292	-0.7901	0.215012
29	0.054911	1.0258	0.152841
30	0.045277	0.8458	0.199109
31	0.005627	0.1051	0.458173
32	-0.056333	-1.0524	0.146673
33	0.064768	1.21	0.113555
34	0.01464	0.2735	0.392313
35	-0.075435	-1.4092	0.079826
36	0.010925	0.2041	0.419198
37	0.019414	0.3627	0.358533
38	0.035265	0.6588	0.25523
39	-0.030034	-0.5611	0.287553
40	-0.055059	-1.0286	0.152194
41	-0.06979	-1.3038	0.096583
42	0.030991	0.579	0.281495
43	-0.038392	-0.7172	0.236857
44	0.02758	0.5152	0.303358
45	0.098953	1.8486	0.032681
46	-0.097573	-1.8228	0.034593
47	0.046249	0.864	0.194087
48	-0.059946	-1.1199	0.131767

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.210985	-3.9415	4.9e-05
2	-0.182058	-3.4011	0.000374
3	-0.132043	-2.4668	0.007057
4	-0.11553	-2.1583	0.015794
5	-0.00381	-0.0712	0.471648
6	-0.124414	-2.3242	0.010343
7	0.031343	0.5855	0.27928
8	0.018075	0.3377	0.367905
9	0.023419	0.4375	0.331006
10	-0.129006	-2.41	0.008234
11	-0.116373	-2.174	0.015187
12	-0.076156	-1.4227	0.077857
13	-0.083008	-1.5507	0.060939
14	0.00514	0.096	0.461781
15	-0.010048	-0.1877	0.425607
16	0.001499	0.028	0.488838
17	-0.082087	-1.5335	0.063027
18	-0.068807	-1.2854	0.099748
19	0.034618	0.6467	0.259118
20	-0.062283	-1.1635	0.122704
21	0.033925	0.6338	0.26332
22	-0.050827	-0.9495	0.171503
23	-0.09377	-1.7518	0.040347
24	0.019461	0.3636	0.358202
25	-0.046866	-0.8755	0.190946
26	0.018458	0.3448	0.365217
27	-0.039433	-0.7367	0.23091
28	-0.102284	-1.9108	0.028423
29	0.001783	0.0333	0.486722
30	0.057327	1.071	0.142463
31	0.041436	0.7741	0.2197
32	-0.013314	-0.2487	0.401858
33	0.038976	0.7281	0.233511
34	0.037317	0.6971	0.243092
35	-0.064614	-1.2071	0.114108
36	0.012495	0.2334	0.407781
37	0.013928	0.2602	0.397435
38	0.005713	0.1067	0.457536
39	0.005938	0.1109	0.455864
40	-0.057468	-1.0736	0.141875
41	-0.100086	-1.8698	0.031178
42	-0.035044	-0.6547	0.256557
43	-0.09848	-1.8398	0.033326
44	-0.01857	-0.3469	0.364431
45	0.022711	0.4243	0.335813
46	-0.083093	-1.5523	0.060748
47	0.029951	0.5595	0.288078
48	-0.063225	-1.1811	0.119177

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293362944mne35gqsae8n13e/1hbhz1293363059.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293362944mne35gqsae8n13e/1hbhz1293363059.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293362944mne35gqsae8n13e/2hbhz1293363059.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293362944mne35gqsae8n13e/2hbhz1293363059.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; 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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