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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: Sat, 11 Dec 2010 23:31:44 +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/12/t1292110184xl54unnw1c0opv0.htm/, Retrieved Sun, 12 Dec 2010 00:29:46 +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/12/t1292110184xl54unnw1c0opv0.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 «

100918 105017 108666 116083 117359 102191 102617 106640 108783 112534 113149 117125 107597 108745 111311 115669 114585 101628 97493 99180 100247 97657 95378 89406 82880 82662 83469 86371 86822 73899 71415 76335 76844 78192 80651 81485 78872 81632 84822 92175 92844 77443 77550 80367 83117 86622 90999 90276 91982 96279 106810 109483 110159 98305 99450 101536 99925 102850 101993 108928 107605

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.907745	7.0897	0
2	0.78833	6.1571	0
3	0.714772	5.5825	0
4	0.676077	5.2803	1e-06
5	0.652454	5.0958	2e-06
6	0.602182	4.7032	8e-06
7	0.53039	4.1425	5.4e-05
8	0.426862	3.3339	0.00073
9	0.320941	2.5066	0.007435
10	0.249686	1.9501	0.027881
11	0.223439	1.7451	0.043
12	0.184606	1.4418	0.077234
13	0.057766	0.4512	0.326734
14	-0.078275	-0.6113	0.27162
15	-0.168315	-1.3146	0.096786
16	-0.22553	-1.7614	0.041587
17	-0.258535	-2.0192	0.023932
18	-0.302557	-2.363	0.010665
19	-0.351555	-2.7457	0.003961
20	-0.411775	-3.2161	0.00104
21	-0.477623	-3.7304	0.000211
22	-0.500667	-3.9103	0.000117
23	-0.475228	-3.7116	0.000224
24	-0.448397	-3.5021	0.000435
25	-0.483642	-3.7774	0.000181
26	-0.521075	-4.0697	6.9e-05
27	-0.518535	-4.0499	7.4e-05
28	-0.485399	-3.7911	0.000173
29	-0.437828	-3.4195	0.000562
30	-0.39668	-3.0982	0.001471
31	-0.35085	-2.7402	0.004021
32	-0.320247	-2.5012	0.007539
33	-0.294305	-2.2986	0.012484
34	-0.241844	-1.8889	0.031834
35	-0.164112	-1.2818	0.10239
36	-0.097532	-0.7618	0.224572
37	-0.077974	-0.609	0.272393
38	-0.070339	-0.5494	0.29238
39	-0.044738	-0.3494	0.363991
40	-0.019632	-0.1533	0.439321
41	0.010768	0.0841	0.466626
42	0.037955	0.2964	0.38395
43	0.068558	0.5355	0.297142
44	0.085966	0.6714	0.252246
45	0.088055	0.6877	0.247113
46	0.103742	0.8103	0.210472
47	0.122901	0.9599	0.17045
48	0.143082	1.1175	0.13408

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.907745	7.0897	0
2	-0.202674	-1.5829	0.059304
3	0.225822	1.7637	0.041393
4	0.075971	0.5934	0.277569
5	0.0807	0.6303	0.26543
6	-0.139113	-1.0865	0.140765
7	-0.050442	-0.394	0.347491
8	-0.263742	-2.0599	0.021841
9	-0.078701	-0.6147	0.270528
10	0.004068	0.0318	0.487379
11	0.148486	1.1597	0.125343
12	-0.149612	-1.1685	0.123574
13	-0.428606	-3.3475	7e-04
14	0.008885	0.0694	0.472453
15	0.022885	0.1787	0.429369
16	-0.06416	-0.5011	0.30905
17	0.017512	0.1368	0.445831
18	-0.067225	-0.525	0.300727
19	0.041571	0.3247	0.373268
20	-0.001661	-0.013	0.494847
21	-0.069646	-0.544	0.294229
22	0.043705	0.3414	0.367006
23	0.043048	0.3362	0.368932
24	0.017255	0.1348	0.446619
25	-0.160306	-1.252	0.107669
26	0.058592	0.4576	0.324425
27	-0.005283	-0.0413	0.483612
28	0.037277	0.2911	0.385966
29	-0.070215	-0.5484	0.292709
30	0.027328	0.2134	0.415847
31	0.061818	0.4828	0.315479
32	-0.016181	-0.1264	0.449925
33	0.073461	0.5738	0.284123
34	-0.036877	-0.288	0.387154
35	-0.046999	-0.3671	0.357417
36	-0.039111	-0.3055	0.380525
37	-0.014823	-0.1158	0.454107
38	-0.070516	-0.5507	0.291908
39	-0.084205	-0.6577	0.256614
40	-0.171701	-1.341	0.092442
41	0.01691	0.1321	0.44768
42	-0.030863	-0.241	0.405164
43	0.025646	0.2003	0.420956
44	-0.005906	-0.0461	0.481679
45	0.031891	0.2491	0.40207
46	-0.005241	-0.0409	0.48374
47	-0.059721	-0.4664	0.321282
48	0.087764	0.6855	0.247825

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292110184xl54unnw1c0opv0/1xtmf1292110302.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292110184xl54unnw1c0opv0/1xtmf1292110302.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292110184xl54unnw1c0opv0/2xtmf1292110302.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292110184xl54unnw1c0opv0/2xtmf1292110302.ps (open in new window)

Parameters (Session):

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 (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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