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Autocorrelation function D=d=0, Lambda=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: Mon, 21 Dec 2009 06:47:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403303146xiu7ay28ohuu.htm/, Retrieved Mon, 21 Dec 2009 14:48:25 +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/2009/Dec/21/t1261403303146xiu7ay28ohuu.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5

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	0.254465	1.9874	0.025684
2	0.005223	0.0408	0.483796
3	0.145657	1.1376	0.129865
4	0.059413	0.464	0.322138
5	0.281848	2.2013	0.015754
6	0.30924	2.4152	0.009368
7	0.172826	1.3498	0.091032
8	-0.016577	-0.1295	0.448707
9	-0.095706	-0.7475	0.228821
10	-0.292391	-2.2836	0.012944
11	-0.007335	-0.0573	0.47725
12	0.42662	3.332	0.000734
13	-0.055862	-0.4363	0.332082
14	-0.265195	-2.0712	0.021287
15	-0.214449	-1.6749	0.049537
16	-0.138002	-1.0778	0.142676
17	0.039369	0.3075	0.379762
18	0.005935	0.0464	0.48159
19	0.002193	0.0171	0.493196
20	-0.151769	-1.1854	0.120237
21	-0.215484	-1.683	0.048745
22	-0.260895	-2.0377	0.022964
23	-0.073897	-0.5772	0.282979
24	0.23609	1.8439	0.035026
25	-0.05752	-0.4492	0.327422
26	-0.275686	-2.1532	0.017634
27	-0.194924	-1.5224	0.066538
28	-0.107866	-0.8425	0.20141
29	-0.021398	-0.1671	0.433914
30	-0.003125	-0.0244	0.490305
31	-0.012369	-0.0966	0.461678
32	-0.148017	-1.1561	0.126084
33	-0.160928	-1.2569	0.106793
34	-0.131822	-1.0296	0.15364
35	-0.080086	-0.6255	0.26699
36	0.185416	1.4481	0.076348
37	0.012261	0.0958	0.462012
38	-0.178901	-1.3973	0.083698
39	-0.057859	-0.4519	0.326476
40	-0.009721	-0.0759	0.469865
41	0.014077	0.1099	0.456406
42	0.12008	0.9379	0.176009
43	0.065227	0.5094	0.30614
44	-0.0252	-0.1968	0.422312
45	0.052783	0.4122	0.340801
46	0.004483	0.035	0.486092
47	0.055537	0.4338	0.332998
48	0.216634	1.692	0.047877
49	0.080492	0.6287	0.265958
50	0.006645	0.0519	0.47939
51	0.03396	0.2652	0.395861
52	0.000412	0.0032	0.498721
53	0.024199	0.189	0.425361
54	0.053167	0.4152	0.33971
55	0.008381	0.0655	0.474013
56	-0.01334	-0.1042	0.458681
57	-0.024543	-0.1917	0.424311
58	-0.054664	-0.4269	0.335462
59	-0.027045	-0.2112	0.416708
60	-5.7e-05	-4e-04	0.499822

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.254465	1.9874	0.025684
2	-0.063651	-0.4971	0.310442
3	0.172246	1.3453	0.091757
4	-0.027508	-0.2148	0.415303
5	0.318221	2.4854	0.007849
6	0.153226	1.1967	0.11802
7	0.128414	1.0029	0.159925
8	-0.156151	-1.2196	0.113659
9	-0.122063	-0.9533	0.17209
10	-0.493977	-3.8581	0.000139
11	0.015669	0.1224	0.451499
12	0.411531	3.2142	0.001046
13	-0.078073	-0.6098	0.272141
14	-0.175057	-1.3672	0.088284
15	-0.108901	-0.8505	0.199174
16	0.191317	1.4942	0.070135
17	-0.000241	-0.0019	0.499251
18	-0.203348	-1.5882	0.058706
19	-0.033288	-0.26	0.397874
20	-0.089243	-0.697	0.244223
21	0.022426	0.1752	0.430769
22	0.054534	0.4259	0.335831
23	-0.074172	-0.5793	0.282259
24	-0.075765	-0.5917	0.278105
25	-0.025574	-0.1997	0.421175
26	0.020762	0.1622	0.43586
27	0.049887	0.3896	0.349085
28	-0.167436	-1.3077	0.097939
29	-0.145946	-1.1399	0.129397
30	-0.001582	-0.0124	0.49509
31	0.046262	0.3613	0.359555
32	-0.054554	-0.4261	0.335774
33	-0.082385	-0.6434	0.261173
34	0.104517	0.8163	0.208752
35	-0.098169	-0.7667	0.223101
36	-0.012567	-0.0981	0.461068
37	0.029849	0.2331	0.408223
38	0.009044	0.0706	0.471961
39	-0.062104	-0.485	0.31469
40	-0.050588	-0.3951	0.347071
41	-0.075213	-0.5874	0.279541
42	0.111164	0.8682	0.194339
43	-0.064011	-0.4999	0.309458
44	0.055511	0.4336	0.333072
45	0.080362	0.6277	0.266288
46	-0.045595	-0.3561	0.361494
47	0.047058	0.3675	0.357245
48	-0.045611	-0.3562	0.361447
49	-0.023231	-0.1814	0.428313
50	-0.020651	-0.1613	0.4362
51	-0.137281	-1.0722	0.143927
52	-0.058143	-0.4541	0.32568
53	-0.096196	-0.7513	0.227677
54	-0.084088	-0.6567	0.256907
55	0.041573	0.3247	0.373262
56	0.089103	0.6959	0.244563
57	-0.028388	-0.2217	0.412637
58	-0.024944	-0.1948	0.423092
59	0.010299	0.0804	0.468075
60	0.021329	0.1666	0.434125

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403303146xiu7ay28ohuu/1riqt1261403232.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403303146xiu7ay28ohuu/1riqt1261403232.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403303146xiu7ay28ohuu/2lflw1261403232.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403303146xiu7ay28ohuu/2lflw1261403232.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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