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Paper Statistiek

*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, 27 Dec 2010 19:09:24 +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/27/t1293476899oyl4sl2idb32bnc.htm/, Retrieved Mon, 27 Dec 2010 20:08:20 +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/27/t1293476899oyl4sl2idb32bnc.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:

Partial Autocorrelation Function - Handelbalans België (1995-2009)

Dataseries X:

» Textbox « » Textfile « » CSV «

2540,9 2370,3 1807,5 1834,8 786,8 1561,4 1347,2 1549,8 1553,8 1822,5 3078,7 1589,1 1791,5 2558,1 2111,8 2083,1 2052,1 2243,5 2622 1952,6 808,9 1709,8 1582,1 865,6 1116,1 1119,4 2350 1975,6 2536,5 2785 2819,7 1829,5 758,3 2921,6 2482 1892,7 1855,1 2151,3 1642,2 1640,5 1366,1 1532,8 824,4 -518,7 -978,5 1162,5 1243,4 1199,5 883,1 1437,2 534,5 -1901,9 -2521,1 -1721,1 -3094,5 -3694,8 -2492,1 -464,6 -626,1 -1711,4

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	0.811988	6.2896	0
2	0.659591	5.1092	2e-06
3	0.616111	4.7724	6e-06
4	0.528626	4.0947	6.4e-05
5	0.365002	2.8273	0.003185
6	0.235933	1.8275	0.036297
7	0.268913	2.083	0.020761
8	0.27149	2.1029	0.019837
9	0.188528	1.4603	0.074708
10	0.15358	1.1896	0.119439
11	0.201241	1.5588	0.062151
12	0.209096	1.6196	0.055276
13	0.101206	0.7839	0.218079
14	0.028151	0.2181	0.414063
15	0.045208	0.3502	0.363714
16	0.032624	0.2527	0.400679
17	-0.045331	-0.3511	0.36336
18	-0.078874	-0.611	0.27177
19	-0.053447	-0.414	0.340175
20	-0.055573	-0.4305	0.334199
21	-0.112076	-0.8681	0.194389
22	-0.173479	-1.3438	0.092043
23	-0.130349	-1.0097	0.158351
24	-0.142849	-1.1065	0.136463
25	-0.206398	-1.5987	0.057565
26	-0.191988	-1.4871	0.071108
27	-0.114008	-0.8831	0.190353
28	-0.099262	-0.7689	0.222489
29	-0.113395	-0.8784	0.191629
30	-0.096289	-0.7459	0.229335
31	-0.060366	-0.4676	0.320884
32	-0.051675	-0.4003	0.345188
33	-0.090838	-0.7036	0.242193
34	-0.106151	-0.8222	0.207097
35	-0.105852	-0.8199	0.207752
36	-0.127037	-0.984	0.164527
37	-0.176353	-1.366	0.088515
38	-0.19299	-1.4949	0.070092
39	-0.171585	-1.3291	0.094425
40	-0.192536	-1.4914	0.070551
41	-0.238455	-1.8471	0.034835
42	-0.23894	-1.8508	0.03456
43	-0.215174	-1.6667	0.05039
44	-0.190027	-1.4719	0.073131
45	-0.168933	-1.3085	0.097839
46	-0.147578	-1.1431	0.128762
47	-0.097628	-0.7562	0.226236
48	-0.091506	-0.7088	0.240596

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.811988	6.2896	0
2	0.00078	0.006	0.497599
3	0.235753	1.8261	0.036403
4	-0.114759	-0.8889	0.188797
5	-0.223578	-1.7318	0.044221
6	-0.089478	-0.6931	0.245464
7	0.345041	2.6727	0.004838
8	0.048622	0.3766	0.35389
9	-0.087191	-0.6754	0.251015
10	-0.067491	-0.5228	0.301525
11	0.07048	0.5459	0.293567
12	0.025402	0.1968	0.422339
13	-0.151848	-1.1762	0.122079
14	-0.107609	-0.8335	0.203925
15	0.040269	0.3119	0.37809
16	0.086808	0.6724	0.251952
17	-0.003468	-0.0269	0.48933
18	-0.054413	-0.4215	0.337455
19	-0.119744	-0.9275	0.178682
20	0.004654	0.036	0.485682
21	0.020849	0.1615	0.436122
22	-0.160057	-1.2398	0.109939
23	0.108092	0.8373	0.202879
24	-0.095862	-0.7425	0.230328
25	0.030972	0.2399	0.40561
26	0.113874	0.8821	0.190631
27	0.092887	0.7195	0.237313
28	-0.173618	-1.3448	0.09187
29	0.082308	0.6376	0.263095
30	-0.090843	-0.7037	0.24218
31	0.001888	0.0146	0.494189
32	0.095363	0.7387	0.23149
33	-0.03761	-0.2913	0.385904
34	-0.101055	-0.7828	0.21842
35	-0.080177	-0.621	0.26846
36	0.00727	0.0563	0.477638
37	-0.051901	-0.402	0.344547
38	-0.019251	-0.1491	0.440981
39	-0.062768	-0.4862	0.314299
40	-0.056748	-0.4396	0.330916
41	-0.08206	-0.6356	0.263716
42	0.059806	0.4633	0.322428
43	0.022977	0.178	0.42967
44	0.020647	0.1599	0.436737
45	0.133986	1.0379	0.151752
46	-0.113449	-0.8788	0.191515
47	0.000451	0.0035	0.498612
48	-0.084881	-0.6575	0.256691

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/14y4j1293476961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/14y4j1293476961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/2fplm1293476961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/2fplm1293476961.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/3fplm1293476961.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293476899oyl4sl2idb32bnc/3fplm1293476961.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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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