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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: Sun, 19 Dec 2010 16:26:19 +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/19/t1292775850oixm4mot57e321m.htm/, Retrieved Sun, 19 Dec 2010 17:24:13 +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/19/t1292775850oixm4mot57e321m.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 «

562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274 560576 548854 531673 525919 511038 498662 555362 564591 541657 527070 509846 514258 516922 507561 492622 490243 469357 477580 528379 533590 517945 506174 501866 516141 528222 532638 536322 536535 523597 536214 586570 596594 580523 564478 557560 575093 580112 574761 563250 551531 537034 544686 600991 604378 586111 563668 548604

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	0.209489	1.7527	0.042015
2	0.297996	2.4932	0.007513
3	0.303723	2.5411	0.006634
4	0.200908	1.6809	0.048618
5	0.125268	1.0481	0.149107
6	0.167811	1.404	0.082369
7	0.062675	0.5244	0.300837
8	0.116779	0.977	0.165957
9	0.035726	0.2989	0.382949
10	-0.118386	-0.9905	0.162674
11	0.173871	1.4547	0.07511
12	-0.155845	-1.3039	0.09827
13	-0.130535	-1.0921	0.13926
14	0.038842	0.325	0.373085
15	-0.065921	-0.5515	0.291512
16	-0.087334	-0.7307	0.233705
17	-0.042358	-0.3544	0.362056
18	-0.11122	-0.9305	0.177646
19	-0.0426	-0.3564	0.361299
20	-0.094065	-0.787	0.216968
21	-0.256291	-2.1443	0.017742
22	-0.099057	-0.8288	0.205026
23	-0.148765	-1.2447	0.108704
24	-0.250089	-2.0924	0.020015
25	-0.086957	-0.7275	0.234663
26	-0.221478	-1.853	0.034047
27	-0.251241	-2.102	0.019575
28	-0.220201	-1.8423	0.034831
29	-0.144043	-1.2051	0.116103
30	-0.122792	-1.0274	0.153896
31	0.014007	0.1172	0.453522
32	-0.137835	-1.1532	0.126373
33	0.070542	0.5902	0.278479
34	-0.01921	-0.1607	0.436386
35	0.059947	0.5016	0.308777
36	-0.003053	-0.0255	0.489847
37	-0.017021	-0.1424	0.443583
38	-0.001169	-0.0098	0.496112
39	-0.003356	-0.0281	0.48884
40	0.027063	0.2264	0.410765
41	0.001497	0.0125	0.49502
42	0.067689	0.5663	0.286492
43	-0.030026	-0.2512	0.401191
44	0.04111	0.3439	0.365958
45	-0.033673	-0.2817	0.389491
46	-0.015014	-0.1256	0.450198
47	0.017148	0.1435	0.443167
48	0.032733	0.2739	0.392497

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.209489	1.7527	0.042015
2	0.265775	2.2236	0.014701
3	0.227566	1.904	0.030513
4	0.066606	0.5573	0.289562
5	-0.042649	-0.3568	0.361148
6	0.036502	0.3054	0.380483
7	-0.043602	-0.3648	0.35818
8	0.048067	0.4022	0.344398
9	-0.036046	-0.3016	0.381933
10	-0.204266	-1.709	0.04594
11	0.207566	1.7366	0.043426
12	-0.181914	-1.522	0.066257
13	-0.123442	-1.0328	0.152628
14	0.12055	1.0086	0.158323
15	0.003318	0.0278	0.488965
16	0.002525	0.0211	0.491601
17	-0.058318	-0.4879	0.313565
18	-0.046699	-0.3907	0.348598
19	0.022785	0.1906	0.424681
20	-0.066576	-0.557	0.289647
21	-0.166901	-1.3964	0.083505
22	-0.122954	-1.0287	0.15358
23	0.0393	0.3288	0.371641
24	-0.065798	-0.5505	0.291862
25	-0.030229	-0.2529	0.400536
26	-0.108171	-0.905	0.184278
27	-0.111927	-0.9364	0.176131
28	-0.095514	-0.7991	0.213459
29	0.081362	0.6807	0.249145
30	0.042365	0.3545	0.362032
31	0.142244	1.1901	0.119013
32	-0.024389	-0.204	0.419453
33	0.053859	0.4506	0.326828
34	-0.107922	-0.9029	0.184828
35	0.160655	1.3441	0.091622
36	-0.124914	-1.0451	0.149785
37	-0.15194	-1.2712	0.103929
38	-0.012156	-0.1017	0.459643
39	-0.089676	-0.7503	0.227799
40	0.0263	0.22	0.413241
41	0.005107	0.0427	0.48302
42	-0.014196	-0.1188	0.452898
43	0.03409	0.2852	0.38816
44	-0.053385	-0.4466	0.328254
45	-0.038199	-0.3196	0.375114
46	-0.109066	-0.9125	0.182317
47	0.075818	0.6343	0.263965
48	-0.000185	-0.0015	0.499385

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/1o8zu1292775977.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/1o8zu1292775977.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/2ghyx1292775977.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/2ghyx1292775977.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/3ghyx1292775977.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292775850oixm4mot57e321m/3ghyx1292775977.ps (open in new window)

Parameters (Session):

par1 = Niet-werkende werkzoekenden in Belgie ; par2 = http://www.nbb.be/belgostat/ ; par3 = Niet-werkende werkzoekenden in Belgie ; par4 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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