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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: Tue, 28 Dec 2010 08:41:49 +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/28/t1293525609gsk6gr6ilx169vw.htm/, Retrieved Tue, 28 Dec 2010 09:40:09 +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/28/t1293525609gsk6gr6ilx169vw.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 «

547.344 554.788 562.325 560.854 555.332 543.599 536.662 542.722 593.530 610.763 612.613 611.324 594.167 595.454 590.865 589.379 584.428 573.100 567.456 569.028 620.735 628.884 628.232 612.117 595.404 597.141 593.408 590.072 579.799 574.205 572.775 572.942 619.567 625.809 619.916 587.625 565.742 557.274 560.576 548.854 531.673 525.919 511.038 498.662 555.362 564.591 541.657 527.070 509.846 514.258 516.922 507.561 492.622 490.243 469.357 477.580 528.379 533.590 517.945 506.174 501.866 516.141 528.222 532.638 536.322 536.535 523.597 536.214 586.570 596.594 580.523 564.478 557.560 575.093 580.112 574.761 563.250 551.531 537.034 544.686 600.991 604.378 586.111 563.668 548.604

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.276319	2.5325	0.006593
2	-0.25494	-2.3366	0.010922
3	-0.351435	-3.221	0.000909
4	-0.242419	-2.2218	0.014493
5	0.094336	0.8646	0.19486
6	0.233912	2.1438	0.017468
7	0.123402	1.131	0.130638
8	-0.192378	-1.7632	0.040754
9	-0.292315	-2.6791	0.00444
10	-0.236838	-2.1707	0.01639
11	0.247427	2.2677	0.012957
12	0.768056	7.0393	0
13	0.156858	1.4376	0.077128
14	-0.267707	-2.4536	0.008106
15	-0.334561	-3.0663	0.001458
16	-0.20648	-1.8924	0.03094
17	0.084815	0.7773	0.21957
18	0.180861	1.6576	0.050563
19	0.061402	0.5628	0.28755
20	-0.209758	-1.9225	0.028968
21	-0.268405	-2.46	0.007972
22	-0.193565	-1.7741	0.039839
23	0.209127	1.9167	0.029339
24	0.605993	5.554	0
25	0.095515	0.8754	0.191924
26	-0.267634	-2.4529	0.00812
27	-0.302137	-2.7691	0.003458
28	-0.183615	-1.6829	0.048058
29	0.070177	0.6432	0.260929
30	0.151056	1.3845	0.084943
31	0.044474	0.4076	0.342297
32	-0.193815	-1.7763	0.039648
33	-0.213127	-1.9533	0.027054
34	-0.139295	-1.2767	0.10262
35	0.193573	1.7741	0.039833
36	0.491721	4.5067	1.1e-05
37	0.054307	0.4977	0.309985
38	-0.215734	-1.9772	0.025648
39	-0.211815	-1.9413	0.027786
40	-0.10689	-0.9797	0.165033
41	0.082951	0.7603	0.224613
42	0.128767	1.1802	0.120632
43	0.0295	0.2704	0.393769
44	-0.14617	-1.3397	0.091982
45	-0.160908	-1.4747	0.072009
46	-0.063838	-0.5851	0.28003
47	0.167727	1.5372	0.063996
48	0.351522	3.2218	0.000907

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.276319	2.5325	0.006593
2	-0.358678	-3.2873	0.000739
3	-0.194595	-1.7835	0.039059
4	-0.19895	-1.8234	0.035899
5	0.080086	0.734	0.232497
6	0.015065	0.1381	0.445257
7	0.00352	0.0323	0.487169
8	-0.220475	-2.0207	0.023249
9	-0.117355	-1.0756	0.142598
10	-0.254019	-2.3281	0.011155
11	0.27854	2.5529	0.006246
12	0.623465	5.7141	0
13	-0.294943	-2.7032	0.004155
14	0.044145	0.4046	0.343402
15	0.052611	0.4822	0.315464
16	0.030276	0.2775	0.391045
17	-0.073228	-0.6711	0.251984
18	-0.138625	-1.2705	0.103703
19	-0.12303	-1.1276	0.131352
20	-0.09735	-0.8922	0.187411
21	-0.068708	-0.6297	0.265294
22	-0.034247	-0.3139	0.377196
23	-0.164558	-1.5082	0.067628
24	0.029273	0.2683	0.394566
25	-0.011553	-0.1059	0.457963
26	-0.062342	-0.5714	0.284635
27	-0.005424	-0.0497	0.480236
28	-0.091171	-0.8356	0.202875
29	-0.040618	-0.3723	0.355314
30	-0.028678	-0.2628	0.396658
31	-0.029845	-0.2735	0.392558
32	-0.073556	-0.6741	0.251034
33	-0.025738	-0.2359	0.407045
34	-0.035576	-0.3261	0.372596
35	-0.019027	-0.1744	0.430989
36	-0.058215	-0.5336	0.29753
37	-0.049768	-0.4561	0.324735
38	0.038325	0.3513	0.363137
39	0.048446	0.444	0.329087
40	0.029304	0.2686	0.394458
41	-0.029329	-0.2688	0.394371
42	-0.022109	-0.2026	0.419956
43	0.011217	0.1028	0.45918
44	0.057684	0.5287	0.29921
45	-0.098976	-0.9071	0.183466
46	0.049003	0.4491	0.327252
47	-0.154766	-1.4185	0.079879
48	-0.112914	-1.0349	0.151848

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/1cc4b1293525706.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/1cc4b1293525706.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/2m3le1293525706.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/2m3le1293525706.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/3m3le1293525706.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525609gsk6gr6ilx169vw/3m3le1293525706.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 = 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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