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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: Fri, 17 Dec 2010 18:01:53 +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/17/t1292608812qzkc02eq50ibs4q.htm/, Retrieved Fri, 17 Dec 2010 19:00:15 +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/17/t1292608812qzkc02eq50ibs4q.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 «

31.514 27.071 29.462 26.105 22.397 23.843 21.705 18.089 20.764 25.316 17.704 15.548 28.029 29.383 36.438 32.034 22.679 24.319 18.004 17.537 20.366 22.782 19.169 13.807 29.743 25.591 29.096 26.482 22.405 27.044 17.970 18.730 19.684 19.785 18.479 10.698 31.956 29.506 34.506 27.165 26.736 23.691 18.157 17.328 18.205 20.995 17.382 9.367 31.124 26.551 30.651 25.859 25.100 25.778 20.418 18.688 20.424 24.776 19.814 12.738 31.566 30.111 30.019 31.934 25.826 26.835 20.205 17.789 20.520 22.518 15.572 11.509 25.447 24.090 27.786 26.195 20.516 22.759 19.028 16.971 20.036 22.485 18.730 14.538

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.378921	3.4729	0.000408
2	0.149573	1.3709	0.087035
3	-0.020125	-0.1844	0.427054
4	-0.187765	-1.7209	0.044476
5	-0.262158	-2.4027	0.009238
6	-0.467771	-4.2872	2.4e-05
7	-0.280825	-2.5738	0.005907
8	-0.216831	-1.9873	0.025074
9	-0.091541	-0.839	0.201928
10	0.042945	0.3936	0.347437
11	0.246048	2.2551	0.013365
12	0.789873	7.2393	0
13	0.301056	2.7592	0.003555
14	0.132102	1.2107	0.114697
15	0.00599	0.0549	0.478176
16	-0.157871	-1.4469	0.075822
17	-0.240412	-2.2034	0.015152
18	-0.459241	-4.209	3.2e-05
19	-0.28256	-2.5897	0.00566
20	-0.231306	-2.12	0.01848
21	-0.131603	-1.2062	0.115571
22	0.013613	0.1248	0.450504
23	0.206122	1.8891	0.031162
24	0.658164	6.0322	0
25	0.275472	2.5247	0.006729
26	0.11231	1.0293	0.153137
27	0.023463	0.215	0.415128
28	-0.108909	-0.9982	0.160533
29	-0.179938	-1.6492	0.051425
30	-0.364842	-3.3438	0.000618
31	-0.215659	-1.9765	0.025687
32	-0.201762	-1.8492	0.033975
33	-0.141473	-1.2966	0.099157
34	0.002581	0.0237	0.490592
35	0.136295	1.2492	0.107538
36	0.512387	4.6961	5e-06
37	0.240998	2.2088	0.014957
38	0.10756	0.9858	0.16353
39	0.050056	0.4588	0.323791
40	-0.053389	-0.4893	0.312946
41	-0.13222	-1.2118	0.11449
42	-0.241397	-2.2124	0.014825
43	-0.1474	-1.3509	0.090171
44	-0.155719	-1.4272	0.078616
45	-0.110047	-1.0086	0.158032
46	-0.017063	-0.1564	0.438052
47	0.074381	0.6817	0.248648
48	0.35593	3.2622	8e-04

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.378921	3.4729	0.000408
2	0.006997	0.0641	0.474511
3	-0.092314	-0.8461	0.199958
4	-0.17836	-1.6347	0.052928
5	-0.148591	-1.3619	0.088442
6	-0.369537	-3.3869	0.000539
7	-0.019346	-0.1773	0.429848
8	-0.154251	-1.4137	0.080568
9	-0.079873	-0.7321	0.233087
10	-0.075222	-0.6894	0.24623
11	0.137572	1.2609	0.105423
12	0.712835	6.5332	0
13	-0.408183	-3.7411	0.000167
14	-0.080208	-0.7351	0.232158
15	0.026798	0.2456	0.403292
16	-0.023059	-0.2113	0.416568
17	-0.081799	-0.7497	0.227766
18	-0.068141	-0.6245	0.266989
19	-0.005009	-0.0459	0.481746
20	-0.059311	-0.5436	0.294079
21	-0.025792	-0.2364	0.406854
22	0.0942	0.8634	0.195199
23	0.033609	0.308	0.379412
24	-0.101514	-0.9304	0.177417
25	0.021722	0.1991	0.421338
26	-0.124999	-1.1456	0.127599
27	-0.019989	-0.1832	0.427542
28	0.055425	0.508	0.306401
29	0.037166	0.3406	0.367114
30	0.104159	0.9546	0.171252
31	-0.027602	-0.253	0.400451
32	-0.04683	-0.4292	0.334435
33	0.002632	0.0241	0.490408
34	0.026559	0.2434	0.404139
35	-0.163049	-1.4944	0.069413
36	-0.045957	-0.4212	0.337343
37	0.059041	0.5411	0.294929
38	0.042025	0.3852	0.350545
39	-0.033893	-0.3106	0.378424
40	0.067747	0.6209	0.268169
41	-0.00397	-0.0364	0.485529
42	0.155908	1.4289	0.078367
43	-0.092219	-0.8452	0.200199
44	0.015607	0.143	0.443302
45	0.071566	0.6559	0.256837
46	-0.167294	-1.5333	0.064483
47	0.029262	0.2682	0.394604
48	-0.056234	-0.5154	0.303815

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/1rryo1292608911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/1rryo1292608911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/2j0y91292608911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/2j0y91292608911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/3j0y91292608911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292608812qzkc02eq50ibs4q/3j0y91292608911.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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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