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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 18:08:19 +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/17/t1292609172bgmbdhnub78of53.htm/, Retrieved Fri, 17 Dec 2010 19:06:13 +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/17/t1292609172bgmbdhnub78of53.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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.357494	-3.0123	0.001795
2	0.158374	1.3345	0.093155
3	-0.174794	-1.4728	0.072607
4	-0.103129	-0.869	0.193894
5	0.00357	0.0301	0.488042
6	0.025604	0.2157	0.414904
7	-0.04798	-0.4043	0.34361
8	0.153195	1.2908	0.100473
9	0.072962	0.6148	0.270328
10	-0.045447	-0.3829	0.351452
11	-0.052467	-0.4421	0.329884
12	-0.19318	-1.6278	0.054003
13	-0.154818	-1.3045	0.098134
14	0.107784	0.9082	0.183422
15	0.08929	0.7524	0.227158
16	0.049413	0.4164	0.3392
17	0.019447	0.1639	0.435154
18	-0.012459	-0.105	0.458342
19	-0.071869	-0.6056	0.273362
20	-0.114484	-0.9647	0.168996
21	0.158118	1.3323	0.093507
22	-0.285158	-2.4028	0.009444
23	0.399343	3.3649	0.000619
24	-0.160739	-1.3544	0.08995
25	0.166156	1.4001	0.082925
26	-0.013374	-0.1127	0.455295
27	-0.027193	-0.2291	0.409713
28	-0.13132	-1.1065	0.136118
29	0.155706	1.312	0.096872
30	-0.135364	-1.1406	0.128935
31	0.089766	0.7564	0.22596
32	0.012755	0.1075	0.457358
33	-0.104662	-0.8819	0.190405
34	0.124384	1.0481	0.14908
35	-0.05836	-0.4917	0.312207
36	-0.110815	-0.9337	0.176801
37	0.044008	0.3708	0.355939
38	-0.089993	-0.7583	0.225392
39	0.085564	0.721	0.236647
40	0.021812	0.1838	0.427351
41	-0.036862	-0.3106	0.378504
42	0.029668	0.25	0.40166
43	-0.01454	-0.1225	0.451418
44	0.077991	0.6572	0.256599
45	-0.095737	-0.8067	0.211269
46	0.095623	0.8057	0.211543
47	-0.045412	-0.3826	0.351562
48	-0.030736	-0.259	0.398199

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.357494	-3.0123	0.001795
2	0.035052	0.2953	0.384294
3	-0.123553	-1.0411	0.150687
4	-0.239721	-2.0199	0.023583
5	-0.110636	-0.9322	0.177187
6	-0.009314	-0.0785	0.468834
7	-0.117054	-0.9863	0.163664
8	0.064709	0.5452	0.293646
9	0.198299	1.6709	0.049572
10	0.023381	0.197	0.422191
11	-0.071848	-0.6054	0.273422
12	-0.181269	-1.5274	0.065552
13	-0.33239	-2.8008	0.003282
14	-0.1496	-1.2606	0.105799
15	0.055603	0.4685	0.320425
16	-0.029384	-0.2476	0.402583
17	-0.102528	-0.8639	0.195271
18	0.004114	0.0347	0.486222
19	-0.047362	-0.3991	0.345516
20	-0.210645	-1.7749	0.040098
21	0.23076	1.9444	0.027904
22	-0.20237	-1.7052	0.046265
23	0.052039	0.4385	0.331182
24	-0.044248	-0.3728	0.355189
25	-0.084901	-0.7154	0.238357
26	0.004612	0.0389	0.484555
27	0.195223	1.645	0.052197
28	-0.03648	-0.3074	0.379726
29	0.094128	0.7931	0.215171
30	0.046266	0.3898	0.348909
31	-0.114445	-0.9643	0.169077
32	-0.11569	-0.9748	0.16648
33	-0.100038	-0.8429	0.201049
34	0.027233	0.2295	0.409582
35	-0.019998	-0.1685	0.433331
36	-0.05684	-0.4789	0.316725
37	-0.048154	-0.4058	0.343073
38	-0.113522	-0.9566	0.171018
39	0.060402	0.509	0.306179
40	0.087566	0.7378	0.231522
41	-0.067616	-0.5697	0.285324
42	-0.003218	-0.0271	0.489223
43	0.053203	0.4483	0.327652
44	-0.121504	-1.0238	0.1547
45	0.04412	0.3718	0.355588
46	0.095431	0.8041	0.212008
47	0.106928	0.901	0.185319
48	-0.180414	-1.5202	0.066451

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/1oogp1292609295.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/1oogp1292609295.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/2zxxs1292609295.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/2zxxs1292609295.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/3zxxs1292609295.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292609172bgmbdhnub78of53/3zxxs1292609295.ps (open in new window)

Parameters (Session):

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

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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