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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 16 Jan 2011 12:32:26 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay.htm/, Retrieved Sun, 16 Jan 2011 13:30:43 +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/2011/Jan/16/t1295181040oro5ljczcav4qay.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18073 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320 24977 25204 27390 26434 27525 30695 32436 30160 30236

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	'Gwilym Jenkins' @ www.wessa.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.031689	0.2689	0.394392
2	-0.215919	-1.8321	0.035533
3	0.083832	0.7113	0.239587
4	0.140857	1.1952	0.117963
5	-0.178329	-1.5132	0.067307
6	-0.077646	-0.6589	0.256046
7	0.000735	0.0062	0.497519
8	-0.094618	-0.8029	0.212348
9	0.005262	0.0446	0.482255
10	-0.147738	-1.2536	0.107021
11	0.042511	0.3607	0.359685
12	0.16087	1.365	0.088248
13	-0.007047	-0.0598	0.476243
14	-0.081043	-0.6877	0.246933
15	0.10167	0.8627	0.195584
16	0.191434	1.6244	0.054333
17	-0.13216	-1.1214	0.132919
18	-0.155043	-1.3156	0.096244
19	-0.049745	-0.4221	0.337106
20	0.054659	0.4638	0.322096
21	-0.073431	-0.6231	0.267598
22	0.038108	0.3234	0.373682
23	0.111293	0.9444	0.174073
24	0.012053	0.1023	0.459413
25	-0.059318	-0.5033	0.308134
26	-0.01888	-0.1602	0.436585
27	0.157273	1.3345	0.093122
28	-0.005978	-0.0507	0.479841
29	-0.006004	-0.0509	0.479756
30	-0.082831	-0.7028	0.242209
31	0.035333	0.2998	0.382592
32	-0.085113	-0.7222	0.236252
33	0.060236	0.5111	0.305414
34	0.022706	0.1927	0.423882
35	-0.120197	-1.0199	0.155594
36	0.011172	0.0948	0.462369
37	0.022725	0.1928	0.423817
38	-0.058823	-0.4991	0.309605
39	0.015462	0.1312	0.447993
40	0.043273	0.3672	0.357281
41	-0.108088	-0.9172	0.18106
42	-0.013893	-0.1179	0.453243
43	0.052517	0.4456	0.328604
44	-0.145327	-1.2331	0.110767
45	0.037289	0.3164	0.376306
46	0.039766	0.3374	0.368388
47	-0.063534	-0.5391	0.295739
48	-0.017412	-0.1477	0.44148

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.031689	0.2689	0.394392
2	-0.217141	-1.8425	0.034759
3	0.104046	0.8829	0.190125
4	0.089935	0.7631	0.223943
5	-0.160953	-1.3657	0.088137
6	-0.020815	-0.1766	0.43015
7	-0.086101	-0.7306	0.233701
8	-0.106896	-0.907	0.183706
9	0.053065	0.4503	0.326933
10	-0.227099	-1.927	0.028963
11	0.096556	0.8193	0.207658
12	0.101256	0.8592	0.196545
13	-0.043896	-0.3725	0.355319
14	0.024269	0.2059	0.418714
15	-0.002302	-0.0195	0.492235
16	0.156077	1.3244	0.094786
17	-0.085194	-0.7229	0.236044
18	-0.145736	-1.2366	0.110125
19	-0.085676	-0.727	0.234795
20	-0.003796	-0.0322	0.487196
21	0.001766	0.015	0.494043
22	0.129132	1.0957	0.138427
23	0.061934	0.5255	0.300416
24	0.00952	0.0808	0.46792
25	-0.048751	-0.4137	0.340173
26	-0.050484	-0.4284	0.33483
27	0.09798	0.8314	0.204251
28	-0.066935	-0.568	0.285915
29	0.091008	0.7722	0.221253
30	-0.057289	-0.4861	0.314181
31	0.016575	0.1406	0.444272
32	-0.090741	-0.77	0.221921
33	0.166393	1.4119	0.081144
34	0.025469	0.2161	0.414756
35	-0.138827	-1.178	0.12134
36	-0.003351	-0.0284	0.488699
37	-0.062938	-0.534	0.297479
38	-0.110906	-0.9411	0.174907
39	0.08322	0.7061	0.241188
40	-0.04558	-0.3868	0.350038
41	0.017732	0.1505	0.440412
42	-0.017202	-0.146	0.44218
43	-0.099386	-0.8433	0.200922
44	-0.110322	-0.9361	0.176171
45	0.000226	0.0019	0.499237
46	-0.005111	-0.0434	0.482766
47	-0.000959	-0.0081	0.496766
48	0.000516	0.0044	0.498261

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/16twh1295181145.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/16twh1295181145.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/2n8nh1295181145.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/2n8nh1295181145.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/3lgbl1295181145.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295181040oro5ljczcav4qay/3lgbl1295181145.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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