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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: Wed, 29 Dec 2010 13:04:46 +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/29/t1293627752xagwuxncl4ag5pn.htm/, Retrieved Wed, 29 Dec 2010 14:02:35 +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/29/t1293627752xagwuxncl4ag5pn.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 «

01.303763 01.416094 01.052458 01.312283 01.309429 01.492409 01.026556 01.005406 01.334886 01.393873 01.128092 01.122787 01.213104 01.253528 01.094796 00.912944 01.195130 00.927499 00.965333 01.198078 00.966362 00.973685 00.994801 00.826262 00.688888 00.781307 00.604791 01.086240 00.774026 01.026032 00.676435 00.830525 00.791624 00.752391 00.670202 00.880336 00.914297 00.961042 00.930194 00.867966 00.989160 00.997288 00.798744 00.975379 00.934721 00.973234 00.815300 00.940209 00.794493 00.931340 00.922050 00.784517 00.822098 00.891026 00.807306 00.951441 01.147907 01.172609 01.281051 01.165962 00.978911 01.410951 01.197838 01.288368 01.102253 01.197657 01.299984 01.198611 01.299252 01.097604 01.399770 01.398396 01.401880 01.699717 01.397610 01.500135 01.400136 01.400427 01.341477 01.338580 01.482977 01.163253 01.328468 01.234550 01.484741 01.336579 01.339292 01.405225 01.333491 01.149740

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	0.540793	4.7762	4e-06
2	0.573057	5.0611	1e-06
3	0.477042	4.2131	3.4e-05
4	0.449183	3.9671	8e-05
5	0.42536	3.7567	0.000165
6	0.316004	2.7909	0.003303
7	0.321021	2.8352	0.002915
8	0.358574	3.1668	0.0011
9	0.304344	2.6879	0.004393
10	0.164735	1.4549	0.074854
11	0.189818	1.6764	0.048829
12	-0.028712	-0.2536	0.400244
13	0.141743	1.2518	0.107185
14	0.079485	0.702	0.242388
15	0.066233	0.585	0.280133
16	0.106719	0.9425	0.174419
17	0.055775	0.4926	0.311842
18	0.104471	0.9227	0.179514
19	0.020125	0.1777	0.429695
20	-0.022	-0.1943	0.423222
21	-0.013719	-0.1212	0.451937
22	-0.048421	-0.4276	0.335044
23	-0.071695	-0.6332	0.264231
24	-0.090752	-0.8015	0.212638
25	-0.102974	-0.9094	0.182958
26	-0.052378	-0.4626	0.322473
27	-0.077695	-0.6862	0.247317
28	-0.071909	-0.6351	0.263615
29	-0.068659	-0.6064	0.273011
30	-0.084151	-0.7432	0.229795
31	-0.090565	-0.7998	0.213114
32	-0.137618	-1.2154	0.113939
33	-0.179732	-1.5874	0.058239
34	-0.095989	-0.8477	0.199586
35	-0.127458	-1.1257	0.131876
36	-0.113096	-0.9988	0.160481

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.540793	4.7762	4e-06
2	0.396584	3.5025	0.000383
3	0.12674	1.1193	0.133215
4	0.07736	0.6832	0.248245
5	0.080914	0.7146	0.238489
6	-0.088618	-0.7827	0.218099
7	0.01457	0.1287	0.448972
8	0.16534	1.4602	0.07412
9	0.015115	0.1335	0.447075
10	-0.240961	-2.1281	0.018243
11	-0.003232	-0.0285	0.48865
12	-0.313084	-2.7651	0.00355
13	0.186447	1.6467	0.051826
14	0.191005	1.6869	0.047808
15	0.00485	0.0428	0.482973
16	0.0291	0.257	0.398926
17	-0.042542	-0.3757	0.354071
18	-0.006043	-0.0534	0.478787
19	-0.042245	-0.3731	0.355043
20	0.00374	0.033	0.486868
21	0.002457	0.0217	0.491371
22	-0.216311	-1.9104	0.029878
23	-0.035695	-0.3152	0.376707
24	-0.163209	-1.4414	0.076734
25	0.078299	0.6915	0.245646
26	0.23311	2.0588	0.021427
27	0.024898	0.2199	0.413263
28	0.091432	0.8075	0.210915
29	-0.067799	-0.5988	0.275526
30	-0.043982	-0.3884	0.349376
31	-0.059818	-0.5283	0.299396
32	-0.125876	-1.1117	0.13484
33	-0.102633	-0.9064	0.18375
34	-0.04572	-0.4038	0.343737
35	-0.001349	-0.0119	0.495261
36	-0.052292	-0.4618	0.322745

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/1bq1w1293627884.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/1bq1w1293627884.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/2mh0z1293627884.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/2mh0z1293627884.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/3mh0z1293627884.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293627752xagwuxncl4ag5pn/3mh0z1293627884.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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