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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: Thu, 16 Dec 2010 18:45:46 +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/16/t12925250148f9mfp35qa0shab.htm/, Retrieved Thu, 16 Dec 2010 19:43:37 +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/16/t12925250148f9mfp35qa0shab.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 «

294912 293488 290555 284736 281818 287854 316263 325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224 275902 271115 277509 279681 276239 271037 266148 259497 266795 298305 303725 289742 276444 268606

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.155785	1.3034	0.098357
2	0.155908	1.3044	0.098181
3	0.184191	1.5411	0.063906
4	0.162539	1.3599	0.089112
5	0.087633	0.7332	0.232946
6	0.115831	0.9691	0.167913
7	0.009518	0.0796	0.468378
8	0.115227	0.9641	0.169169
9	-0.004877	-0.0408	0.483784
10	-0.080696	-0.6751	0.250903
11	0.195174	1.6329	0.053486
12	-0.009484	-0.0793	0.468491
13	-0.093917	-0.7858	0.217328
14	0.140101	1.1722	0.122551
15	0.016263	0.1361	0.446079
16	-0.001906	-0.0159	0.493661
17	-0.019397	-0.1623	0.435774
18	-0.02448	-0.2048	0.419157
19	0.091104	0.7622	0.224241
20	-0.01589	-0.1329	0.447307
21	-0.190442	-1.5933	0.057794
22	-0.059299	-0.4961	0.310677
23	0.017121	0.1432	0.443253
24	-0.235349	-1.9691	0.026452
25	-0.053513	-0.4477	0.327868
26	-0.252421	-2.1119	0.019132
27	-0.223422	-1.8693	0.032883
28	-0.197055	-1.6487	0.051847
29	-0.093648	-0.7835	0.217984
30	-0.133258	-1.1149	0.13435
31	-0.002139	-0.0179	0.492887
32	-0.17894	-1.4971	0.069429
33	0.044578	0.373	0.355151
34	0.001307	0.0109	0.495652
35	0.011899	0.0996	0.46049
36	-0.044388	-0.3714	0.355739
37	-0.062752	-0.525	0.300613
38	-0.042499	-0.3556	0.361615
39	-0.039517	-0.3306	0.370957
40	-0.034653	-0.2899	0.386363
41	-0.049713	-0.4159	0.339368
42	-0.008695	-0.0727	0.471107
43	-0.045468	-0.3804	0.352394
44	-0.022914	-0.1917	0.424261
45	-0.041359	-0.346	0.365178
46	-0.051873	-0.434	0.33281
47	0.004219	0.0353	0.485972
48	0.029652	0.2481	0.402396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.155785	1.3034	0.098357
2	0.134914	1.1288	0.131424
3	0.1484	1.2416	0.109264
4	0.107132	0.8963	0.186573
5	0.015935	0.1333	0.447161
6	0.051071	0.4273	0.335241
7	-0.063753	-0.5334	0.297724
8	0.077931	0.652	0.258264
9	-0.058153	-0.4865	0.314053
10	-0.115697	-0.968	0.16819
11	0.218605	1.829	0.035831
12	-0.059616	-0.4988	0.309749
13	-0.108645	-0.909	0.183238
14	0.159967	1.3384	0.092552
15	-0.028095	-0.2351	0.407425
16	-0.01439	-0.1204	0.452256
17	-0.056071	-0.4691	0.320221
18	-0.007288	-0.061	0.475775
19	0.086238	0.7215	0.236498
20	-0.061263	-0.5126	0.304936
21	-0.142988	-1.1963	0.117804
22	-0.108484	-0.9076	0.18359
23	0.089794	0.7513	0.227505
24	-0.148738	-1.2444	0.108746
25	-0.044332	-0.3709	0.355912
26	-0.206495	-1.7277	0.04423
27	-0.126556	-1.0588	0.146656
28	-0.062187	-0.5203	0.30225
29	0.073226	0.6127	0.271044
30	-0.057376	-0.48	0.316348
31	0.086097	0.7203	0.236857
32	-0.00899	-0.0752	0.47013
33	0.112293	0.9395	0.175349
34	-0.050018	-0.4185	0.338438
35	0.151091	1.2641	0.10519
36	-0.067498	-0.5647	0.287031
37	-0.124167	-1.0389	0.151223
38	0.051597	0.4317	0.333647
39	-0.092643	-0.7751	0.220444
40	0.080581	0.6742	0.251205
41	0.004699	0.0393	0.484374
42	-0.042915	-0.3591	0.360318
43	0.019463	0.1628	0.435558
44	-0.010023	-0.0839	0.466703
45	-0.038568	-0.3227	0.373948
46	-0.055875	-0.4675	0.320802
47	-0.002396	-0.02	0.492031
48	-0.002945	-0.0246	0.490206

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/10zvy1292525142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/10zvy1292525142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/2tqu11292525142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/2tqu11292525142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/3tqu11292525142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925250148f9mfp35qa0shab/3tqu11292525142.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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