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(Partial) Autocorrelation Function

*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, 26 Nov 2009 06:00:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259240493kynrfxy77dhkj93.htm/, Retrieved Thu, 26 Nov 2009 14:01:36 +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/2009/Nov/26/t1259240493kynrfxy77dhkj93.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

1.4 1 -0.8 -2.9 -0.7 -0.7 1.5 3 3.2 3.1 3.9 1 1.3 0.8 1.2 2.9 3.9 4.5 4.5 3.3 2 1.5 1 2.1 3 4 5.1 4.5 4.2 3.3 2.7 1.8 1.4 0.5 -0.4 0.8 0.7 1.9 2 1.1 0.9 0.4 0.7 2.1 2.8 3.9 3.5 2 2 1.5 2.5 3.1 2.7 2.8 2.5 3 3.2 2.8 2.4 2 1.8 1.1 -1.5 -3.7

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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.446977	-3.5195	0.000408
2	0.136018	1.071	0.144159
3	0.051982	0.4093	0.341862
4	-0.356131	-2.8042	0.003364
5	0.016624	0.1309	0.448139
6	0.152239	1.1987	0.117596
7	-0.282824	-2.227	0.014795
8	0.292866	2.306	0.012233
9	0.005919	0.0466	0.481488
10	-0.03917	-0.3084	0.379396
11	0.174271	1.3722	0.087471
12	-0.17537	-1.3809	0.086139
13	0.017809	0.1402	0.444468
14	-0.030343	-0.2389	0.405977
15	-0.086692	-0.6826	0.248697
16	0.039825	0.3136	0.377445
17	0.005956	0.0469	0.481374
18	0.026529	0.2089	0.417611
19	0.029694	0.2338	0.40795
20	0.127038	1.0003	0.160528
21	-0.129752	-1.0217	0.155454
22	0.073674	0.5801	0.281973
23	-0.038762	-0.3052	0.380613
24	-0.153724	-1.2104	0.115355
25	0.123485	0.9723	0.167334
26	-0.085142	-0.6704	0.252544
27	-0.01761	-0.1387	0.445084
28	0.120298	0.9472	0.1736
29	-0.030725	-0.2419	0.404816
30	-0.022385	-0.1763	0.430331
31	0.14341	1.1292	0.13158
32	-0.205541	-1.6184	0.055323
33	0.113706	0.8953	0.187039
34	-0.073925	-0.5821	0.281311
35	-0.033194	-0.2614	0.397335
36	0.146097	1.1504	0.127205

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.446977	-3.5195	0.000408
2	-0.079693	-0.6275	0.266317
3	0.103132	0.8121	0.209931
4	-0.357588	-2.8156	0.003259
5	-0.419572	-3.3037	0.000794
6	0.049555	0.3902	0.348864
7	-0.214421	-1.6884	0.048184
8	-0.195081	-1.5361	0.064805
9	0.000175	0.0014	0.499454
10	0.087625	0.69	0.246397
11	0.067043	0.5279	0.299728
12	-0.085713	-0.6749	0.251123
13	0.123395	0.9716	0.16751
14	0.041798	0.3291	0.371589
15	-0.048132	-0.379	0.352994
16	-0.046078	-0.3628	0.358989
17	-0.030823	-0.2427	0.40452
18	0.019492	0.1535	0.439258
19	-0.14387	-1.1328	0.130823
20	0.173148	1.3634	0.088849
21	0.013176	0.1037	0.458853
22	-0.037592	-0.296	0.38411
23	0.119113	0.9379	0.175968
24	-0.046407	-0.3654	0.358026
25	0.04288	0.3376	0.368388
26	-0.083113	-0.6544	0.257626
27	-0.020493	-0.1614	0.436168
28	-0.102587	-0.8078	0.211154
29	-0.063581	-0.5006	0.3092
30	-0.060358	-0.4753	0.318135
31	-0.052488	-0.4133	0.340409
32	-0.061076	-0.4809	0.316135
33	-0.031477	-0.2478	0.402536
34	-0.019401	-0.1528	0.439539
35	-0.000321	-0.0025	0.498995
36	0.166981	1.3148	0.096709

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259240493kynrfxy77dhkj93/1kgs21259240418.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259240493kynrfxy77dhkj93/1kgs21259240418.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259240493kynrfxy77dhkj93/2bush1259240418.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259240493kynrfxy77dhkj93/2bush1259240418.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; 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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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