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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, 04 Dec 2009 06:55:13 -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/Dec/04/t125993497191ocuhrmoynq94f.htm/, Retrieved Fri, 04 Dec 2009 14:56:13 +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/2009/Dec/04/t125993497191ocuhrmoynq94f.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 «

3.2 1.9 0 0.6 0.2 0.9 2.4 4.7 9.4 12.5 15.8 18.2 16.8 17.3 19.3 17.9 20.2 18.7 20.1 18.2 18.4 18.2 18.9 19.9 21.3 20 19.5 19.6 20.9 21 19.9 19.6 20.9 21.7 22.9 21.5 21.3 23.5 21.6 24.5 22.2 23.5 20.9 20.7 18.1 17.1 14.8 13.8 15.2 16 17.6 15 15 16.3 19.4 21.3 20.5 21.1 21.6 22.6

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	-0.0278	-0.1906	0.424836
2	0.409869	2.8099	0.0036
3	-0.116406	-0.798	0.214432
4	0.133345	0.9142	0.182647
5	0.06213	0.4259	0.336048
6	-0.026953	-0.1848	0.427099
7	-0.099685	-0.6834	0.248853
8	-0.11058	-0.7581	0.226088
9	-0.062863	-0.431	0.334233
10	-0.075163	-0.5153	0.304383
11	0.021782	0.1493	0.440967
12	-0.328145	-2.2497	0.014597
13	0.014196	0.0973	0.461442
14	-0.214759	-1.4723	0.073801
15	0.095009	0.6513	0.258997
16	-0.003173	-0.0218	0.491368
17	0.00798	0.0547	0.4783
18	-0.017158	-0.1176	0.45343
19	0.023239	0.1593	0.437049
20	-0.04516	-0.3096	0.379116
21	0.194555	1.3338	0.094348
22	-0.129044	-0.8847	0.190415
23	0.248131	1.7011	0.047766
24	-0.027215	-0.1866	0.426399
25	0.238006	1.6317	0.054714
26	0.061567	0.4221	0.337446
27	0.02746	0.1883	0.425742
28	-0.076434	-0.524	0.301369
29	-0.026092	-0.1789	0.4294
30	-0.029992	-0.2056	0.418989
31	-0.046289	-0.3173	0.376196
32	-0.055878	-0.3831	0.351693
33	-0.195443	-1.3399	0.093361
34	-0.011043	-0.0757	0.469986
35	-0.22661	-1.5536	0.063499
36	-0.013158	-0.0902	0.464253

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.0278	-0.1906	0.424836
2	0.409412	2.8068	0.00363
3	-0.11818	-0.8102	0.210954
4	-0.040517	-0.2778	0.391203
5	0.188868	1.2948	0.100855
6	-0.110899	-0.7603	0.22544
7	-0.228294	-1.5651	0.062134
8	-0.009114	-0.0625	0.475221
9	0.039308	0.2695	0.394369
10	-0.097298	-0.667	0.254004
11	0.07789	0.534	0.297935
12	-0.316956	-2.1729	0.01743
13	-0.028983	-0.1987	0.421677
14	0.091803	0.6294	0.266077
15	-0.042984	-0.2947	0.384766
16	0.093416	0.6404	0.262501
17	0.052949	0.363	0.359116
18	-0.146255	-1.0027	0.160576
19	0.008915	0.0611	0.475762
20	-0.092246	-0.6324	0.265093
21	0.155798	1.0681	0.145465
22	-0.084035	-0.5761	0.283644
23	0.218748	1.4997	0.070195
24	0.018052	0.1238	0.451017
25	0.061419	0.4211	0.337813
26	0.011846	0.0812	0.46781
27	-0.114779	-0.7869	0.21765
28	-0.11829	-0.811	0.21074
29	0.079103	0.5423	0.295086
30	0.028278	0.1939	0.423558
31	-0.080471	-0.5517	0.291891
32	-0.044664	-0.3062	0.380402
33	-0.026538	-0.1819	0.428209
34	-0.171447	-1.1754	0.122881
35	0.012517	0.0858	0.465991
36	-0.083118	-0.5698	0.285754

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993497191ocuhrmoynq94f/1xtd41259934911.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993497191ocuhrmoynq94f/1xtd41259934911.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993497191ocuhrmoynq94f/23usk1259934911.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993497191ocuhrmoynq94f/23usk1259934911.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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 (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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