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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, 17 Dec 2009 00:47:23 -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/17/t12610362771j3rqx0g0sjnk4q.htm/, Retrieved Thu, 17 Dec 2009 08:51:20 +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/17/t12610362771j3rqx0g0sjnk4q.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 «

98,8 100,5 110,4 96,4 101,9 106,2 81 94,7 101 109,4 102,3 90,7 96,2 96,1 106 103,1 102 104,7 86 92,1 106,9 112,6 101,7 92 97,4 97 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3

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	-0.539175	-3.6964	0.000285
2	-0.101653	-0.6969	0.244651
3	0.389642	2.6713	0.005175
4	-0.439125	-3.0105	0.002093
5	0.220085	1.5088	0.069019
6	0.194838	1.3357	0.094033
7	-0.315699	-2.1643	0.017776
8	0.050991	0.3496	0.36411
9	0.177564	1.2173	0.11478
10	-0.22023	-1.5098	0.068891
11	0.057215	0.3922	0.348324
12	0.180342	1.2364	0.111234
13	-0.350446	-2.4025	0.010142
14	0.222496	1.5254	0.066936
15	0.097479	0.6683	0.25361
16	-0.325404	-2.2309	0.01525
17	0.299464	2.053	0.02283
18	-0.015065	-0.1033	0.45909
19	-0.281943	-1.9329	0.029643
20	0.285952	1.9604	0.027946
21	-0.044152	-0.3027	0.381731
22	-0.220115	-1.509	0.068992
23	0.384033	2.6328	0.005712
24	-0.215091	-1.4746	0.073495
25	-0.121602	-0.8337	0.204345
26	0.279803	1.9182	0.030584
27	-0.225353	-1.5449	0.064534
28	0.128851	0.8834	0.19077
29	0.050968	0.3494	0.364167
30	-0.215284	-1.4759	0.073318
31	0.15715	1.0774	0.143408
32	-0.025733	-0.1764	0.430362
33	0.010535	0.0722	0.471365
34	-0.061375	-0.4208	0.337922
35	0.028117	0.1928	0.423988
36	-0.039846	-0.2732	0.392961

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.539175	-3.6964	0.000285
2	-0.553176	-3.7924	0.000213
3	0.01271	0.0871	0.465468
4	-0.332941	-2.2825	0.013514
5	-0.153696	-1.0537	0.148707
6	0.161553	1.1076	0.136845
7	0.194929	1.3364	0.093932
8	-0.173966	-1.1926	0.119497
9	0.00375	0.0257	0.489799
10	-0.011512	-0.0789	0.468715
11	-0.226381	-1.552	0.063686
12	-0.077886	-0.534	0.297944
13	-0.211484	-1.4499	0.076869
14	-0.142769	-0.9788	0.166351
15	-0.03442	-0.236	0.407241
16	-0.106967	-0.7333	0.2335
17	-0.042869	-0.2939	0.385066
18	0.17723	1.215	0.115213
19	-0.029977	-0.2055	0.41903
20	-0.184924	-1.2678	0.105562
21	-0.061595	-0.4223	0.337375
22	-0.205145	-1.4064	0.083091
23	-0.000359	-0.0025	0.499023
24	0.045862	0.3144	0.3773
25	0.141754	0.9718	0.168059
26	0.037016	0.2538	0.40039
27	-0.030928	-0.212	0.416499
28	0.228081	1.5636	0.062305
29	0.039679	0.272	0.393398
30	-0.156023	-1.0696	0.145122
31	0.022903	0.157	0.437953
32	-0.128989	-0.8843	0.190516
33	0.034428	0.236	0.407219
34	-0.025806	-0.1769	0.430167
35	-0.059166	-0.4056	0.34343
36	-0.000283	-0.0019	0.499231

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610362771j3rqx0g0sjnk4q/12ezw1261036042.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610362771j3rqx0g0sjnk4q/12ezw1261036042.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610362771j3rqx0g0sjnk4q/2a9o11261036042.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610362771j3rqx0g0sjnk4q/2a9o11261036042.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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