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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: Tue, 01 Dec 2009 13:38:29 -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/01/t1259699943636tjjbjqm8zdzj.htm/, Retrieved Tue, 01 Dec 2009 21:39:05 +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/01/t1259699943636tjjbjqm8zdzj.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 «

7.3 7.6 7.5 7.6 7.9 7.9 8.1 8.2 8 7.5 6.8 6.5 6.6 7.6 8 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5

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	0.51197	3.9657	9.9e-05
2	-0.07737	-0.5993	0.275614
3	-0.544377	-4.2167	4.2e-05
4	-0.463927	-3.5936	0.00033
5	-0.154578	-1.1974	0.117939
6	0.191939	1.4868	0.071158
7	0.277519	2.1496	0.017812
8	0.207712	1.6089	0.05644
9	-0.012414	-0.0962	0.461858
10	-0.104128	-0.8066	0.211548
11	-0.048879	-0.3786	0.353154
12	-0.005914	-0.0458	0.481807
13	0.108349	0.8393	0.202326
14	0.028728	0.2225	0.41233
15	-0.059314	-0.4594	0.323787
16	-0.174647	-1.3528	0.090596
17	-0.135481	-1.0494	0.149094
18	-0.010201	-0.079	0.468642
19	0.183021	1.4177	0.080729
20	0.276135	2.1389	0.01826
21	0.240458	1.8626	0.03371
22	-0.048433	-0.3752	0.354432
23	-0.320037	-2.479	0.008002
24	-0.377496	-2.9241	0.002434
25	-0.17389	-1.3469	0.091531
26	0.126467	0.9796	0.165605
27	0.269857	2.0903	0.020418
28	0.167948	1.3009	0.09913
29	-0.022608	-0.1751	0.430787
30	-0.218673	-1.6938	0.047741
31	-0.189321	-1.4665	0.07387
32	-0.075945	-0.5883	0.27928
33	0.036165	0.2801	0.39017
34	0.023789	0.1843	0.427212
35	0.006284	0.0487	0.480668
36	-0.085177	-0.6598	0.255961

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.51197	3.9657	9.9e-05
2	-0.460076	-3.5637	0.000362
3	-0.43149	-3.3423	0.000717
4	0.095489	0.7397	0.231196
5	-0.07422	-0.5749	0.283751
6	-0.020984	-0.1625	0.435714
7	-0.031679	-0.2454	0.403497
8	0.067437	0.5224	0.301669
9	-0.066264	-0.5133	0.30482
10	0.077287	0.5987	0.275825
11	0.170786	1.3229	0.095444
12	-0.143282	-1.1099	0.135745
13	0.247024	1.9134	0.030233
14	-0.135356	-1.0485	0.149316
15	-0.063649	-0.493	0.311898
16	-0.040275	-0.312	0.378073
17	-0.062817	-0.4866	0.314166
18	0.019615	0.1519	0.439874
19	0.035612	0.2758	0.391807
20	0.215467	1.669	0.050164
21	0.008946	0.0693	0.472493
22	-0.134698	-1.0434	0.150482
23	-0.036771	-0.2848	0.388378
24	-0.067674	-0.5242	0.301034
25	0.013104	0.1015	0.459746
26	-0.077879	-0.6032	0.274309
27	-0.029097	-0.2254	0.411224
28	-0.150306	-1.1643	0.124463
29	0.016923	0.1311	0.448072
30	-0.157452	-1.2196	0.113691
31	-0.006514	-0.0505	0.479963
32	-0.076683	-0.594	0.277378
33	-0.119326	-0.9243	0.179517
34	-0.115896	-0.8977	0.186459
35	0.052359	0.4056	0.343251
36	-0.157291	-1.2184	0.113927

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699943636tjjbjqm8zdzj/1b6961259699907.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699943636tjjbjqm8zdzj/1b6961259699907.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699943636tjjbjqm8zdzj/2t10y1259699907.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699943636tjjbjqm8zdzj/2t10y1259699907.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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