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Workshop 8

*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, 27 Nov 2009 05:40:33 -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/27/t1259325682p46gcn4zguzkkop.htm/, Retrieved Fri, 27 Nov 2009 13:41:24 +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/27/t1259325682p46gcn4zguzkkop.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 «

62 64 62 64 64 69 69 65 56 58 53 62 55 60 59 58 53 57 57 53 54 53 57 57 55 49 50 49 54 58 58 52 56 52 59 53 52 53 51 50 56 52 46 48 46 48 48 49 53 48 51 48 50 55 52 53 52 55 53 53 56 54 52 55 54 59 56 56 51 53 52 51 46 49 46 55 57 53 52 53 50 54 53 50 51 52 47 51 49 53 52 45 53 51 48 48 48 48 40 43 40 39 39 36 41 39 40 39 46 40 37 37 44 41 40 36 38 43 42 45 46

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	0.843505	9.2786	0
2	0.79573	8.753	0
3	0.724456	7.969	0
4	0.704262	7.7469	0
5	0.660744	7.2682	0
6	0.612381	6.7362	0
7	0.542585	5.9684	0
8	0.50717	5.5789	0
9	0.465717	5.1229	1e-06
10	0.440963	4.8506	2e-06
11	0.428013	4.7081	3e-06
12	0.398826	4.3871	1.2e-05
13	0.347079	3.8179	0.000107
14	0.300018	3.3002	0.000635
15	0.277249	3.0497	0.001407
16	0.263362	2.897	0.002237
17	0.249078	2.7399	0.003539
18	0.194057	2.1346	0.017404
19	0.155687	1.7126	0.044677
20	0.10869	1.1956	0.117097
21	0.080774	0.8885	0.188013
22	0.067221	0.7394	0.23054
23	0.091607	1.0077	0.157811
24	0.064914	0.7141	0.238284
25	0.064928	0.7142	0.238235
26	0.058207	0.6403	0.261603
27	0.074744	0.8222	0.206294
28	0.072264	0.7949	0.214112
29	0.076711	0.8438	0.200216
30	0.042122	0.4633	0.321974
31	0.017606	0.1937	0.423379
32	-0.001746	-0.0192	0.492353
33	-0.023545	-0.259	0.398038
34	-0.046949	-0.5164	0.303244
35	-0.04881	-0.5369	0.296159
36	-0.070085	-0.7709	0.221125

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.843505	9.2786	0
2	0.291955	3.2115	0.000846
3	0.011176	0.1229	0.451181
4	0.142183	1.564	0.060213
5	0.017936	0.1973	0.421962
6	-0.054825	-0.6031	0.273794
7	-0.10748	-1.1823	0.119706
8	0.027098	0.2981	0.383078
9	-0.000278	-0.0031	0.498784
10	0.024982	0.2748	0.39197
11	0.098723	1.086	0.139828
12	-0.008829	-0.0971	0.461396
13	-0.117476	-1.2922	0.099369
14	-0.077675	-0.8544	0.197279
15	0.030988	0.3409	0.366896
16	0.031485	0.3463	0.364845
17	0.029461	0.3241	0.373222
18	-0.101802	-1.1198	0.132503
19	-0.04165	-0.4582	0.323831
20	-0.076991	-0.8469	0.19936
21	-0.042536	-0.4679	0.320349
22	0.057082	0.6279	0.265625
23	0.200608	2.2067	0.014612
24	-0.02477	-0.2725	0.392861
25	0.030985	0.3408	0.366911
26	0.038914	0.4281	0.334685
27	-0.003392	-0.0373	0.485148
28	-0.075906	-0.835	0.202691
29	0.017821	0.196	0.422456
30	-0.063621	-0.6998	0.24269
31	-0.085778	-0.9436	0.173638
32	-0.001915	-0.0211	0.491613
33	-0.05197	-0.5717	0.284302
34	-0.086017	-0.9462	0.172968
35	0.065739	0.7231	0.235497
36	0.021933	0.2413	0.404879

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325682p46gcn4zguzkkop/1ws2m1259325632.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325682p46gcn4zguzkkop/1ws2m1259325632.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325682p46gcn4zguzkkop/20cbl1259325632.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325682p46gcn4zguzkkop/20cbl1259325632.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; 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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