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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, 26 Nov 2009 11:48:39 -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/t12592614377db3lflqtwtjyc3.htm/, Retrieved Thu, 26 Nov 2009 19:50:40 +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/t12592614377db3lflqtwtjyc3.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 «

10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680

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	0.935269	7.2446	0
2	0.870198	6.7405	0
3	0.812261	6.2917	0
4	0.750912	5.8165	0
5	0.679598	5.2641	1e-06
6	0.613817	4.7546	6e-06
7	0.556358	4.3095	3.1e-05
8	0.490803	3.8017	0.000169
9	0.41843	3.2411	0.000972
10	0.366973	2.8426	0.003054
11	0.332082	2.5723	0.006298
12	0.298193	2.3098	0.012178
13	0.256146	1.9841	0.025912
14	0.222171	1.7209	0.045209
15	0.197906	1.533	0.065269
16	0.167455	1.2971	0.099781
17	0.1426	1.1046	0.136877
18	0.126126	0.977	0.166254
19	0.11679	0.9047	0.184634
20	0.085529	0.6625	0.255091
21	0.054511	0.4222	0.33718
22	0.025307	0.196	0.422627
23	-0.002866	-0.0222	0.49118
24	-0.035136	-0.2722	0.393216
25	-0.06244	-0.4837	0.315195
26	-0.0878	-0.6801	0.249529
27	-0.109283	-0.8465	0.200317
28	-0.127099	-0.9845	0.16441
29	-0.142883	-1.1068	0.136406
30	-0.159112	-1.2325	0.111289
31	-0.179412	-1.3897	0.084874
32	-0.201394	-1.56	0.062011
33	-0.223651	-1.7324	0.044171
34	-0.246227	-1.9073	0.030638
35	-0.2672	-2.0697	0.021396
36	-0.284755	-2.2057	0.015623

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.935269	7.2446	0
2	-0.036157	-0.2801	0.390192
3	0.022228	0.1722	0.43194
4	-0.05975	-0.4628	0.322583
5	-0.111743	-0.8656	0.195091
6	-6.5e-05	-5e-04	0.4998
7	0.01887	0.1462	0.442141
8	-0.095404	-0.739	0.231396
9	-0.089378	-0.6923	0.245703
10	0.107478	0.8325	0.204208
11	0.088405	0.6848	0.24806
12	0.006555	0.0508	0.479838
13	-0.089887	-0.6963	0.244476
14	-0.005358	-0.0415	0.483517
15	0.037505	0.2905	0.386212
16	-0.043596	-0.3377	0.368386
17	0.022964	0.1779	0.429708
18	-0.002335	-0.0181	0.492815
19	0.038344	0.297	0.383742
20	-0.149576	-1.1586	0.125603
21	-0.009227	-0.0715	0.471631
22	-0.060522	-0.4688	0.320455
23	-0.018293	-0.1417	0.443898
24	-0.019802	-0.1534	0.439303
25	0.005005	0.0388	0.484603
26	-0.034281	-0.2655	0.395752
27	0.029422	0.2279	0.41025
28	0.052735	0.4085	0.342187
29	-0.045695	-0.354	0.362308
30	-0.065562	-0.5078	0.306713
31	-0.077598	-0.6011	0.275027
32	-0.027461	-0.2127	0.416137
33	-0.04188	-0.3244	0.373381
34	-0.046112	-0.3572	0.361104
35	-0.009067	-0.0702	0.47212
36	-0.009237	-0.0715	0.4716

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592614377db3lflqtwtjyc3/14lvo1259261318.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592614377db3lflqtwtjyc3/14lvo1259261318.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592614377db3lflqtwtjyc3/2vx3s1259261318.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592614377db3lflqtwtjyc3/2vx3s1259261318.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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