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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: Sun, 20 Dec 2009 01:11:29 -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/20/t1261296781ozmddkfwou9fiia.htm/, Retrieved Sun, 20 Dec 2009 09:13:03 +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/20/t1261296781ozmddkfwou9fiia.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 «

101.09 102.71 102.11 101.68 101.7 101.53 101.76 101.15 100.92 100.73 100.55 102.15 100.79 99.93 100.03 100.25 99.6 100.16 100.49 99.72 100.14 98.48 100.38 101.45 98.42 98.6 100.06 98.62 100.84 100.02 97.95 98.32 98.27 97.22 99.28 100.38 99.02 100.32 99.81 100.6 101.19 100.47 101.77 102.32 102.39 101.16 100.63 101.48 101.44 100.09 100.7 100.78 99.81 98.45 98.49 97.48 97.91 96.94 98.53 96.82 95.76

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	0.738476	5.1693	2e-06
2	0.621961	4.3537	3.4e-05
3	0.59945	4.1962	5.7e-05
4	0.402541	2.8178	0.003477
5	0.34937	2.4456	0.00905
6	0.250985	1.7569	0.042592
7	0.057625	0.4034	0.344213
8	0.013397	0.0938	0.462834
9	-0.155387	-1.0877	0.141023
10	-0.266899	-1.8683	0.033853
11	-0.270567	-1.894	0.03207
12	-0.439704	-3.0779	0.001705
13	-0.387417	-2.7119	0.0046
14	-0.317705	-2.2239	0.015397
15	-0.378833	-2.6518	0.005378
16	-0.292309	-2.0462	0.023063
17	-0.250297	-1.7521	0.043008
18	-0.279664	-1.9576	0.02799
19	-0.140961	-0.9867	0.164312
20	-0.151747	-1.0622	0.146669
21	-0.150325	-1.0523	0.148917
22	-0.057557	-0.4029	0.344388
23	-0.117359	-0.8215	0.207666
24	-0.078498	-0.5495	0.292585
25	-0.015678	-0.1097	0.456531
26	-0.077944	-0.5456	0.293905
27	-0.079675	-0.5577	0.289787
28	-0.075013	-0.5251	0.300944
29	-0.100674	-0.7047	0.242161
30	-0.059278	-0.4149	0.339997
31	-0.099479	-0.6964	0.244749
32	-0.066423	-0.465	0.322009
33	0.002462	0.0172	0.49316
34	-0.017264	-0.1208	0.452152
35	0.028984	0.2029	0.420031
36	0.064058	0.4484	0.327918

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.738476	5.1693	2e-06
2	0.16851	1.1796	0.121933
3	0.210765	1.4754	0.073257
4	-0.294257	-2.0598	0.022375
5	0.107717	0.754	0.227224
6	-0.174391	-1.2207	0.114014
7	-0.186535	-1.3057	0.098868
8	-0.006868	-0.0481	0.480926
9	-0.284108	-1.9888	0.026164
10	0.019805	0.1386	0.445153
11	-0.043898	-0.3073	0.379963
12	-0.224935	-1.5745	0.060899
13	0.285517	1.9986	0.025607
14	0.003186	0.0223	0.491148
15	0.058932	0.4125	0.340878
16	-0.040671	-0.2847	0.388539
17	-0.009153	-0.0641	0.474588
18	-0.101985	-0.7139	0.239339
19	0.028478	0.1993	0.421407
20	-0.165855	-1.161	0.125636
21	-0.114923	-0.8045	0.212508
22	-0.045156	-0.3161	0.376637
23	-0.111768	-0.7824	0.218879
24	-0.019816	-0.1387	0.445123
25	0.086045	0.6023	0.274871
26	0.005576	0.039	0.484513
27	-0.169016	-1.1831	0.121236
28	0.050863	0.356	0.361668
29	0.03492	0.2444	0.403957
30	-0.123121	-0.8618	0.196485
31	-0.009384	-0.0657	0.473946
32	0.037612	0.2633	0.396718
33	-0.028332	-0.1983	0.421805
34	0.033447	0.2341	0.407931
35	-0.04379	-0.3065	0.380249
36	-0.068686	-0.4808	0.316399

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261296781ozmddkfwou9fiia/1juw71261296687.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261296781ozmddkfwou9fiia/1juw71261296687.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261296781ozmddkfwou9fiia/22uxv1261296687.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261296781ozmddkfwou9fiia/22uxv1261296687.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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