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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 04:04:18 -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/t1261307097sdkk2ijn3rupvr6.htm/, Retrieved Sun, 20 Dec 2009 12:04:59 +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/t1261307097sdkk2ijn3rupvr6.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 «

2.64 2.75 2.7 2.87 3.03 3.14 3.02 2.86 3.07 2.93 2.83 2.72 2.73 2.72 2.77 2.61 2.47 2.3 2.38 2.43 2.39 2.6 2.84 2.87 2.92 3.08 3.33 3.48 3.57 3.66 3.77 3.75 3.75 3.81 3.82 3.89 4.05 4.1 4.07 4.26 4.4 4.61 4.63 4.48 4.46 4.45 4.32 4.52 4.21 3.97 4.12 4.5 4.73 5.26 5.2 4.94 4.95 4.52 3.85 3.41 2.95 2.68 2.53 2.44 2.16 2.2 2.1 2.29 2.03 2.05 1.94

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	0.951598	8.0183	0
2	0.883358	7.4433	0
3	0.796262	6.7094	0
4	0.705228	5.9424	0
5	0.605953	5.1059	1e-06
6	0.512503	4.3184	2.5e-05
7	0.415579	3.5017	0.000402
8	0.333444	2.8097	0.003201
9	0.263585	2.221	0.014771
10	0.19603	1.6518	0.051498
11	0.132226	1.1142	0.134485
12	0.074528	0.628	0.266015
13	0.024074	0.2029	0.419915
14	-0.01105	-0.0931	0.463039
15	-0.041172	-0.3469	0.364838
16	-0.075794	-0.6387	0.262552
17	-0.105984	-0.893	0.187427
18	-0.134811	-1.1359	0.129901
19	-0.173791	-1.4644	0.07375
20	-0.21097	-1.7777	0.039871
21	-0.256219	-2.1589	0.017118
22	-0.298305	-2.5136	0.007111
23	-0.327847	-2.7625	0.003649
24	-0.345423	-2.9106	0.002408
25	-0.364114	-3.0681	0.001524
26	-0.377554	-3.1813	0.001087
27	-0.389322	-3.2805	0.000804
28	-0.397255	-3.3473	0.000654
29	-0.398735	-3.3598	0.000629
30	-0.396746	-3.343	0.000663
31	-0.394192	-3.3215	0.000708
32	-0.392979	-3.3113	0.000731
33	-0.392865	-3.3103	0.000733
34	-0.385567	-3.2488	0.000886
35	-0.372277	-3.1369	0.001243
36	-0.354761	-2.9893	0.00192

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.951598	8.0183	0
2	-0.234812	-1.9786	0.025873
3	-0.204776	-1.7255	0.044397
4	-0.028006	-0.236	0.407064
5	-0.115419	-0.9725	0.167043
6	0.030481	0.2568	0.399023
7	-0.105671	-0.8904	0.188129
8	0.093661	0.7892	0.216311
9	0.048472	0.4084	0.342092
10	-0.133992	-1.129	0.131341
11	-0.030114	-0.2537	0.400214
12	-0.021549	-0.1816	0.428217
13	0.010287	0.0867	0.465584
14	0.094076	0.7927	0.215298
15	-0.068234	-0.5749	0.283572
16	-0.124516	-1.0492	0.148824
17	0.015442	0.1301	0.448423
18	-0.057294	-0.4828	0.315374
19	-0.172361	-1.4523	0.075406
20	0.017268	0.1455	0.442363
21	-0.112785	-0.9503	0.172581
22	0.032523	0.274	0.392425
23	0.08156	0.6872	0.247086
24	-0.017802	-0.15	0.440593
25	-0.082002	-0.691	0.245922
26	-0.063834	-0.5379	0.296174
27	-0.042605	-0.359	0.360333
28	-0.024829	-0.2092	0.417439
29	-0.015253	-0.1285	0.449047
30	0.002991	0.0252	0.489981
31	-0.018204	-0.1534	0.439262
32	-0.145691	-1.2276	0.111824
33	-0.079904	-0.6733	0.251476
34	0.073119	0.6161	0.269895
35	-0.000759	-0.0064	0.497456
36	0.051413	0.4332	0.333087

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261307097sdkk2ijn3rupvr6/1pt671261307056.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261307097sdkk2ijn3rupvr6/1pt671261307056.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261307097sdkk2ijn3rupvr6/2w3601261307056.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261307097sdkk2ijn3rupvr6/2w3601261307056.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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