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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 05 May 2010 17:35:13 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/05/t12730809439pow9iqlxcf49pq.htm/, Retrieved Wed, 05 May 2010 19:35:46 +0200

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/2010/May/05/t12730809439pow9iqlxcf49pq.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

2 2.4 1.5 1.2 1.5 0.6 2.7 3.7 4.9 6.6 7.4 7.2 5.3 4.7 6.1 6.6 7 7.5 6.6 7.8 4.7 5.4 4.3 4.5 5.8 4.6 5.2 3.6 4.8 6.7 6.3 4.8 8.7 6.8 7.4 9 7.9 9.1 8.7 9.8 6.4 6.1 4.7 4.8 4.2 2.8 6.1 5.8 4.9 4.6 4.1 3.6 5.9 4.5 4.8 5.7 5 7 4.6 2.6 5 4.1 3.2 0 2.3 3.8 4.5 5.9 5 4.2 4.5 6

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.719201	6.1026	0
2	0.587262	4.9831	2e-06
3	0.451584	3.8318	0.000135
4	0.294616	2.4999	0.007351
5	0.211913	1.7981	0.038173
6	0.056674	0.4809	0.316025
7	-7.6e-05	-6e-04	0.499743
8	-0.05958	-0.5056	0.307357
9	-0.075381	-0.6396	0.262222
10	-0.120412	-1.0217	0.155164
11	-0.140337	-1.1908	0.118822
12	-0.209788	-1.7801	0.039639
13	-0.135364	-1.1486	0.12726
14	-0.090048	-0.7641	0.223657
15	-0.072268	-0.6132	0.270835
16	-0.06367	-0.5403	0.295343
17	0.006997	0.0594	0.476412
18	0.140249	1.1901	0.118968
19	0.130416	1.1066	0.136071
20	0.186918	1.5861	0.058555
21	0.13021	1.1049	0.136447
22	0.116929	0.9922	0.162218
23	0.054611	0.4634	0.32224
24	-0.077801	-0.6602	0.255628
25	-0.093794	-0.7959	0.214363
26	-0.18626	-1.5805	0.059192
27	-0.204011	-1.7311	0.043859
28	-0.183725	-1.559	0.061696
29	-0.255916	-2.1715	0.016594
30	-0.30508	-2.5887	0.005824
31	-0.323669	-2.7464	0.003803
32	-0.342035	-2.9023	0.002457
33	-0.342877	-2.9094	0.002407
34	-0.368539	-3.1272	0.001273
35	-0.292485	-2.4818	0.007703
36	-0.175805	-1.4918	0.070066
37	-0.131872	-1.119	0.133435
38	-0.049909	-0.4235	0.336598
39	-0.034691	-0.2944	0.384665
40	-0.008619	-0.0731	0.47095
41	0.0224	0.1901	0.424896
42	0.015799	0.1341	0.446865
43	0.006936	0.0589	0.476617
44	-0.04958	-0.4207	0.337614
45	-0.039505	-0.3352	0.36922
46	-0.041136	-0.3491	0.364034
47	-0.040398	-0.3428	0.366377
48	-0.029752	-0.2525	0.400706

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.719201	6.1026	0
2	0.145029	1.2306	0.111237
3	-0.029255	-0.2482	0.402329
4	-0.126371	-1.0723	0.143585
5	0.021078	0.1789	0.429278
6	-0.176136	-1.4946	0.0697
7	0.031829	0.2701	0.393938
8	-0.027555	-0.2338	0.407897
9	0.05042	0.4278	0.335027
10	-0.108116	-0.9174	0.180999
11	0.00011	9e-04	0.499627
12	-0.186184	-1.5798	0.059266
13	0.227554	1.9309	0.028719
14	0.009619	0.0816	0.467588
15	0.019689	0.1671	0.433892
16	-0.143803	-1.2202	0.113184
17	0.228698	1.9406	0.028113
18	0.122377	1.0384	0.151278
19	-0.074886	-0.6354	0.263581
20	0.016678	0.1415	0.443928
21	-0.097726	-0.8292	0.204857
22	-0.023664	-0.2008	0.420711
23	-0.126955	-1.0772	0.142483
24	-0.187003	-1.5868	0.058473
25	0.13515	1.1468	0.127634
26	-0.075461	-0.6403	0.262003
27	-0.03537	-0.3001	0.382474
28	0.012504	0.1061	0.457898
29	-0.126911	-1.0769	0.142565
30	-0.058551	-0.4968	0.310413
31	-0.118089	-1.002	0.159846
32	-0.033579	-0.2849	0.38826
33	-0.083823	-0.7113	0.23961
34	-0.048156	-0.4086	0.342016
35	0.090895	0.7713	0.221535
36	0.042047	0.3568	0.361151
37	-0.036651	-0.311	0.37835
38	-0.033398	-0.2834	0.388846
39	-0.100798	-0.8553	0.197611
40	-0.052808	-0.4481	0.327718
41	0.009238	0.0784	0.468868
42	0.001469	0.0125	0.495045
43	-0.069132	-0.5866	0.279653
44	-0.003397	-0.0288	0.488544
45	-0.016688	-0.1416	0.443895
46	-0.051184	-0.4343	0.332682
47	0.068812	0.5839	0.280559
48	0.025581	0.2171	0.414389

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/05/t12730809439pow9iqlxcf49pq/1e9ch1273080911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730809439pow9iqlxcf49pq/1e9ch1273080911.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730809439pow9iqlxcf49pq/2e9ch1273080911.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730809439pow9iqlxcf49pq/2e9ch1273080911.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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