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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: Tue, 21 Dec 2010 10:50:06 +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/Dec/21/t1292928464hfnvgpb5m6179io.htm/, Retrieved Tue, 21 Dec 2010 11:47:45 +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/2010/Dec/21/t1292928464hfnvgpb5m6179io.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485 18730 14538 27561 25985 34670 32066 27186 29586 21359 21553 19573 24256 22380

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.392051	-3.5718	0.000297
2	0.10011	0.912	0.182194
3	-0.135083	-1.2307	0.110963
4	-0.059338	-0.5406	0.295116
5	0.023101	0.2105	0.416912
6	0.033635	0.3064	0.380022
7	-0.057534	-0.5242	0.300782
8	0.139599	1.2718	0.103497
9	0.092468	0.8424	0.200987
10	-0.097793	-0.8909	0.187769
11	-0.030485	-0.2777	0.390954
12	-0.165608	-1.5088	0.067579
13	-0.084359	-0.7685	0.222172
14	0.081172	0.7395	0.230842
15	0.10826	0.9863	0.163427
16	-0.05346	-0.487	0.313756
17	0.014322	0.1305	0.44825
18	0.020296	0.1849	0.426876
19	-0.107418	-0.9786	0.165304
20	-0.016781	-0.1529	0.439432
21	0.124314	1.1326	0.130331
22	-0.289833	-2.6405	0.004944
23	0.420085	3.8272	0.000125
24	-0.230755	-2.1023	0.01928
25	0.146743	1.3369	0.092456
26	-0.009358	-0.0853	0.466133
27	-0.027004	-0.246	0.403139
28	-0.081579	-0.7432	0.229723
29	0.127866	1.1649	0.123695
30	-0.083963	-0.7649	0.223239
31	0.050289	0.4582	0.324019
32	0.041668	0.3796	0.352602
33	-0.11119	-1.013	0.157004
34	0.121233	1.1045	0.136286
35	-0.026606	-0.2424	0.404536
36	-0.111398	-1.0149	0.156555
37	0.038539	0.3511	0.3632
38	-0.045782	-0.4171	0.338843
39	-1.6e-05	-1e-04	0.499942
40	0.031855	0.2902	0.386189
41	-0.042416	-0.3864	0.350083
42	0.015951	0.1453	0.442405
43	0.016938	0.1543	0.43887
44	0.079727	0.7263	0.234835
45	-0.165452	-1.5073	0.06776
46	0.149747	1.3643	0.088087
47	-0.104034	-0.9478	0.172993
48	-0.008647	-0.0788	0.4687

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.392051	-3.5718	0.000297
2	-0.063328	-0.5769	0.282769
3	-0.140202	-1.2773	0.102528
4	-0.193174	-1.7599	0.041054
5	-0.096621	-0.8803	0.190629
6	-0.014563	-0.1327	0.447386
7	-0.101046	-0.9206	0.179972
8	0.075869	0.6912	0.245686
9	0.239129	2.1786	0.0161
10	0.049805	0.4537	0.325599
11	-0.030828	-0.2809	0.389761
12	-0.159269	-1.451	0.075273
13	-0.290041	-2.6424	0.004919
14	-0.205417	-1.8714	0.032404
15	0.005164	0.047	0.481295
16	-0.092009	-0.8382	0.202152
17	-0.148369	-1.3517	0.09007
18	0.028877	0.2631	0.396569
19	-0.046372	-0.4225	0.336887
20	-0.089003	-0.8109	0.209884
21	0.283594	2.5837	0.005764
22	-0.201874	-1.8392	0.034734
23	0.125525	1.1436	0.128042
24	-0.066667	-0.6074	0.272635
25	-0.075402	-0.6869	0.247015
26	0.031473	0.2867	0.387515
27	0.117822	1.0734	0.143099
28	-0.069972	-0.6375	0.262784
29	0.013787	0.1256	0.450176
30	0.05618	0.5118	0.305068
31	-0.047366	-0.4315	0.333602
32	-0.033255	-0.303	0.381335
33	-0.025543	-0.2327	0.408279
34	-0.012475	-0.1137	0.454893
35	0.029943	0.2728	0.392843
36	-0.074301	-0.6769	0.250171
37	0.015465	0.1409	0.444148
38	-0.099263	-0.9043	0.18422
39	-0.02187	-0.1992	0.42128
40	0.012997	0.1184	0.453014
41	-0.15481	-1.4104	0.081082
42	0.019362	0.1764	0.430207
43	0.06991	0.6369	0.262967
44	-0.003013	-0.0275	0.489082
45	0.079593	0.7251	0.235208
46	0.075443	0.6873	0.2469
47	0.066182	0.6029	0.274094
48	-0.157748	-1.4371	0.077217

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292928464hfnvgpb5m6179io/1qlx61292928602.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292928464hfnvgpb5m6179io/1qlx61292928602.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292928464hfnvgpb5m6179io/2qlx61292928602.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292928464hfnvgpb5m6179io/2qlx61292928602.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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