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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, 03 Dec 2009 09:14:25 -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/03/t1259857024f8mlvhxq2199yhn.htm/, Retrieved Thu, 03 Dec 2009 17:17:07 +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/03/t1259857024f8mlvhxq2199yhn.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 «

8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8 8.1 8

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	0.496339	3.4387	0.000609
2	-0.061079	-0.4232	0.337031
3	-0.482081	-3.34	0.000814
4	-0.45395	-3.1451	0.001424
5	-0.122351	-0.8477	0.200414
6	0.242197	1.678	0.049925
7	0.295761	2.0491	0.02297
8	0.141233	0.9785	0.166369
9	-0.115029	-0.7969	0.214704
10	-0.199037	-1.379	0.087149
11	-0.125819	-0.8717	0.193856
12	-0.06763	-0.4686	0.320754
13	0.051252	0.3551	0.36204
14	0.104817	0.7262	0.235623
15	0.030636	0.2123	0.416405
16	-0.125626	-0.8704	0.194217
17	-0.184778	-1.2802	0.103317
18	-0.06185	-0.4285	0.335099
19	0.105588	0.7315	0.234005
20	0.285164	1.9757	0.026978
21	0.268208	1.8582	0.03464
22	0.040848	0.283	0.389196
23	-0.266281	-1.8449	0.035617
24	-0.356647	-2.4709	0.008539
25	-0.166089	-1.1507	0.127779
26	0.073025	0.5059	0.30761
27	0.17341	1.2014	0.117741
28	0.125241	0.8677	0.19494
29	0.010019	0.0694	0.472474
30	-0.162428	-1.1253	0.133022
31	-0.133141	-0.9224	0.18046
32	-0.08131	-0.5633	0.287915
33	0.015607	0.1081	0.457172
34	0.012524	0.0868	0.465608
35	0.057418	0.3978	0.346269
36	0.04104	0.2843	0.388688
37	0.019461	0.1348	0.446656
38	0.014644	0.1015	0.459807
39	0.031214	0.2163	0.414852
40	0.047206	0.3271	0.372525
41	0.05395	0.3738	0.355108
42	0.003468	0.024	0.490465
43	-0.013487	-0.0934	0.46297
44	-0.039114	-0.271	0.393781
45	-0.049133	-0.3404	0.367519
46	0.00501	0.0347	0.486228
47	0.02158	0.1495	0.440889
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.496339	3.4387	0.000609
2	-0.407925	-2.8262	0.003423
3	-0.377133	-2.6129	0.005977
4	-0.023873	-0.1654	0.434662
5	0.072958	0.5055	0.307772
6	0.079413	0.5502	0.292371
7	-0.109396	-0.7579	0.226102
8	-0.001945	-0.0135	0.494652
9	-0.038959	-0.2699	0.394191
10	0.041306	0.2862	0.387987
11	-0.007024	-0.0487	0.480693
12	-0.205495	-1.4237	0.080499
13	0.073121	0.5066	0.307379
14	0.053253	0.3689	0.356895
15	-0.130767	-0.906	0.184737
16	-0.218064	-1.5108	0.068699
17	-0.031353	-0.2172	0.414478
18	0.176753	1.2246	0.113355
19	-0.016649	-0.1153	0.454326
20	0.12266	0.8498	0.199824
21	0.048211	0.334	0.36991
22	-0.021997	-0.1524	0.439756
23	-0.106424	-0.7373	0.232257
24	-0.080991	-0.5611	0.288663
25	0.055731	0.3861	0.350558
26	-0.131152	-0.9086	0.184037
27	-0.141471	-0.9801	0.165965
28	-0.062694	-0.4344	0.332989
29	0.077381	0.5361	0.29718
30	-0.123762	-0.8574	0.197729
31	-0.022583	-0.1565	0.438163
32	-0.089394	-0.6193	0.269312
33	0.009191	0.0637	0.474746
34	-0.070935	-0.4915	0.312673
35	0.002623	0.0182	0.492789
36	-0.047172	-0.3268	0.372612
37	0.006547	0.0454	0.482006
38	0.088771	0.615	0.270723
39	-0.108011	-0.7483	0.228959
40	-0.061538	-0.4263	0.335881
41	0.076507	0.5301	0.299258
42	-0.053501	-0.3707	0.35626
43	0.030525	0.2115	0.416703
44	0.010284	0.0712	0.471747
45	0.015724	0.1089	0.456854
46	-0.049221	-0.341	0.367292
47	-0.084922	-0.5884	0.279525
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259857024f8mlvhxq2199yhn/1psnu1259856864.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259857024f8mlvhxq2199yhn/1psnu1259856864.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259857024f8mlvhxq2199yhn/2elej1259856864.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259857024f8mlvhxq2199yhn/2elej1259856864.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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