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model A

*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: Wed, 29 Dec 2010 11:03:25 +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/29/t1293620600djlv7hsghk6fo7t.htm/, Retrieved Wed, 29 Dec 2010 12:03:23 +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/29/t1293620600djlv7hsghk6fo7t.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 «

16 17 23 24 27 31 40 47 43 60 64 65 65 55 57 57 57 65 69 70 71 71 73 68 65 57 41 21 21 17 9 11 6 -2 0 5 3 7 4 8 9 14 12 12 7 15 14 19 39 12 11 17 16 25 24 28 25 31 24 24

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	32 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.061301	0.4203	0.338106
2	0.198398	1.3602	0.090135
3	0.420398	2.8821	0.002969
4	0.003998	0.0274	0.489124
5	0.085897	0.5889	0.279382
6	0.182415	1.2506	0.10864
7	0.023025	0.1578	0.437626
8	0.022223	0.1524	0.439779
9	0.035524	0.2435	0.404324
10	-0.147105	-1.0085	0.159189
11	-0.089968	-0.6168	0.270174
12	-0.24711	-1.6941	0.048432
13	-0.045264	-0.3103	0.378848
14	-0.053791	-0.3688	0.356976
15	-0.130796	-0.8967	0.187226
16	-0.044225	-0.3032	0.38154
17	0.03889	0.2666	0.395467
18	-0.223191	-1.5301	0.066345
19	-0.051024	-0.3498	0.364023
20	0.007209	0.0494	0.480396
21	-0.192159	-1.3174	0.097049
22	-0.009731	-0.0667	0.473548
23	0.036918	0.2531	0.400649
24	-0.171125	-1.1732	0.123319
25	-0.037932	-0.26	0.397981
26	-0.080997	-0.5553	0.290666
27	-0.126847	-0.8696	0.194464
28	0.112521	0.7714	0.222165
29	-0.108675	-0.745	0.229978
30	0.009125	0.0626	0.475193
31	0.062232	0.4266	0.335794
32	-0.074951	-0.5138	0.304887
33	0.026351	0.1807	0.428707
34	-0.034146	-0.2341	0.407964
35	-0.035396	-0.2427	0.40466
36	0.075575	0.5181	0.303404
37	0.001156	0.0079	0.496854
38	0.00488	0.0335	0.486727
39	0.001219	0.0084	0.496683
40	-0.005671	-0.0389	0.484577
41	-0.008933	-0.0612	0.475713
42	-0.014833	-0.1017	0.459718
43	-0.003823	-0.0262	0.489602
44	0.005758	0.0395	0.484339
45	0.013789	0.0945	0.462544
46	0.008893	0.061	0.475822
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.061301	0.4203	0.338106
2	0.195375	1.3394	0.093437
3	0.416019	2.8521	0.003218
4	-0.053965	-0.37	0.356534
5	-0.089142	-0.6111	0.27203
6	0.022997	0.1577	0.437702
7	0.058543	0.4014	0.344989
8	-0.02637	-0.1808	0.428656
9	-0.078169	-0.5359	0.297278
10	-0.203841	-1.3975	0.084418
11	-0.098572	-0.6758	0.251247
12	-0.242718	-1.664	0.051384
13	0.131345	0.9005	0.186234
14	0.148316	1.0168	0.157226
15	0.075862	0.5201	0.302724
16	-0.100718	-0.6905	0.246641
17	0.098012	0.6719	0.252456
18	-0.150282	-1.0303	0.154075
19	-0.03725	-0.2554	0.399775
20	-0.03574	-0.245	0.403753
21	-0.066759	-0.4577	0.324647
22	-0.137833	-0.9449	0.174762
23	0.032119	0.2202	0.413337
24	-0.113392	-0.7774	0.220415
25	0.04614	0.3163	0.376581
26	-0.109369	-0.7498	0.228558
27	0.07251	0.4971	0.310717
28	0.213746	1.4654	0.074739
29	0.0088	0.0603	0.476074
30	-0.138445	-0.9491	0.173704
31	-0.061557	-0.422	0.33747
32	-0.04741	-0.325	0.373302
33	0.009066	0.0622	0.475352
34	-0.174618	-1.1971	0.118632
35	0.011031	0.0756	0.470018
36	-0.034349	-0.2355	0.407427
37	0.012668	0.0868	0.465581
38	0.046675	0.32	0.375198
39	0.016805	0.1152	0.454385
40	0.062635	0.4294	0.334796
41	0.014519	0.0995	0.460569
42	-0.065617	-0.4498	0.327444
43	-0.027478	-0.1884	0.425695
44	-0.103722	-0.7111	0.240273
45	-0.10587	-0.7258	0.235777
46	-0.001476	-0.0101	0.495986
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620600djlv7hsghk6fo7t/1rl9g1293620572.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620600djlv7hsghk6fo7t/1rl9g1293620572.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620600djlv7hsghk6fo7t/2rl9g1293620572.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620600djlv7hsghk6fo7t/2rl9g1293620572.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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