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WS 9 - (Partial) Autocorrelation Function

*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: Mon, 06 Dec 2010 20:14:07 +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/06/t1291666417ienszvm0pzsz9gr.htm/, Retrieved Mon, 06 Dec 2010 21:13:38 +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/06/t1291666417ienszvm0pzsz9gr.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 «

1576.23 1546.37 1545.05 1552.34 1594.3 1605.78 1673.21 1612.94 1566.34 1530.17 1582.54 1702.16 1701.93 1811.15 1924.2 2034.25 2011.13 2013.04 2151.67 1902.09 1944.01 1916.67 1967.31 2119.88 2216.38 2522.83 2647.64 2631.23 2693.41 3021.76 2953.67 2796.8 2672.05 2251.23 2046.08 2420.04 2608.89 2660.47 2493.98 2541.7 2554.6 2699.61 2805.48 2956.66 3149.51 3372.5 3379.33 3517.54 3527.34 3281.06 3089.65 3222.76 3165.76 3232.43 3229.54 3071.74 2850.17

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	0.2811	2.1036	0.019961
2	-0.049751	-0.3723	0.355536
3	-0.067626	-0.5061	0.307398
4	-0.133594	-0.9997	0.160872
5	-0.155363	-1.1626	0.124954
6	0.060732	0.4545	0.32562
7	0.013958	0.1045	0.458591
8	-0.190948	-1.4289	0.07929
9	-0.178262	-1.334	0.093803
10	-0.06787	-0.5079	0.306761
11	-0.038541	-0.2884	0.387048
12	0.050364	0.3769	0.35384
13	-0.167429	-1.2529	0.10772
14	-0.058247	-0.4359	0.332299
15	0.016889	0.1264	0.44994
16	0.125712	0.9407	0.175438
17	0.092188	0.6899	0.246562
18	0.139136	1.0412	0.151129
19	0.077235	0.578	0.2828
20	-0.173235	-1.2964	0.100082
21	-0.051322	-0.3841	0.351196
22	0.159459	1.1933	0.118896
23	0.062306	0.4663	0.321421
24	-0.002687	-0.0201	0.492013
25	0.013622	0.1019	0.459585
26	-0.053687	-0.4018	0.344695
27	-0.124367	-0.9307	0.178007
28	-0.047456	-0.3551	0.361913
29	0.033487	0.2506	0.401522
30	0.055891	0.4183	0.338681
31	0.021723	0.1626	0.435724
32	-0.039983	-0.2992	0.382944
33	0.026837	0.2008	0.420779
34	-0.043417	-0.3249	0.373232
35	-0.042293	-0.3165	0.376404
36	-0.005911	-0.0442	0.482436
37	0.02193	0.1641	0.435119
38	-0.046465	-0.3477	0.364679
39	-0.019145	-0.1433	0.443297
40	0.000126	9e-04	0.499626
41	-0.011459	-0.0857	0.465986
42	-0.017047	-0.1276	0.449473
43	-0.021898	-0.1639	0.435211
44	-0.031034	-0.2322	0.408599
45	-0.019405	-0.1452	0.442533
46	-0.007427	-0.0556	0.477938
47	0.036746	0.275	0.39217
48	0.03829	0.2865	0.387763

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.2811	2.1036	0.019961
2	-0.139816	-1.0463	0.149961
3	-0.013714	-0.1026	0.459314
4	-0.127312	-0.9527	0.172414
5	-0.09711	-0.7267	0.235217
6	0.126484	0.9465	0.173975
7	-0.084132	-0.6296	0.265763
8	-0.203315	-1.5215	0.066884
9	-0.103294	-0.773	0.221391
10	-0.027221	-0.2037	0.419661
11	-0.033814	-0.253	0.400581
12	-0.002799	-0.0209	0.491681
13	-0.342742	-2.5648	0.006515
14	0.072059	0.5392	0.295928
15	-0.026847	-0.2009	0.420751
16	0.085433	0.6393	0.26261
17	-0.086567	-0.6478	0.259879
18	0.016091	0.1204	0.452294
19	0.070511	0.5277	0.29991
20	-0.209457	-1.5674	0.061324
21	0.036645	0.2742	0.392459
22	0.097228	0.7276	0.234949
23	-0.009782	-0.0732	0.470952
24	-0.021286	-0.1593	0.437006
25	0.020006	0.1497	0.440766
26	-0.046109	-0.345	0.365676
27	0.042786	0.3202	0.37501
28	-0.145288	-1.0872	0.140796
29	0.099089	0.7415	0.230739
30	0.080335	0.6012	0.275077
31	0.002133	0.016	0.49366
32	-0.008131	-0.0608	0.47585
33	-0.036674	-0.2744	0.392378
34	-0.051771	-0.3874	0.349958
35	0.056346	0.4217	0.337445
36	-0.05177	-0.3874	0.349961
37	0.000402	0.003	0.498804
38	-0.037223	-0.2785	0.390809
39	0.002479	0.0186	0.492632
40	-0.059295	-0.4437	0.329476
41	-0.110244	-0.825	0.206438
42	0.070993	0.5313	0.298669
43	-0.058516	-0.4379	0.331573
44	-0.057805	-0.4326	0.333494
45	-0.059692	-0.4467	0.328411
46	-0.00947	-0.0709	0.471877
47	-0.047563	-0.3559	0.361617
48	-0.038656	-0.2893	0.38672

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291666417ienszvm0pzsz9gr/144001291666443.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291666417ienszvm0pzsz9gr/144001291666443.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291666417ienszvm0pzsz9gr/244001291666443.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291666417ienszvm0pzsz9gr/244001291666443.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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