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acf

*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, 28 Dec 2009 06:15:02 -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/28/t1262006143oysb5p71zkmmqlj.htm/, Retrieved Mon, 28 Dec 2009 14:15:45 +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/2009/Dec/28/t1262006143oysb5p71zkmmqlj.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 «

14.3 14.2 15.9 15.3 15.5 15.1 15 12.1 15.8 16.9 15.1 13.7 14.8 14.7 16 15.4 15 15.5 15.1 11.7 16.3 16.7 15 14.9 14.6 15.3 17.9 16.4 15.4 17.9 15.9 13.9 17.8 17.9 17.4 16.7 16 16.6 19.1 17.8 17.2 18.6 16.3 15.1 19.2 17.7 19.1 18 17.5 17.8 21.1 17.2 19.4 19.8 17.6 16.2 19.5 19.9 20 17.3 18.9 18.6 21.4 18.6 19.8 20.8 19.6 17.7 19.8 22.2 20.7 17.9

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	0.61491	5.2177	1e-06
2	0.469227	3.9815	8.1e-05
3	0.557195	4.728	5e-06
4	0.591773	5.0214	2e-06
5	0.536491	4.5523	1.1e-05
6	0.625843	5.3105	1e-06
7	0.469601	3.9847	8e-05
8	0.485618	4.1206	5e-05
9	0.412329	3.4987	0.000403
10	0.275056	2.3339	0.011197
11	0.386388	3.2786	0.000804
12	0.607963	5.1587	1e-06
13	0.316751	2.6877	0.004465
14	0.216131	1.8339	0.035398
15	0.238031	2.0198	0.023565
16	0.25118	2.1313	0.018238
17	0.254507	2.1596	0.017069
18	0.29471	2.5007	0.007336
19	0.163413	1.3866	0.08492
20	0.163978	1.3914	0.084194
21	0.09271	0.7867	0.217027
22	-0.038923	-0.3303	0.371076
23	0.087442	0.742	0.23026
24	0.19285	1.6364	0.053061
25	-0.021749	-0.1845	0.427053
26	-0.091617	-0.7774	0.219736
27	-0.093321	-0.7919	0.215522
28	-0.082541	-0.7004	0.242974
29	-0.069185	-0.5871	0.279501
30	-0.040832	-0.3465	0.365
31	-0.12291	-1.0429	0.150236
32	-0.106496	-0.9037	0.184597
33	-0.204313	-1.7337	0.04363
34	-0.274614	-2.3302	0.011302
35	-0.166256	-1.4107	0.081316
36	-0.079816	-0.6773	0.250206
37	-0.224197	-1.9024	0.030561
38	-0.287098	-2.4361	0.008661
39	-0.295088	-2.5039	0.007275
40	-0.24381	-2.0688	0.021078
41	-0.254385	-2.1585	0.017111
42	-0.235643	-1.9995	0.024664
43	-0.290244	-2.4628	0.008089
44	-0.252736	-2.1445	0.017683
45	-0.333681	-2.8314	0.003002
46	-0.37372	-3.1711	0.001116
47	-0.303557	-2.5758	0.006027
48	-0.211399	-1.7938	0.038524
49	-0.288478	-2.4478	0.008406
50	-0.335067	-2.8431	0.002905
51	-0.313512	-2.6602	0.00481
52	-0.264136	-2.2413	0.014046
53	-0.247372	-2.099	0.019661
54	-0.217673	-1.847	0.034427
55	-0.237031	-2.0113	0.02402
56	-0.221629	-1.8806	0.032037
57	-0.245644	-2.0844	0.020338
58	-0.244767	-2.0769	0.020689
59	-0.201204	-1.7073	0.04604
60	-0.15022	-1.2747	0.103264

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.61491	5.2177	1e-06
2	0.14651	1.2432	0.108917
3	0.362911	3.0794	0.001468
4	0.23929	2.0304	0.023003
5	0.12633	1.0719	0.143662
6	0.337142	2.8607	0.002764
7	-0.195594	-1.6597	0.050666
8	0.176953	1.5015	0.0688
9	-0.306311	-2.5991	0.005665
10	-0.336578	-2.856	0.002802
11	0.203028	1.7227	0.044614
12	0.331925	2.8165	0.003131
13	-0.21421	-1.8176	0.03664
14	-0.025571	-0.217	0.414419
15	-0.194994	-1.6546	0.051181
16	0.00072	0.0061	0.497572
17	0.039179	0.3324	0.370259
18	-0.039478	-0.335	0.369305
19	0.077113	0.6543	0.257493
20	-0.161213	-1.3679	0.087792
21	-0.010238	-0.0869	0.465507
22	-0.14831	-1.2585	0.106146
23	0.04021	0.3412	0.366975
24	-0.076831	-0.6519	0.258259
25	-0.074678	-0.6337	0.264153
26	0.035362	0.3001	0.382499
27	-0.054005	-0.4583	0.324076
28	0.129271	1.0969	0.13817
29	-0.123572	-1.0485	0.148949
30	0.09882	0.8385	0.202258
31	0.011751	0.0997	0.460425
32	0.002449	0.0208	0.491739
33	-0.069327	-0.5883	0.2791
34	-0.057729	-0.4898	0.312867
35	-0.122512	-1.0395	0.151015
36	0.065817	0.5585	0.289126
37	-0.033642	-0.2855	0.388056
38	-0.037241	-0.316	0.376458
39	0.047321	0.4015	0.344609
40	0.013236	0.1123	0.455446
41	-0.008842	-0.075	0.470201
42	-0.049907	-0.4235	0.336606
43	-0.065044	-0.5519	0.291359
44	-0.011433	-0.097	0.461492
45	0.053722	0.4558	0.324937
46	-0.087186	-0.7398	0.230914
47	-0.005065	-0.043	0.48292
48	-0.057922	-0.4915	0.31229
49	0.028737	0.2438	0.404024
50	0.0779	0.661	0.255359
51	0.088138	0.7479	0.228484
52	0.015967	0.1355	0.446304
53	0.067475	0.5725	0.284369
54	0.00762	0.0647	0.474312
55	-0.011316	-0.096	0.461886
56	-0.099886	-0.8476	0.199745
57	-0.043239	-0.3669	0.357385
58	0.054501	0.4625	0.322573
59	-0.06126	-0.5198	0.302396
60	-0.079387	-0.6736	0.251355

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006143oysb5p71zkmmqlj/1g8ob1262006099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006143oysb5p71zkmmqlj/1g8ob1262006099.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006143oysb5p71zkmmqlj/2i8wj1262006099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006143oysb5p71zkmmqlj/2i8wj1262006099.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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