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autocorrelation function paper d=0,D=1

*Unverified author*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 17 Dec 2008 05:28:16 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t122951706864y9zrmmls0nw6g.htm/, Retrieved Wed, 17 Dec 2008 13:31:12 +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/2008/Dec/17/t122951706864y9zrmmls0nw6g.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

12.5 14.8 15.9 14.8 12.9 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 21.2 21.4 21.7 23.2 21.5 22.9 23.2 18.6

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	0.092002	0.7861	0.217187
2	0.278359	2.3783	0.010006
3	0.534343	4.5654	1e-05
4	0.109558	0.9361	0.176164
5	0.159572	1.3634	0.088476
6	0.332798	2.8434	0.002893
7	-0.078036	-0.6667	0.25352
8	0.107822	0.9212	0.179983
9	0.198641	1.6972	0.04696
10	-0.092172	-0.7875	0.216763
11	-0.033537	-0.2865	0.387639
12	0.044664	0.3816	0.351931
13	-0.144822	-1.2374	0.109959
14	-0.055549	-0.4746	0.318241
15	-0.021719	-0.1856	0.42665
16	-0.256374	-2.1905	0.015843
17	0.009918	0.0847	0.46635
18	-0.021188	-0.181	0.428421
19	-0.182929	-1.563	0.061195
20	-0.004592	-0.0392	0.484405
21	0.040732	0.348	0.364417
22	-0.210831	-1.8013	0.037889
23	0.192925	1.6484	0.051789
24	-0.192902	-1.6482	0.051809
25	-0.043037	-0.3677	0.357077
26	0.094001	0.8031	0.212249
27	-0.101553	-0.8677	0.19421
28	-0.066159	-0.5653	0.286815
29	0.091763	0.784	0.217782
30	-0.133304	-1.1389	0.129224
31	0.00031	0.0026	0.498948
32	0.038333	0.3275	0.372108
33	-0.153055	-1.3077	0.097539
34	0.014961	0.1278	0.44932
35	0.099789	0.8526	0.198335
36	-0.067766	-0.579	0.282189
37	0.069452	0.5934	0.277375
38	0.128341	1.0965	0.138222
39	0.009266	0.0792	0.468557
40	0.134573	1.1498	0.126991
41	0.118321	1.0109	0.157694
42	0.036077	0.3082	0.379388
43	0.134248	1.147	0.12756
44	0.187826	1.6048	0.05643
45	-0.067251	-0.5746	0.283667
46	0.173678	1.4839	0.071069
47	0.016088	0.1375	0.445526
48	-0.051075	-0.4364	0.331924
49	0.114361	0.9771	0.165873
50	-0.090548	-0.7736	0.220821
51	-0.119958	-1.0249	0.154393
52	0.043406	0.3709	0.355908
53	-0.153879	-1.3147	0.096356
54	-0.161354	-1.3786	0.086113
55	-0.056166	-0.4799	0.316373
56	-0.191226	-1.6338	0.053299
57	-0.156866	-1.3403	0.092158
58	-0.098344	-0.8403	0.201755
59	-0.209694	-1.7916	0.038669
60	-0.126055	-1.077	0.142509

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.092002	0.7861	0.217187
2	0.272199	2.3257	0.011409
3	0.534449	4.5663	1e-05
4	0.055707	0.476	0.317761
5	-0.157485	-1.3456	0.091306
6	0.018743	0.1601	0.436606
7	-0.208088	-1.7779	0.039792
8	-0.048932	-0.4181	0.338559
9	0.134876	1.1524	0.126462
10	0.057497	0.4913	0.312359
11	-0.167858	-1.4342	0.077896
12	-0.164619	-1.4065	0.081909
13	-0.050108	-0.4281	0.334911
14	0.041444	0.3541	0.362145
15	0.08984	0.7676	0.222603
16	-0.134442	-1.1487	0.127221
17	0.055407	0.4734	0.318671
18	0.089198	0.7621	0.224226
19	0.013358	0.1141	0.454725
20	-0.029147	-0.249	0.402018
21	0.097062	0.8293	0.20482
22	-0.145794	-1.2457	0.108436
23	0.149936	1.2811	0.102115
24	-0.267107	-2.2822	0.012698
25	0.070973	0.6064	0.273068
26	0.011488	0.0982	0.46104
27	0.005853	0.05	0.480126
28	-0.032973	-0.2817	0.389476
29	-0.009443	-0.0807	0.467957
30	-0.033368	-0.2851	0.388188
31	-0.032031	-0.2737	0.392554
32	0.000121	0.001	0.499589
33	-0.018191	-0.1554	0.438458
34	0.098576	0.8422	0.201204
35	0.131858	1.1266	0.131802
36	0.089003	0.7604	0.22472
37	0.068768	0.5876	0.279322
38	-0.048189	-0.4117	0.340872
39	0.046207	0.3948	0.347074
40	-0.065652	-0.5609	0.288282
41	0.024	0.2051	0.419048
42	0.039712	0.3393	0.36768
43	0.039655	0.3388	0.367862
44	-0.008043	-0.0687	0.472701
45	-0.118299	-1.0107	0.157739
46	-0.119588	-1.0218	0.155134
47	-0.036896	-0.3152	0.376738
48	-0.111469	-0.9524	0.172021
49	0.13425	1.147	0.127557
50	-0.028558	-0.244	0.403957
51	-0.001168	-0.01	0.496031
52	-0.096304	-0.8228	0.206645
53	0.001483	0.0127	0.494964
54	-0.036096	-0.3084	0.379326
55	-0.006302	-0.0538	0.478603
56	-0.000702	-0.006	0.497615
57	-0.04322	-0.3693	0.356496
58	-0.076338	-0.6522	0.258151
59	-0.022581	-0.1929	0.423773
60	0.043743	0.3737	0.354841

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122951706864y9zrmmls0nw6g/1g01a1229516894.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122951706864y9zrmmls0nw6g/1g01a1229516894.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122951706864y9zrmmls0nw6g/2j1pu1229516894.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122951706864y9zrmmls0nw6g/2j1pu1229516894.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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