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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: Fri, 12 Dec 2008 07:06:36 -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/12/t1229091267f0g25uah67u2i8b.htm/, Retrieved Fri, 12 Dec 2008 15:14:29 +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/12/t1229091267f0g25uah67u2i8b.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 «

44.9 48.1 52.3 48.9 52.6 60.3 50.5 41.6 56 51.4 52.9 54.9 43.9 51 51.9 54.3 50.3 57.2 48.8 41.1 58 63 53.8 54.7 55.5 56.1 69.6 69.4 57.2 68 53.3 47.9 60.8 61.7 57.8 51.4 50.5 48.1 58.7 54 56.1 60.4 51.2 50.7 56.4 53.3 52.6 47.7 49.5 48.5 55.3 49.8 57.4 64.6 53 41.5 55.9 58.4 53.5 50.6 58.5

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	0.243776	1.904	0.030818
2	-0.085121	-0.6648	0.254337
3	0.189326	1.4787	0.072186
4	0.076091	0.5943	0.277258
5	0.077845	0.608	0.272725
6	0.306866	2.3967	0.009812
7	0.109291	0.8536	0.198335
8	-0.086939	-0.679	0.249848
9	-0.012229	-0.0955	0.46211
10	-0.208121	-1.6255	0.054608
11	-0.025585	-0.1998	0.421141
12	0.372895	2.9124	0.002502
13	-0.048227	-0.3767	0.353865
14	-0.269508	-2.1049	0.019712
15	-0.092586	-0.7231	0.236186
16	-0.052655	-0.4112	0.341166
17	-0.125056	-0.9767	0.166283
18	0.058347	0.4557	0.325111
19	-0.041656	-0.3253	0.373017
20	-0.221445	-1.7295	0.044385
21	-0.140836	-1.1	0.137834
22	-0.285188	-2.2274	0.01481
23	-0.098465	-0.769	0.22242
24	0.155006	1.2106	0.115352
25	-0.110167	-0.8604	0.196459
26	-0.256748	-2.0053	0.024688
27	-0.034349	-0.2683	0.394697
28	-0.0477	-0.3726	0.355387
29	-0.107192	-0.8372	0.202876
30	0.076457	0.5971	0.27631
31	0.030675	0.2396	0.40573
32	-0.031484	-0.2459	0.403293
33	0.022248	0.1738	0.431314
34	-0.118187	-0.9231	0.179804
35	0.035286	0.2756	0.391895
36	0.196167	1.5321	0.065332
37	0.020217	0.1579	0.437527
38	-0.102196	-0.7982	0.213933
39	0.045798	0.3577	0.360904
40	0.016105	0.1258	0.450157
41	-0.057497	-0.4491	0.327489
42	0.051222	0.4001	0.345256
43	0.04878	0.381	0.352268
44	-0.022631	-0.1768	0.430143
45	0.015555	0.1215	0.451852
46	-0.024298	-0.1898	0.425057
47	0.030581	0.2388	0.406012
48	0.112542	0.879	0.19143
49	0.020281	0.1584	0.437331
50	-0.08285	-0.6471	0.260005
51	0.001701	0.0133	0.494721
52	0.02118	0.1654	0.43458
53	-0.060346	-0.4713	0.319547
54	0.007953	0.0621	0.475336
55	0.057243	0.4471	0.328198
56	-0.014761	-0.1153	0.454297
57	-0.025007	-0.1953	0.4229
58	0.006793	0.0531	0.478931
59	0.001288	0.0101	0.496003
60	-0.018488	-0.1444	0.442833

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.243776	1.904	0.030818
2	-0.153681	-1.2003	0.117335
3	0.273018	2.1323	0.018507
4	-0.083858	-0.655	0.25748
5	0.171569	1.34	0.092609
6	0.223148	1.7428	0.0432
7	-0.027161	-0.2121	0.416355
8	-0.05887	-0.4598	0.323651
9	-0.087662	-0.6847	0.248075
10	-0.31089	-2.4281	0.009071
11	0.135279	1.0566	0.147439
12	0.282139	2.2036	0.01567
13	-0.195928	-1.5302	0.065563
14	-0.062954	-0.4917	0.312354
15	-0.167025	-1.3045	0.09848
16	0.118303	0.924	0.17957
17	-0.127472	-0.9956	0.161692
18	-0.009621	-0.0751	0.470175
19	-0.103359	-0.8073	0.211326
20	-0.046053	-0.3597	0.360163
21	-0.021709	-0.1696	0.432961
22	-0.194919	-1.5224	0.066543
23	0.06675	0.5213	0.30201
24	-0.042681	-0.3333	0.370008
25	-0.01983	-0.1549	0.438716
26	-0.016104	-0.1258	0.450162
27	0.071256	0.5565	0.289943
28	-0.081232	-0.6344	0.264082
29	0.030637	0.2393	0.405846
30	-0.107696	-0.8411	0.201779
31	0.072269	0.5644	0.287263
32	0.044534	0.3478	0.364585
33	0.022734	0.1776	0.429831
34	-0.070713	-0.5523	0.291384
35	0.005766	0.045	0.482114
36	-0.010656	-0.0832	0.466971
37	-0.003317	-0.0259	0.489708
38	-0.034764	-0.2715	0.393455
39	-0.112887	-0.8817	0.190707
40	0.023136	0.1807	0.428603
41	-0.072555	-0.5667	0.286507
42	-0.031183	-0.2435	0.404201
43	-0.038941	-0.3041	0.381028
44	-0.068229	-0.5329	0.298025
45	0.054049	0.4221	0.337206
46	0.059829	0.4673	0.320983
47	-0.002579	-0.0201	0.491999
48	-0.037745	-0.2948	0.384576
49	-0.014778	-0.1154	0.454247
50	-0.045835	-0.358	0.360796
51	-0.06571	-0.5132	0.304828
52	0.010442	0.0816	0.467633
53	-0.046504	-0.3632	0.358852
54	0.015092	0.1179	0.453277
55	0.069705	0.5444	0.29407
56	-0.027932	-0.2182	0.414018
57	0.038978	0.3044	0.38092
58	0.022747	0.1777	0.42979
59	-0.095107	-0.7428	0.230224
60	-0.095531	-0.7461	0.229231

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229091267f0g25uah67u2i8b/1jy5p1229090794.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229091267f0g25uah67u2i8b/1jy5p1229090794.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229091267f0g25uah67u2i8b/2rvfa1229090794.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229091267f0g25uah67u2i8b/2rvfa1229090794.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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