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WERKLOOSHEID

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 23 Nov 2010 18:58:57 +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/Nov/23/t1290538642xwq9p8tr61vhz45.htm/, Retrieved Tue, 23 Nov 2010 19:57:24 +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/Nov/23/t1290538642xwq9p8tr61vhz45.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

8.6 8.5 8.4 8.0 7.9 8.1 8.6 8.8 8.8 8.6 8.3 8.3 8.3 8.4 8.4 8.5 8.6 8.6 8.6 8.6 8.6 8.5 8.4 8.4 8.4 8.5 8.5 8.6 8.6 8.4 8.2 8.0 8.0 8.0 8.0 7.9 7.9 7.8 7.9 8.0 7.9 7.4 7.2 7.0 7.0 7.1 7.2 7.2 7.0 6.9 6.8 6.8 6.8 6.9 7.2 7.3 7.2 7.1 7.1 7.3 7.5 7.6 7.7 7.7 7.7 7.8 8.0 8.1 8.1 8.0 8.1 8.2 8.3 8.4 8.6 8.6 8.7 8.8 8.9

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	0.947771	8.424	0
2	0.869633	7.7295	0
3	0.795177	7.0677	0
4	0.753459	6.6969	0
5	0.729625	6.4851	0
6	0.710783	6.3176	0
7	0.672097	5.9737	0
8	0.613031	5.4487	0
9	0.544041	4.8355	3e-06
10	0.476296	4.2334	3.1e-05
11	0.409025	3.6355	0.000246
12	0.335694	2.9837	0.001894
13	0.259212	2.3039	0.011928
14	0.186354	1.6564	0.050809
15	0.117833	1.0473	0.149072
16	0.049253	0.4378	0.331372
17	-0.016176	-0.1438	0.443022
18	-0.07299	-0.6488	0.25919
19	-0.122972	-1.093	0.138858
20	-0.172836	-1.5362	0.064242
21	-0.226149	-2.0101	0.023919
22	-0.285107	-2.5341	0.006626
23	-0.343352	-3.0518	0.001549
24	-0.393455	-3.4971	0.000388
25	-0.422108	-3.7518	0.000167
26	-0.428897	-3.8121	0.000136
27	-0.431704	-3.8371	0.000125
28	-0.444197	-3.9481	8.5e-05
29	-0.458828	-4.0782	5.4e-05
30	-0.464488	-4.1285	4.5e-05
31	-0.460107	-4.0895	5.2e-05
32	-0.455725	-4.0506	5.9e-05
33	-0.455266	-4.0465	6e-05
34	-0.451539	-4.0134	6.8e-05
35	-0.440979	-3.9195	9.4e-05
36	-0.410395	-3.6477	0.000236
37	-0.36959	-3.285	0.000761
38	-0.324564	-2.8848	0.002523
39	-0.3077	-2.7349	0.003851
40	-0.30771	-2.735	0.00385
41	-0.311524	-2.7689	0.003503
42	-0.300012	-2.6666	0.004646
43	-0.279528	-2.4845	0.007544
44	-0.245023	-2.1778	0.016202
45	-0.205228	-1.8241	0.035959
46	-0.165136	-1.4678	0.07307
47	-0.131163	-1.1658	0.123602
48	-0.105746	-0.9399	0.175069

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.947771	8.424	0
2	-0.281497	-2.502	0.007208
3	0.061343	0.5452	0.293566
4	0.272029	2.4178	0.008958
5	0.004421	0.0393	0.484376
6	0.001147	0.0102	0.495946
7	-0.152235	-1.3531	0.089943
8	-0.108894	-0.9679	0.168031
9	-0.047826	-0.4251	0.335966
10	-0.092199	-0.8195	0.207488
11	-0.142403	-1.2657	0.10467
12	-0.175499	-1.5599	0.061394
13	-0.069702	-0.6195	0.268677
14	-0.015643	-0.139	0.444886
15	-0.076325	-0.6784	0.249752
16	-0.104277	-0.9268	0.178417
17	0.004323	0.0384	0.484724
18	0.08577	0.7623	0.224063
19	0.021651	0.1924	0.423945
20	-0.05201	-0.4623	0.322579
21	-0.042846	-0.3808	0.35218
22	-0.051918	-0.4615	0.322869
23	-0.017434	-0.155	0.438624
24	-0.035511	-0.3156	0.376558
25	0.064145	0.5701	0.285104
26	0.101847	0.9052	0.184047
27	-0.036142	-0.3212	0.374439
28	-0.053756	-0.4778	0.317058
29	0.072721	0.6464	0.259961
30	0.091602	0.8142	0.208995
31	-0.011723	-0.1042	0.45864
32	-0.142323	-1.265	0.104796
33	-0.0891	-0.7919	0.215384
34	0.064376	0.5722	0.284409
35	-0.007757	-0.0689	0.472604
36	0.065666	0.5837	0.280558
37	-0.053483	-0.4754	0.317919
38	0.057122	0.5077	0.306534
39	-0.221505	-1.9688	0.026243
40	-0.100589	-0.8941	0.187003
41	-0.051454	-0.4573	0.324342
42	-0.013155	-0.1169	0.453608
43	-0.064777	-0.5757	0.283211
44	0.038455	0.3418	0.366707
45	0.060037	0.5336	0.297552
46	0.075024	0.6668	0.253413
47	0.05261	0.4676	0.320676
48	-0.027933	-0.2483	0.402283

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290538642xwq9p8tr61vhz45/12nea1290538735.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290538642xwq9p8tr61vhz45/12nea1290538735.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290538642xwq9p8tr61vhz45/22nea1290538735.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290538642xwq9p8tr61vhz45/22nea1290538735.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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