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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: Thu, 17 Dec 2009 08:21:07 -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/17/t12610633318l1xhcu48usliiz.htm/, Retrieved Thu, 17 Dec 2009 16:22:13 +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/17/t12610633318l1xhcu48usliiz.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 «

9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.3

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	0.338787	2.646	0.005173
2	-0.293741	-2.2942	0.012618
3	-0.524927	-4.0998	6.2e-05
4	-0.353261	-2.7591	0.003821
5	0.14385	1.1235	0.132813
6	0.534865	4.1774	4.8e-05
7	0.353638	2.762	0.00379
8	-0.055407	-0.4327	0.333363
9	-0.337058	-2.6325	0.005361
10	-0.320437	-2.5027	0.00751
11	-0.015503	-0.1211	0.452012
12	0.36243	2.8307	0.003141
13	0.083552	0.6526	0.258244
14	-0.062562	-0.4886	0.31343
15	-0.077677	-0.6067	0.273159
16	-0.089742	-0.7009	0.243014
17	-0.004962	-0.0388	0.484605
18	0.092874	0.7254	0.2355
19	0.024648	0.1925	0.423991
20	-0.053055	-0.4144	0.340028
21	-0.060532	-0.4728	0.319032
22	-0.057246	-0.4471	0.328191
23	0.043691	0.3412	0.36705
24	0.162297	1.2676	0.104882
25	-0.107607	-0.8404	0.201973
26	-0.142257	-1.1111	0.135451
27	-0.07361	-0.5749	0.283732
28	-0.0155	-0.1211	0.452022
29	0.08337	0.6511	0.2587
30	0.129205	1.0091	0.158451
31	0.038949	0.3042	0.381005
32	-0.119718	-0.935	0.17673
33	-0.168459	-1.3157	0.096598
34	0.004972	0.0388	0.484574
35	0.170489	1.3316	0.09398
36	0.234245	1.8295	0.036105
37	-0.023358	-0.1824	0.427925
38	-0.176908	-1.3817	0.086052
39	-0.19283	-1.506	0.068608
40	-0.03732	-0.2915	0.385836
41	0.162779	1.2713	0.104216
42	0.266514	2.0815	0.020794
43	0.072205	0.5639	0.287432
44	-0.189759	-1.4821	0.071735
45	-0.260279	-2.0328	0.023214
46	-0.063229	-0.4938	0.311599
47	0.133846	1.0454	0.149988
48	0.20761	1.6215	0.055036
49	0.048666	0.3801	0.352598
50	-0.102338	-0.7993	0.213612
51	-0.147979	-1.1557	0.126145
52	-0.062166	-0.4855	0.314519
53	0.026747	0.2089	0.41761
54	0.083597	0.6529	0.258132
55	0.045368	0.3543	0.362155
56	-0.060264	-0.4707	0.319774
57	-0.07979	-0.6232	0.267744
58	-0.018831	-0.1471	0.441778
59	-0.000926	-0.0072	0.497128
60	4.1e-05	3e-04	0.499872

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.338787	2.646	0.005173
2	-0.461485	-3.6043	0.000315
3	-0.320284	-2.5015	0.007533
4	-0.242161	-1.8913	0.031665
5	0.092272	0.7207	0.236933
6	0.260768	2.0367	0.023015
7	0.042936	0.3353	0.36926
8	0.075394	0.5888	0.27907
9	0.039029	0.3048	0.380767
10	0.002664	0.0208	0.491735
11	0.005742	0.0448	0.482189
12	0.152503	1.1911	0.119118
13	-0.462645	-3.6134	0.000306
14	0.122538	0.9571	0.171159
15	0.077066	0.6019	0.274734
16	0.009713	0.0759	0.469889
17	-0.054732	-0.4275	0.33527
18	-0.007281	-0.0569	0.47742
19	0.095286	0.7442	0.229805
20	-0.023436	-0.183	0.427688
21	-0.040923	-0.3196	0.375175
22	-0.15172	-1.185	0.120313
23	0.069146	0.5401	0.295564
24	0.048327	0.3774	0.353575
25	-0.160628	-1.2545	0.107215
26	-0.080789	-0.631	0.265203
27	-0.093364	-0.7292	0.234336
28	0.067198	0.5248	0.3008
29	-0.013997	-0.1093	0.456654
30	-0.02691	-0.2102	0.417117
31	0.062994	0.492	0.312242
32	-0.030995	-0.2421	0.404765
33	-0.001027	-0.008	0.496814
34	0.245071	1.9141	0.030153
35	-0.001732	-0.0135	0.494626
36	0.030063	0.2348	0.407576
37	0.036255	0.2832	0.389008
38	-0.099943	-0.7806	0.219034
39	-0.082796	-0.6467	0.26014
40	-0.020555	-0.1605	0.436493
41	-0.043395	-0.3389	0.367913
42	0.098403	0.7686	0.222562
43	-0.093287	-0.7286	0.23452
44	0.049075	0.3833	0.351418
45	0.065422	0.511	0.30561
46	-0.018286	-0.1428	0.443451
47	-0.028146	-0.2198	0.41337
48	-0.108355	-0.8463	0.200352
49	0.006629	0.0518	0.479438
50	-0.069072	-0.5395	0.295762
51	0.033728	0.2634	0.396554
52	-0.094608	-0.7389	0.231398
53	-0.033613	-0.2625	0.396901
54	-0.056771	-0.4434	0.329525
55	0.042219	0.3297	0.371363
56	0.002309	0.018	0.492837
57	-0.05797	-0.4528	0.326165
58	-0.086107	-0.6725	0.251896
59	0.068003	0.5311	0.298631
60	0.006334	0.0495	0.480353

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610633318l1xhcu48usliiz/1dveq1261063265.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610633318l1xhcu48usliiz/1dveq1261063265.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610633318l1xhcu48usliiz/2csor1261063265.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610633318l1xhcu48usliiz/2csor1261063265.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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