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Autocorrelation

*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 10:50:14 -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/t1261072294ctmeats26rlndgt.htm/, Retrieved Thu, 17 Dec 2009 18:51:37 +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/t1261072294ctmeats26rlndgt.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 «

100 97.56592292 93.71196755 92.69776876 89.65517241 89.04665314 98.98580122 105.6795132 101.6227181 98.37728195 94.11764706 93.30628803 94.72616633 93.30628803 90.87221095 89.85801217 88.43813387 87.42393509 98.17444219 103.4482759 104.0567951 102.0283976 95.53752535 95.53752535 96.55172414 96.34888438 95.3346856 93.50912779 92.29208925 92.49492901 104.8681542 106.4908722 106.0851927 105.2738337 103.2454361 103.8539554 105.2738337 104.8681542 103.4482759 103.2454361 101.6227181 102.8397566 115.4158215 117.6470588 117.2413793 114.6044625 110.9533469 112.5760649 113.9959432 113.7931034 112.5760649 110.3448276 108.9249493 110.1419878 120.4868154 123.9350913 124.3407708 123.9350913 120.4868154 120.6896552 119.8782961 119.4726166 118.4584178 116.2271805 115.010142 115.4158215 125.9634888 127.5862069 127.3833671 124.137931 120.6896552 121.0953347 120.2839757 119.6754564 117.6470588 116.4300203 116.2271805 116.2271805 125.7606491 126.9776 etc...

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	0.929593	9.6606	0
2	0.820284	8.5246	0
3	0.736322	7.6521	0
4	0.694028	7.2125	0
5	0.689724	7.1678	0
6	0.678496	7.0511	0
7	0.644606	6.6989	0
8	0.609186	6.3308	0
9	0.607271	6.3109	0
10	0.638694	6.6375	0
11	0.69154	7.1867	0
12	0.707129	7.3487	0
13	0.614604	6.3872	0
14	0.494864	5.1428	1e-06
15	0.394759	4.1025	4e-05
16	0.332745	3.458	0.00039
17	0.306164	3.1817	0.000956
18	0.272695	2.8339	0.002744
19	0.223952	2.3274	0.010905
20	0.176356	1.8327	0.034798
21	0.164292	1.7074	0.045313
22	0.183829	1.9104	0.029366
23	0.216076	2.2455	0.013385
24	0.213189	2.2155	0.014411
25	0.122494	1.273	0.102877
26	0.015048	0.1564	0.438013
27	-0.068805	-0.715	0.238063
28	-0.118763	-1.2342	0.1099
29	-0.140393	-1.459	0.073733
30	-0.167972	-1.7456	0.04186
31	-0.204333	-2.1235	0.017998
32	-0.239553	-2.4895	0.007158
33	-0.243586	-2.5314	0.0064
34	-0.220116	-2.2875	0.012057
35	-0.183047	-1.9023	0.029899
36	-0.174606	-1.8146	0.036184
37	-0.241984	-2.5148	0.006692
38	-0.325345	-3.3811	0.000503
39	-0.38751	-4.0271	5.3e-05
40	-0.415048	-4.3133	1.8e-05
41	-0.418066	-4.3447	1.6e-05
42	-0.425133	-4.4181	1.2e-05
43	-0.439656	-4.569	7e-06
44	-0.452948	-4.7072	4e-06
45	-0.438312	-4.5551	7e-06
46	-0.40187	-4.1764	3e-05
47	-0.355417	-3.6936	0.000174
48	-0.331127	-3.4412	0.000412
49	-0.368656	-3.8312	0.000107
50	-0.418491	-4.3491	1.6e-05
51	-0.449895	-4.6754	4e-06
52	-0.455468	-4.7334	3e-06
53	-0.441953	-4.5929	6e-06
54	-0.429495	-4.4634	1e-05
55	-0.424775	-4.4144	1.2e-05
56	-0.417673	-4.3406	1.6e-05
57	-0.386975	-4.0216	5.4e-05
58	-0.33882	-3.5211	0.000315
59	-0.282081	-2.9315	0.002059
60	-0.247617	-2.5733	0.005715

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.929593	9.6606	0
2	-0.322835	-3.355	0.000548
3	0.227816	2.3675	0.009843
4	0.149579	1.5545	0.061499
5	0.181249	1.8836	0.031155
6	-0.121831	-1.2661	0.104101
7	-0.00269	-0.028	0.488876
8	0.099581	1.0349	0.151519
9	0.252541	2.6245	0.004968
10	0.100635	1.0458	0.148987
11	0.212268	2.206	0.014753
12	-0.218739	-2.2732	0.012496
13	-0.666358	-6.925	0
14	0.125601	1.3053	0.097285
15	-0.187577	-1.9494	0.026923
16	-0.099057	-1.0294	0.152789
17	-0.064272	-0.6679	0.2528
18	-0.007077	-0.0735	0.470753
19	0.02039	0.2119	0.416291
20	-0.08158	-0.8478	0.199212
21	0.161354	1.6768	0.048233
22	0.001474	0.0153	0.493902
23	-0.090393	-0.9394	0.174812
24	0.058115	0.6039	0.273573
25	-0.118403	-1.2305	0.110596
26	0.056478	0.5869	0.279237
27	0.049733	0.5168	0.303163
28	-0.077804	-0.8086	0.210273
29	-0.006246	-0.0649	0.474182
30	0.012058	0.1253	0.450253
31	0.04391	0.4563	0.324536
32	-0.115213	-1.1973	0.1169
33	-0.056993	-0.5923	0.277447
34	0.051401	0.5342	0.29716
35	0.04422	0.4595	0.323382
36	-0.009832	-0.1022	0.459404
37	-0.052117	-0.5416	0.294598
38	-0.063378	-0.6586	0.255763
39	-0.009054	-0.0941	0.462606
40	0.046558	0.4838	0.314738
41	-0.072225	-0.7506	0.227268
42	0.055359	0.5753	0.283139
43	-0.052041	-0.5408	0.294871
44	0.033385	0.3469	0.364655
45	-0.010561	-0.1098	0.456405
46	-0.031	-0.3222	0.373975
47	0.014607	0.1518	0.439815
48	0.014415	0.1498	0.4406
49	0.016735	0.1739	0.431128
50	0.040236	0.4181	0.338335
51	0.010458	0.1087	0.456828
52	-0.072921	-0.7578	0.225106
53	-0.003129	-0.0325	0.487059
54	0.024571	0.2554	0.399468
55	-0.050373	-0.5235	0.300853
56	0.041597	0.4323	0.333195
57	-0.05289	-0.5497	0.291847
58	0.032995	0.3429	0.366173
59	-0.00476	-0.0495	0.480319
60	-0.036547	-0.3798	0.352419

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261072294ctmeats26rlndgt/1yn0r1261072212.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261072294ctmeats26rlndgt/1yn0r1261072212.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261072294ctmeats26rlndgt/2iedk1261072212.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261072294ctmeats26rlndgt/2iedk1261072212.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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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