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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, 16 Dec 2010 20:50:05 +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/Dec/16/t1292532491z3ykhxi2s9z7vf6.htm/, Retrieved Thu, 16 Dec 2010 21:48:11 +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/Dec/16/t1292532491z3ykhxi2s9z7vf6.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

655362 873127 1107897 1555964 1671159 1493308 2957796 2638691 1305669 1280496 921900 867888 652586 913831 1108544 1555827 1699283 1509458 3268975 2425016 1312703 1365498 934453 775019 651142 843192 1146766 1652601 1465906 1652734 2922334 2702805 1458956 1410363 1019279 936574 708917 885295 1099663 1576220 1487870 1488635 2882530 2677026 1404398 1344370 936865 872705 628151 953712 1160384 1400618 1661511 1495347 2918786 2775677 1407026 1370199 964526 850851 683118 847224 1073256 1514326 1503734 1507712 2865698 2788128 1391596 1366378 946295 859626

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.067835	-0.5254	0.300604
2	0.159939	1.2389	0.110106
3	0.247549	1.9175	0.029969
4	-0.096469	-0.7472	0.228917
5	0.127406	0.9869	0.163831
6	-0.112407	-0.8707	0.193694
7	-0.202835	-1.5712	0.060703
8	-0.030078	-0.233	0.408283
9	-0.176185	-1.3647	0.088718
10	-0.194355	-1.5055	0.068726
11	-0.037405	-0.2897	0.386506
12	-0.465521	-3.6059	0.000317
13	0.018937	0.1467	0.441936
14	0.023464	0.1818	0.428194
15	-0.033775	-0.2616	0.397255
16	0.030577	0.2368	0.40679
17	0.067425	0.5223	0.301703
18	0.239767	1.8572	0.034094
19	0.011074	0.0858	0.465965
20	0.128367	0.9943	0.162028
21	0.096552	0.7479	0.228725
22	0.012223	0.0947	0.462443
23	0.262535	2.0336	0.023211
24	-0.072803	-0.5639	0.287451
25	0.022474	0.1741	0.431192
26	-0.042441	-0.3287	0.371745
27	-0.14926	-1.1562	0.126099
28	0.044153	0.342	0.366771
29	-0.074503	-0.5771	0.283018
30	-0.246165	-1.9068	0.03067
31	0.085805	0.6646	0.254412
32	-0.036537	-0.283	0.389069
33	-0.109341	-0.847	0.200194
34	0.106364	0.8239	0.206632
35	-0.173183	-1.3415	0.092412
36	0.12466	0.9656	0.169057
37	-0.012441	-0.0964	0.461774
38	9.1e-05	7e-04	0.499721
39	0.077045	0.5968	0.276447
40	-0.02772	-0.2147	0.415357
41	-0.010705	-0.0829	0.467097
42	0.08604	0.6665	0.253834
43	-0.03532	-0.2736	0.392669
44	-0.047022	-0.3642	0.358484
45	0.056695	0.4392	0.331062
46	-0.042974	-0.3329	0.370194
47	0.026871	0.2081	0.417912
48	-0.037898	-0.2936	0.385054
49	-0.009297	-0.072	0.471416
50	0.010997	0.0852	0.466201
51	-0.011984	-0.0928	0.463174
52	-0.007381	-0.0572	0.477299
53	-0.000511	-0.004	0.498427
54	0.000186	0.0014	0.499429
55	-0.001239	-0.0096	0.496188
56	-0.000338	-0.0026	0.498961
57	-0.002922	-0.0226	0.49101
58	0.00181	0.014	0.494429
59	-0.000155	-0.0012	0.499522
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.067835	-0.5254	0.300604
2	0.156056	1.2088	0.11574
3	0.27523	2.1319	0.018559
4	-0.089655	-0.6945	0.245035
5	0.028202	0.2184	0.41391
6	-0.151136	-1.1707	0.123175
7	-0.231032	-1.7896	0.039285
8	-0.085424	-0.6617	0.255351
9	-0.047364	-0.3669	0.357501
10	-0.132525	-1.0265	0.15438
11	-0.006664	-0.0516	0.479501
12	-0.428202	-3.3168	0.000775
13	-0.072993	-0.5654	0.286954
14	0.124777	0.9665	0.168832
15	0.240599	1.8637	0.033632
16	-0.112397	-0.8706	0.193714
17	-0.022202	-0.172	0.432017
18	0.125179	0.9696	0.168062
19	-0.164109	-1.2712	0.104285
20	-0.035472	-0.2748	0.39222
21	0.065888	0.5104	0.305835
22	-0.083873	-0.6497	0.25919
23	0.25642	1.9862	0.025791
24	-0.218633	-1.6935	0.047771
25	-0.002953	-0.0229	0.490912
26	-0.07169	-0.5553	0.290375
27	0.052562	0.4071	0.342676
28	-0.002514	-0.0195	0.492263
29	0.164317	1.2728	0.104001
30	-0.048993	-0.3795	0.352828
31	-0.07599	-0.5886	0.279164
32	-0.001798	-0.0139	0.494467
33	0.006947	0.0538	0.478632
34	-0.008352	-0.0647	0.474315
35	0.147689	1.144	0.128585
36	-0.111687	-0.8651	0.195208
37	-0.118322	-0.9165	0.181532
38	-0.094252	-0.7301	0.234093
39	0.019227	0.1489	0.441054
40	-0.020765	-0.1608	0.436376
41	-0.001146	-0.0089	0.496474
42	0.024821	0.1923	0.424092
43	-0.055283	-0.4282	0.335013
44	0.000566	0.0044	0.498259
45	-0.016781	-0.13	0.448506
46	-0.136503	-1.0574	0.147295
47	0.129297	1.0015	0.160297
48	-0.002856	-0.0221	0.491212
49	-0.080549	-0.6239	0.267519
50	-0.014553	-0.1127	0.455312
51	-0.03153	-0.2442	0.403944
52	-0.117389	-0.9093	0.183417
53	0.044676	0.3461	0.365255
54	0.04649	0.3601	0.360014
55	0.017474	0.1354	0.446394
56	-0.042906	-0.3323	0.370393
57	-0.069069	-0.535	0.29731
58	-0.017454	-0.1352	0.446453
59	0.071883	0.5568	0.289866
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/1m6sa1292532600.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/1m6sa1292532600.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/2xg9v1292532600.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/2xg9v1292532600.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/3xg9v1292532600.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292532491z3ykhxi2s9z7vf6/3xg9v1292532600.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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