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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, 23 Dec 2010 07:04:44 +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/23/t1293087786g8vw1cajoshnduu.htm/, Retrieved Thu, 23 Dec 2010 08:03:07 +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/23/t1293087786g8vw1cajoshnduu.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 «

1.3031 1.3241 1.2961 1.2865 1.2305 1.2101 1.2125 1.2350 1.2014 1.1992 1.1791 1.1832 1.2159 1.1922 1.2114 1.2614 1.2812 1.2786 1.2772 1.2815 1.2679 1.2765 1.3247 1.3191 1.3029 1.3234 1.3354 1.3651 1.3453 1.3534 1.3706 1.3638 1.4268 1.4485 1.4635 1.4587 1.4876 1.5189 1.5783 1.5633 1.5554 1.5757 1.5593 1.4660 1.4065 1.2759 1.2705 1.3954 1.2793 1.2694 1.3282 1.3230 1.4135 1.4042 1.4253 1.4322 1.4632 1.4713 1.5016 1.4318

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.010312	0.0792	0.468569
2	-0.02522	-0.1937	0.423532
3	0.164612	1.2644	0.105527
4	-0.07536	-0.5789	0.282446
5	0.142692	1.096	0.138758
6	0.031885	0.2449	0.403688
7	-0.33584	-2.5796	0.006201
8	-0.113863	-0.8746	0.192669
9	-0.068943	-0.5296	0.299202
10	-0.091364	-0.7018	0.242788
11	0.013489	0.1036	0.458916
12	-0.219313	-1.6846	0.048677
13	-0.153105	-1.176	0.122155
14	0.121003	0.9294	0.178223
15	0.11676	0.8968	0.186722
16	0.029299	0.225	0.41136
17	0.028083	0.2157	0.41498
18	-0.01639	-0.1259	0.450123
19	-0.031704	-0.2435	0.404223
20	0.157038	1.2062	0.116271
21	-0.063181	-0.4853	0.314629
22	0.000185	0.0014	0.499436
23	-0.085253	-0.6548	0.257559
24	0.000286	0.0022	0.499126
25	0.106983	0.8218	0.207263
26	-0.018354	-0.141	0.444182
27	-0.090608	-0.696	0.24459
28	-0.087058	-0.6687	0.253146
29	-0.081978	-0.6297	0.265667
30	-0.070313	-0.5401	0.295586
31	0.032391	0.2488	0.402189
32	0.002995	0.023	0.490862
33	-0.088474	-0.6796	0.249713
34	-0.073928	-0.5679	0.286144
35	0.15919	1.2228	0.113141
36	0.007161	0.055	0.478159
37	0.003971	0.0305	0.487886
38	0.045846	0.3522	0.362989
39	0.019665	0.1511	0.440225
40	0.169856	1.3047	0.098533
41	0.096348	0.7401	0.231098
42	-0.027427	-0.2107	0.416934
43	-0.006085	-0.0467	0.481439
44	-0.023351	-0.1794	0.429133
45	-0.02593	-0.1992	0.421407
46	0.038689	0.2972	0.383689
47	-0.059664	-0.4583	0.324214
48	-0.080268	-0.6166	0.269952
49	0.022266	0.171	0.432395
50	-0.042182	-0.324	0.37354
51	0.038078	0.2925	0.385473
52	-0.039035	-0.2998	0.382678
53	-0.010648	-0.0818	0.467546
54	-0.008181	-0.0628	0.475053
55	0.040089	0.3079	0.379609
56	0.001052	0.0081	0.49679
57	0.025663	0.1971	0.422205
58	-0.012867	-0.0988	0.460802
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.010312	0.0792	0.468569
2	-0.025329	-0.1946	0.423206
3	0.165264	1.2694	0.104639
4	-0.082489	-0.6336	0.264391
5	0.160259	1.231	0.111609
6	-0.010949	-0.0841	0.466631
7	-0.3163	-2.4295	0.00909
8	-0.169722	-1.3037	0.098707
9	-0.08035	-0.6172	0.269745
10	-0.016749	-0.1287	0.449036
11	0.018004	0.1383	0.445242
12	-0.139218	-1.0694	0.144633
13	-0.116396	-0.8941	0.187462
14	0.02634	0.2023	0.42018
15	0.12312	0.9457	0.174078
16	0.000373	0.0029	0.498863
17	-0.007993	-0.0614	0.475627
18	-0.027437	-0.2107	0.416905
19	-0.19422	-1.4918	0.070536
20	-0.008999	-0.0691	0.472563
21	-0.096973	-0.7449	0.229656
22	0.106219	0.8159	0.208925
23	-0.103272	-0.7933	0.215405
24	0.064538	0.4957	0.310964
25	0.028002	0.2151	0.415221
26	-0.016012	-0.123	0.451267
27	-0.041495	-0.3187	0.375529
28	-0.136355	-1.0474	0.149602
29	-0.130052	-0.9989	0.160949
30	-0.2228	-1.7114	0.046134
31	-0.030774	-0.2364	0.406977
32	0.0896	0.6882	0.247003
33	-0.019515	-0.1499	0.440678
34	-0.101734	-0.7814	0.218836
35	0.097296	0.7473	0.228912
36	-0.07473	-0.574	0.28407
37	-0.07273	-0.5587	0.289257
38	-0.058997	-0.4532	0.326045
39	0.030397	0.2335	0.408098
40	-0.006913	-0.0531	0.478917
41	-0.001659	-0.0127	0.494938
42	-0.078115	-0.6	0.275397
43	-0.005215	-0.0401	0.484093
44	0.010324	0.0793	0.468531
45	-0.017391	-0.1336	0.447093
46	-0.039734	-0.3052	0.380642
47	-0.000504	-0.0039	0.498462
48	0.0131	0.1006	0.460095
49	-0.045019	-0.3458	0.365362
50	-0.087848	-0.6748	0.251227
51	0.033159	0.2547	0.39992
52	-0.051481	-0.3954	0.346974
53	0.029662	0.2278	0.410281
54	-0.015093	-0.1159	0.45405
55	-0.013203	-0.1014	0.459782
56	-0.068738	-0.528	0.299744
57	-0.082338	-0.6324	0.264769
58	-0.004965	-0.0381	0.484855
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/1h4hy1293087880.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/1h4hy1293087880.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/2mrrc1293087880.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/2mrrc1293087880.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/3mrrc1293087880.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/23/t1293087786g8vw1cajoshnduu/3mrrc1293087880.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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