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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: Sun, 19 Dec 2010 07:13:34 +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/19/t1292742831cteqje2dknxgasn.htm/, Retrieved Sun, 19 Dec 2010 08:13:52 +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/19/t1292742831cteqje2dknxgasn.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 «

5 4 5 6 6 6 7 8 7 8 7 8 8 9 9 8 9 9 10 11 12 13 13 13 14 14 15 15 16 16 17 18 19 20 22 20 22 25 24 25 28 26 27 26 25 27 28 30 31 32 34 34 33 32 34 36 37 40 38 38 36 40 40 42 44 45 47 49 47 49 52 50 50 57 58 58 58 61 61 64 68 40 34 46 36 34 45 55 50 56 72 76 78 77 90 88 97 93 84 67 72 75 71 75 90 78 73 62 65 61 58 33 39 56 79 82 79 73 87 85 83 82 83 92 95 97 87 84 84 89 103 106 109 106 105 115 120 124 121 131 139 133 119 123 120 128 134 126 115 106 99 100 99 99 100 100 108 109 115 114 108 113 118 122 118 121 118 121 121 112 119 116 110 111 106 108

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	0.10612	1.4038	0.08107
2	-0.150541	-1.9915	0.023992
3	-0.117414	-1.5532	0.061086
4	0.066584	0.8808	0.189811
5	-0.044538	-0.5892	0.278251
6	0.047507	0.6285	0.265264
7	-0.073463	-0.9718	0.166241
8	-0.111384	-1.4735	0.07121
9	-0.073302	-0.9697	0.166767
10	0.138051	1.8262	0.034759
11	-0.047571	-0.6293	0.264985
12	-0.086204	-1.1404	0.127845
13	-0.146297	-1.9353	0.027281
14	0.016866	0.2231	0.411854
15	-0.141278	-1.8689	0.031651
16	0.011149	0.1475	0.441459
17	0.117485	1.5542	0.060974
18	0.078027	1.0322	0.151702
19	-0.161531	-2.1369	0.016999
20	-0.116738	-1.5443	0.062161
21	0.080868	1.0698	0.143096
22	0.107933	1.4278	0.077563
23	0.024105	0.3189	0.3751
24	0.008373	0.1108	0.455965
25	-0.021607	-0.2858	0.387671
26	0.072193	0.955	0.170441
27	0.168717	2.2319	0.013445
28	-0.031576	-0.4177	0.338337
29	-0.0728	-0.9631	0.168424
30	0.004521	0.0598	0.476187
31	0.079928	1.0573	0.145906
32	-0.112344	-1.4862	0.069517
33	-0.061033	-0.8074	0.210269
34	-0.148455	-1.9639	0.025564
35	0.008487	0.1123	0.455365
36	-0.01667	-0.2205	0.412863
37	-0.070832	-0.937	0.175019
38	-0.010307	-0.1364	0.44585
39	0.048769	0.6452	0.259836
40	0.07869	1.041	0.149663
41	0.010797	0.1428	0.443295
42	-0.002695	-0.0357	0.485801
43	0.137575	1.8199	0.035238
44	0.018381	0.2432	0.404086
45	0.075515	0.999	0.159593
46	-0.047912	-0.6338	0.263513
47	-0.025098	-0.332	0.370138
48	-0.044326	-0.5864	0.279189
49	0.087458	1.157	0.124432
50	0.038618	0.5109	0.305045
51	-0.064299	-0.8506	0.198078
52	0.00885	0.1171	0.453469
53	0.037277	0.4931	0.311269
54	-0.064656	-0.8553	0.196774
55	-0.077611	-1.0267	0.152989
56	-0.071628	-0.9476	0.172331
57	0.033539	0.4437	0.32891
58	-0.04789	-0.6335	0.263607
59	-0.093867	-1.2417	0.107996
60	0.008085	0.107	0.457473

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.10612	1.4038	0.08107
2	-0.163646	-2.1648	0.015878
3	-0.084653	-1.1199	0.132154
4	0.068433	0.9053	0.183281
5	-0.094769	-1.2537	0.105817
6	0.077059	1.0194	0.15471
7	-0.099592	-1.3175	0.094701
8	-0.099919	-1.3218	0.093979
9	-0.051467	-0.6808	0.248436
10	0.096145	1.2719	0.102553
11	-0.105508	-1.3957	0.082281
12	-0.051629	-0.683	0.247757
13	-0.138699	-1.8348	0.034115
14	-0.010958	-0.145	0.442453
15	-0.201954	-2.6716	0.004131
16	-0.016398	-0.2169	0.414261
17	0.08911	1.1788	0.120036
18	0.003557	0.0471	0.48126
19	-0.145016	-1.9184	0.028346
20	-0.162415	-2.1485	0.016522
21	0.061666	0.8158	0.207871
22	-0.004301	-0.0569	0.477347
23	0.002516	0.0333	0.486744
24	-0.029763	-0.3937	0.347132
25	0.024576	0.3251	0.372743
26	0.044948	0.5946	0.276437
27	0.087593	1.1587	0.124069
28	-0.151154	-1.9996	0.023546
29	0.073484	0.9721	0.166172
30	0.05593	0.7399	0.23018
31	0.029299	0.3876	0.349393
32	-0.170319	-2.2531	0.012747
33	-0.023145	-0.3062	0.379914
34	-0.175671	-2.3239	0.01064
35	0.003599	0.0476	0.481042
36	-0.054852	-0.7256	0.234518
37	-0.121788	-1.6111	0.054479
38	0.082214	1.0876	0.139135
39	-0.062419	-0.8257	0.205042
40	0.075263	0.9956	0.160401
41	-0.085194	-1.127	0.13064
42	0.121234	1.6038	0.055283
43	0.119969	1.587	0.057154
44	-0.02229	-0.2949	0.384221
45	0.065449	0.8658	0.193891
46	0.013006	0.1721	0.431797
47	-0.065382	-0.8649	0.194132
48	-0.100495	-1.3294	0.092719
49	0.037172	0.4917	0.311759
50	0.073468	0.9719	0.166225
51	-0.030348	-0.4015	0.344281
52	-0.006361	-0.0841	0.466518
53	-0.037401	-0.4948	0.310694
54	-0.07947	-1.0513	0.147287
55	0.032302	0.4273	0.33484
56	-0.120575	-1.5951	0.056252
57	0.05424	0.7175	0.237003
58	0.025483	0.3371	0.368218
59	-0.089049	-1.178	0.120196
60	0.00468	0.0619	0.47535

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/1z13b1292742810.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/1z13b1292742810.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/2aakw1292742810.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/2aakw1292742810.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/3aakw1292742810.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742831cteqje2dknxgasn/3aakw1292742810.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; 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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