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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 15:45:40 +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/t1292773507cfxewzfq0e3xvh9.htm/, Retrieved Sun, 19 Dec 2010 16:45:10 +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/t1292773507cfxewzfq0e3xvh9.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 «

5124 4742 5434 5684 6332 6334 5636 5940 6195 6022 4535 4320 4872 4662 4663 5491 6018 6393 5610 5777 6094 6478 5216 5201 4784 4205 4681 4896 5752 6452 5995 5601 6119 6569 5798 5492 5018 4773 5502 5908 5902 6125 5419 5559 5962 6023 5346 5379 4859 5156 5010 5508 6426 6043 5499 5191 5790 5949 5219 4729

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.238091	-1.6323	0.054653
2	-0.12806	-0.8779	0.192223
3	-0.153467	-1.0521	0.149063
4	0.042601	0.2921	0.385763
5	0.175843	1.2055	0.117018
6	-0.023164	-0.1588	0.437252
7	-0.267261	-1.8322	0.036627
8	0.007105	0.0487	0.480678
9	0.143232	0.9819	0.165577
10	-0.028364	-0.1945	0.423329
11	0.030358	0.2081	0.418014
12	-0.290916	-1.9944	0.025962
13	0.20604	1.4125	0.082189
14	-0.036133	-0.2477	0.402717
15	0.143002	0.9804	0.165962
16	-0.135296	-0.9275	0.179192
17	0.184949	1.2679	0.105531
18	0.01531	0.105	0.458427
19	-0.007109	-0.0487	0.480668
20	-0.05633	-0.3862	0.350554
21	-0.030192	-0.207	0.418458
22	0.028543	0.1957	0.422852
23	0.008501	0.0583	0.476888
24	-0.035688	-0.2447	0.40389
25	-0.219692	-1.5061	0.069362
26	0.276646	1.8966	0.032019
27	-0.121153	-0.8306	0.205204
28	0.043471	0.298	0.383501
29	-0.071168	-0.4879	0.313942
30	-0.007748	-0.0531	0.478932
31	0.114059	0.7819	0.219084
32	0.007244	0.0497	0.480301
33	-0.125618	-0.8612	0.196751
34	0.070042	0.4802	0.316661
35	0.00821	0.0563	0.477676
36	0.047586	0.3262	0.372847
37	0.036923	0.2531	0.400636
38	-0.168688	-1.1565	0.126668
39	0.087236	0.5981	0.276335
40	-0.04503	-0.3087	0.379454
41	0.052588	0.3605	0.360034
42	-0.039657	-0.2719	0.393455
43	-0.000454	-0.0031	0.498764
44	-0.028758	-0.1972	0.422277
45	0.039137	0.2683	0.394816
46	-0.010591	-0.0726	0.471214
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.238091	-1.6323	0.054653
2	-0.195849	-1.3427	0.092913
3	-0.260776	-1.7878	0.040129
4	-0.124916	-0.8564	0.198066
5	0.091799	0.6293	0.266087
6	0.02347	0.1609	0.436431
7	-0.255279	-1.7501	0.043313
8	-0.130166	-0.8924	0.188369
9	0.021592	0.148	0.441479
10	-0.13554	-0.9292	0.178762
11	-0.019785	-0.1356	0.446343
12	-0.276233	-1.8938	0.032211
13	0.010781	0.0739	0.470696
14	-0.207886	-1.4252	0.080354
15	0.015385	0.1055	0.458223
16	-0.10997	-0.7539	0.227329
17	0.238334	1.6339	0.054477
18	0.123922	0.8496	0.199937
19	0.036136	0.2477	0.40271
20	0.062726	0.43	0.334571
21	0.079857	0.5475	0.293322
22	0.015802	0.1083	0.457096
23	0.051071	0.3501	0.363904
24	0.01601	0.1098	0.456534
25	-0.149092	-1.0221	0.155977
26	0.136237	0.934	0.17754
27	-0.012717	-0.0872	0.465448
28	-0.041954	-0.2876	0.38745
29	0.110888	0.7602	0.225464
30	-0.015857	-0.1087	0.456948
31	0.072875	0.4996	0.309843
32	-0.121239	-0.8312	0.205039
33	-0.084015	-0.576	0.28369
34	-0.079113	-0.5424	0.295063
35	-0.135438	-0.9285	0.178942
36	-0.040209	-0.2757	0.392008
37	-0.08685	-0.5954	0.277213
38	0.001617	0.0111	0.495602
39	-0.071137	-0.4877	0.314017
40	-0.055054	-0.3774	0.353777
41	-0.036739	-0.2519	0.401121
42	0.060196	0.4127	0.340857
43	-0.012536	-0.0859	0.465938
44	-0.082372	-0.5647	0.287478
45	-0.023093	-0.1583	0.437443
46	-0.060461	-0.4145	0.340198
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/1o3ab1292773536.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/1o3ab1292773536.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/2hc9w1292773536.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/2hc9w1292773536.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/3hc9w1292773536.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292773507cfxewzfq0e3xvh9/3hc9w1292773536.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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