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paper ACF D

*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: Mon, 27 Dec 2010 12:12:17 +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/27/t129345185754kjd9cfcqkmgo4.htm/, Retrieved Mon, 27 Dec 2010 13:11:00 +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/27/t129345185754kjd9cfcqkmgo4.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 «

5.2 7.9 8.7 8.9 15.3 15.4 18.1 19.7 13 12.6 6.2 3.5 3.4 0 9.5 8.9 10.4 13.2 18.9 19 16.3 10.6 5.8 3.6 2.6 5 7.3 9.2 15.7 16.8 18.4 18.1 14.6 7.8 7.6 3.8 5.6 2.2 6.8 11.8 14.9 16.7 16.7 15.9 13.6 9.2 2.8 2.5 4.8 2.8 7.8 9 12.9 16.4 21.8 17.8 13.5 10 10.4 5.5 4 6.8 5.7 9.1 13.6 15 20.9 20.4 14 13.7 7.1 0.8 2.1 1.3 3.9 10.7 11.1 16.4 17.1 17.3 12.9 10.9 5.3 0.7 -0.2 6.5 8.6 8.5 13.3 16.2 17.5 21.2 14.8 10.3 7.3 5.1 4.4 6.2 7.7 9.3 15.6 16.3 16.6 17.4 15.3 9.7 3.7 4.6 5.4 3.1 7.9 10.1 15 15.6 19.7 18.1 17.7 10.7 6.2 4.2 4 5.9 7.1 10.5 15.1 16.8 15.3 18.4 16.1 11.3 7.9 5.6 3.4 4.8 6.5 8.5 15.1 15.7 18.7 19.2 12.9 14.4 6.2 3.3 4.6 7.2 7.8 9.9 13.6 17.1 17.8 18.6 14.7 10.5 8.6 4.4 2.3 2.8 8.8 10.7 13.9 19.3 19.5 20.4 15.3 7.9 8.3 4.5 3.2 5 6.6 11.1 12.8 16.3 17.4 18.9 15.8 11.7 6.4 2.9 4.7 2.4 7.2 10.7 13.4 18.5 18.3 16.8 16.6 14. 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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.153921	2.3242	0.010498
2	0.100275	1.5141	0.065689
3	0.159121	2.4027	0.008538
4	0.020509	0.3097	0.378546
5	0.079085	1.1942	0.11683
6	0.008617	0.1301	0.448298
7	-0.097257	-1.4686	0.071666
8	-0.014853	-0.2243	0.411375
9	0.057159	0.8631	0.194501
10	-0.12401	-1.8725	0.031208
11	-0.017336	-0.2618	0.396867
12	-0.447169	-6.7521	0
13	-0.099362	-1.5003	0.067455
14	-0.011677	-0.1763	0.430102
15	-0.219248	-3.3106	0.000541
16	0.017267	0.2607	0.397269
17	-0.076966	-1.1622	0.123192
18	-0.086574	-1.3072	0.096223
19	-0.010372	-0.1566	0.437842
20	0.002022	0.0305	0.487836
21	-0.155963	-2.355	0.009686
22	0.058918	0.8896	0.187298
23	-0.14106	-2.13	0.017123
24	-0.071066	-1.0731	0.142186
25	0.053181	0.803	0.211401
26	-0.118845	-1.7945	0.037027
27	0.119369	1.8024	0.036399
28	0.003699	0.0559	0.477754
29	0.044279	0.6686	0.252214
30	0.172233	2.6007	0.004956
31	0.154602	2.3344	0.010221
32	-0.020323	-0.3069	0.379611
33	0.136789	2.0655	0.020005
34	0.008903	0.1344	0.446587
35	0.021628	0.3266	0.372145
36	0.095185	1.4373	0.076008
37	-0.002027	-0.0306	0.487802
38	0.093639	1.4139	0.079374
39	0.044874	0.6776	0.249361
40	-0.004066	-0.0614	0.475551
41	0.018624	0.2812	0.3894
42	-0.109907	-1.6596	0.049189
43	-0.127679	-1.9279	0.027554
44	-0.000281	-0.0042	0.498312
45	-0.132862	-2.0062	0.02301
46	0.01016	0.1534	0.439104
47	0.060142	0.9081	0.182384
48	-0.157065	-2.3716	0.009271
49	-0.057709	-0.8714	0.192228
50	0.007722	0.1166	0.453643
51	-0.119494	-1.8043	0.03625
52	-0.033266	-0.5023	0.307969
53	0.018176	0.2744	0.391995
54	-0.017664	-0.2667	0.394962
55	0.073314	1.107	0.134728
56	0.012788	0.1931	0.423527
57	0.065586	0.9903	0.161532
58	0.013778	0.208	0.41769
59	0.030129	0.4549	0.324792
60	0.121791	1.839	0.033608

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.153921	2.3242	0.010498
2	0.078442	1.1845	0.118734
3	0.136889	2.067	0.019933
4	-0.028717	-0.4336	0.332486
5	0.059884	0.9042	0.183415
6	-0.032282	-0.4874	0.313205
7	-0.106962	-1.6151	0.053837
8	-0.005946	-0.0898	0.464271
9	0.08335	1.2586	0.104738
10	-0.124277	-1.8765	0.030929
11	0.01119	0.169	0.432984
12	-0.473696	-7.1526	0
13	0.09455	1.4277	0.077377
14	0.009774	0.1476	0.441399
15	-0.085513	-1.2912	0.098967
16	0.102407	1.5463	0.061709
17	-0.082437	-1.2448	0.107248
18	-0.059367	-0.8964	0.185485
19	-0.071359	-1.0775	0.141199
20	0.017601	0.2658	0.395329
21	-0.058345	-0.881	0.189627
22	-0.007657	-0.1156	0.454029
23	-0.179108	-2.7045	0.003679
24	-0.243765	-3.6808	0.000145
25	0.035278	0.5327	0.297385
26	-0.068743	-1.038	0.150185
27	0.06394	0.9655	0.167666
28	0.0282	0.4258	0.335325
29	-0.013336	-0.2014	0.420296
30	0.092346	1.3944	0.082279
31	0.071302	1.0766	0.14139
32	-0.064901	-0.98	0.164067
33	0.016695	0.2521	0.4006
34	-0.062947	-0.9505	0.171436
35	-0.121303	-1.8316	0.034155
36	-0.166992	-2.5215	0.006184
37	0.146899	2.2181	0.013766
38	-0.068748	-1.0381	0.150169
39	0.130526	1.9709	0.024972
40	-0.031834	-0.4807	0.315601
41	0.00756	0.1142	0.454606
42	-0.045144	-0.6817	0.248072
43	0.000578	0.0087	0.49652
44	-0.043642	-0.659	0.255289
45	-0.081553	-1.2314	0.109715
46	0.093387	1.4101	0.079936
47	-0.126619	-1.9119	0.028571
48	-0.186333	-2.8136	0.002664
49	-0.0134	-0.2023	0.419915
50	0.030234	0.4565	0.324225
51	0.027659	0.4176	0.3383
52	0.005667	0.0856	0.465942
53	0.114518	1.7292	0.042565
54	0.002631	0.0397	0.484171
55	-0.012849	-0.194	0.423166
56	-0.005287	-0.0798	0.46822
57	-0.007141	-0.1078	0.457117
58	-0.002514	-0.038	0.484874
59	0.004078	0.0616	0.475475
60	-0.107334	-1.6207	0.053231

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/1749d1293451934.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/1749d1293451934.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/2ze8g1293451934.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/2ze8g1293451934.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/3ze8g1293451934.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129345185754kjd9cfcqkmgo4/3ze8g1293451934.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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