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ACF 1

*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: Wed, 15 Dec 2010 17:11:50 +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/15/t1292432998tziv8xxaufw1v80.htm/, Retrieved Wed, 15 Dec 2010 18:09:58 +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/15/t1292432998tziv8xxaufw1v80.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 «

12231 13604 15107 10853 13698 11536 8879 11005 13656 12631 10931 8064 12332 12452 14029 10003 12388 10492 9114 9304 9660 10569 8356 5998 10408 11420 11538 10860 10412 9521 7602 8197 10449 11561 8603 8080 10792 11943 11179 9939 10065 11021 9226 9554 11468 9937 8928 8395 11996 12385 15277 12657 11482 16797 11047 11794 13077 11725 10921 9334 11431 13085 16394 15701 14936 18282 12824 14784 16061 14814 14375 13644 16397 19254 21943 16731 22065 20937 18242 19017 20372 20561 18267 16170

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.778554	7.1356	0
2	0.68277	6.2577	0
3	0.651739	5.9733	0
4	0.611601	5.6054	0
5	0.567552	5.2017	1e-06
6	0.489667	4.4879	1.1e-05
7	0.467854	4.288	2.4e-05
8	0.439554	4.0286	6.1e-05
9	0.397376	3.642	0.000233
10	0.323766	2.9674	0.001956
11	0.379539	3.4785	0.000401
12	0.464997	4.2618	2.6e-05
13	0.327301	2.9998	0.001778
14	0.259687	2.3801	0.009787
15	0.228912	2.098	0.019454
16	0.207403	1.9009	0.030373
17	0.183848	1.685	0.047851
18	0.107273	0.9832	0.164172
19	0.086504	0.7928	0.215056
20	0.076643	0.7024	0.242171
21	0.013226	0.1212	0.451903
22	-0.039601	-0.3629	0.358778
23	0.047698	0.4372	0.331558
24	0.105624	0.9681	0.167897
25	0.039558	0.3626	0.358924
26	-0.013671	-0.1253	0.450295
27	-0.042013	-0.3851	0.350583
28	-0.032773	-0.3004	0.382319
29	-0.060213	-0.5519	0.291255
30	-0.132292	-1.2125	0.114364
31	-0.155356	-1.4239	0.079095
32	-0.15752	-1.4437	0.076272
33	-0.223178	-2.0455	0.021969
34	-0.24453	-2.2412	0.013827
35	-0.213878	-1.9602	0.026642
36	-0.155819	-1.4281	0.078485
37	-0.178894	-1.6396	0.052415
38	-0.237495	-2.1767	0.016156
39	-0.228934	-2.0982	0.019445
40	-0.216005	-1.9797	0.025505
41	-0.222235	-2.0368	0.022409
42	-0.28039	-2.5698	0.00597
43	-0.272825	-2.5005	0.007173
44	-0.272198	-2.4947	0.007282
45	-0.299833	-2.748	0.003668
46	-0.294218	-2.6966	0.004232
47	-0.283205	-2.5956	0.005571
48	-0.215664	-1.9766	0.025684
49	-0.215351	-1.9737	0.02585
50	-0.277561	-2.5439	0.006397
51	-0.257857	-2.3633	0.010211
52	-0.242305	-2.2208	0.01453
53	-0.239991	-2.1996	0.015293
54	-0.242616	-2.2236	0.014429
55	-0.224489	-2.0575	0.021371
56	-0.230595	-2.1134	0.018765
57	-0.247496	-2.2683	0.012937
58	-0.244085	-2.2371	0.013965
59	-0.224091	-2.0538	0.021551
60	-0.148599	-1.3619	0.08843

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.778554	7.1356	0
2	0.194549	1.7831	0.039094
3	0.190307	1.7442	0.042392
4	0.075348	0.6906	0.245869
5	0.032694	0.2996	0.382593
6	-0.090762	-0.8318	0.203928
7	0.06222	0.5703	0.285014
8	0.006729	0.0617	0.475485
9	-0.010659	-0.0977	0.461206
10	-0.113273	-1.0382	0.151087
11	0.260677	2.3891	0.009564
12	0.271348	2.4869	0.007432
13	-0.382283	-3.5037	0.000369
14	-0.131106	-1.2016	0.116447
15	-0.022587	-0.207	0.41825
16	-0.026276	-0.2408	0.405139
17	0.021962	0.2013	0.42048
18	-0.060904	-0.5582	0.289099
19	-0.013199	-0.121	0.452
20	0.003804	0.0349	0.486134
21	-0.075084	-0.6882	0.246625
22	0.04635	0.4248	0.336033
23	0.17898	1.6404	0.052333
24	0.012585	0.1153	0.454223
25	-0.053943	-0.4944	0.311159
26	-0.113954	-1.0444	0.149646
27	-0.071458	-0.6549	0.257154
28	-0.005238	-0.048	0.480911
29	-0.069619	-0.6381	0.262583
30	-0.054243	-0.4971	0.310191
31	-0.058382	-0.5351	0.297004
32	0.002346	0.0215	0.49145
33	0.023643	0.2167	0.414488
34	0.081189	0.7441	0.229444
35	-0.155836	-1.4283	0.078462
36	0.069737	0.6392	0.262231
37	0.006072	0.0556	0.477877
38	-0.093702	-0.8588	0.196448
39	0.06071	0.5564	0.289702
40	-0.088803	-0.8139	0.209005
41	-0.013924	-0.1276	0.449381
42	-0.054405	-0.4986	0.309673
43	0.027452	0.2516	0.400981
44	0.027832	0.2551	0.399642
45	0.062468	0.5725	0.284246
46	0.02763	0.2532	0.400355
47	-0.059311	-0.5436	0.294079
48	-0.051481	-0.4718	0.319135
49	0.011819	0.1083	0.456999
50	-0.113937	-1.0442	0.149683
51	-0.0555	-0.5087	0.306158
52	-0.022743	-0.2084	0.417693
53	-0.008672	-0.0795	0.46842
54	0.167251	1.5329	0.064531
55	0.068926	0.6317	0.264645
56	-0.092342	-0.8463	0.199886
57	-0.096161	-0.8813	0.190326
58	0.030149	0.2763	0.391489
59	0.061825	0.5666	0.286238
60	-0.00487	-0.0446	0.482253

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/195ld1292433106.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/195ld1292433106.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/2jf2y1292433106.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/2jf2y1292433106.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/3jf2y1292433106.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292432998tziv8xxaufw1v80/3jf2y1292433106.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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