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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: Wed, 22 Dec 2010 14:21:53 +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/22/t1293027600hyrsxuhtr9vl1oj.htm/, Retrieved Wed, 22 Dec 2010 15:20:02 +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/22/t1293027600hyrsxuhtr9vl1oj.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 «

13.193 15.234 14.718 16.961 13.945 15.876 16.226 18.316 16.748 17.904 17.209 18.950 17.225 18.710 17.236 18.687 17.580 19.568 17.381 19.580 17.260 18.661 15.658 18.674 15.908 17.475 17.725 19.562 16.368 19.555 17.743 19.867 15.703 19.324 18.162 19.074 15.323 19.704 18.375 18.352 13.927 17.795 16.761 18.902 16.239 19.158 18.279 15.698 16.239 18.431 18.414 19.801 14.995 18.706 18.232 19.409 16.263 19.017 20.298 19.891 15.203 17.845 17.502 18.532 15.737 17.770 17.224 17.601 14.940 18.507 17.635 19.392 15.699 17.661 18.243 19.643 15.770 17.344 17.229 17.322 16.152 17.919 16.918 18.114 16.308 17.759 16.021 17.952 15.954 17.762 16.610 17.751 15.458 18.106 15.990 15.349 13.185 15.409 16.007 16.633 14.800 15.974 15.693

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.021071	0.2138	0.415546
2	0.378025	3.8365	0.000108
3	-0.118303	-1.2006	0.116322
4	0.640457	6.4999	0
5	-0.128761	-1.3068	0.097099
6	0.244664	2.4831	0.00732
7	-0.217718	-2.2096	0.014674
8	0.479093	4.8623	2e-06
9	-0.280364	-2.8454	0.002676
10	0.160055	1.6244	0.053675
11	-0.298926	-3.0338	0.001529
12	0.416419	4.2262	2.6e-05
13	-0.256093	-2.5991	0.00536
14	0.154123	1.5642	0.060421
15	-0.277048	-2.8117	0.00295
16	0.404598	4.1062	4e-05
17	-0.241014	-2.446	0.008069
18	0.17529	1.779	0.039094
19	-0.244057	-2.4769	0.00744
20	0.431476	4.379	1.4e-05
21	-0.220589	-2.2387	0.013662
22	0.154136	1.5643	0.060406
23	-0.257061	-2.6089	0.005217
24	0.361081	3.6646	0.000197
25	-0.228862	-2.3227	0.011081
26	0.094945	0.9636	0.168755
27	-0.276588	-2.8071	0.00299
28	0.29327	2.9764	0.001818
29	-0.269386	-2.734	0.003684
30	0.103995	1.0554	0.146848
31	-0.259926	-2.638	0.004817
32	0.302536	3.0704	0.001367
33	-0.279099	-2.8325	0.002778
34	0.089703	0.9104	0.182372
35	-0.209837	-2.1296	0.017793
36	0.264789	2.6873	0.0042
37	-0.245478	-2.4913	0.007162
38	0.096395	0.9783	0.165108
39	-0.186197	-1.8897	0.030805
40	0.256538	2.6036	0.005294
41	-0.225216	-2.2857	0.01216
42	0.084244	0.855	0.197271
43	-0.192649	-1.9552	0.026636
44	0.171724	1.7428	0.042176
45	-0.216595	-2.1982	0.015087
46	0.059433	0.6032	0.273858
47	-0.162578	-1.65	0.050996
48	0.184461	1.8721	0.032017

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.021071	0.2138	0.415546
2	0.377749	3.8337	0.000109
3	-0.153127	-1.5541	0.061618
4	0.607673	6.1672	0
5	-0.293268	-2.9763	0.001818
6	-0.061355	-0.6227	0.267435
7	0.012626	0.1281	0.449144
8	0.129116	1.3104	0.09649
9	-0.28932	-2.9363	0.002049
10	0.066736	0.6773	0.249869
11	-0.025034	-0.2541	0.399976
12	0.113719	1.1541	0.12556
13	0.022146	0.2248	0.411306
14	-0.052414	-0.5319	0.297953
15	0.036657	0.372	0.355318
16	0.084868	0.8613	0.195532
17	-0.073655	-0.7475	0.228228
18	-0.004305	-0.0437	0.482618
19	0.070251	0.713	0.238739
20	0.061257	0.6217	0.26776
21	-0.064947	-0.6591	0.255638
22	-0.05059	-0.5134	0.304373
23	0.014259	0.1447	0.442611
24	-0.047906	-0.4862	0.313931
25	0.019219	0.1951	0.422867
26	-0.113685	-1.1538	0.125631
27	0.051975	0.5275	0.299494
28	-0.040197	-0.408	0.342077
29	-0.037068	-0.3762	0.35377
30	0.087951	0.8926	0.187075
31	0.007119	0.0722	0.471273
32	0.000298	0.003	0.498798
33	-0.107848	-1.0945	0.138136
34	0.028568	0.2899	0.386226
35	0.080746	0.8195	0.2072
36	-0.140119	-1.4221	0.079015
37	0.033923	0.3443	0.365669
38	0.024441	0.248	0.402296
39	0.009016	0.0915	0.463637
40	-0.049821	-0.5056	0.307097
41	0.056208	0.5705	0.284807
42	-0.068113	-0.6913	0.245476
43	-0.027313	-0.2772	0.391092
44	-0.114983	-1.167	0.122962
45	0.074043	0.7515	0.227047
46	0.018698	0.1898	0.424933
47	0.016694	0.1694	0.432896
48	0.024009	0.2437	0.403989

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027600hyrsxuhtr9vl1oj/1q5c31293027710.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027600hyrsxuhtr9vl1oj/1q5c31293027710.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027600hyrsxuhtr9vl1oj/2q5c31293027710.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027600hyrsxuhtr9vl1oj/2q5c31293027710.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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