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acf

*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, 28 Dec 2009 05:46:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/28/t12620044232pxjewby4kh779t.htm/, Retrieved Mon, 28 Dec 2009 13:47:05 +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/2009/Dec/28/t12620044232pxjewby4kh779t.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

13.4 13.5 14.8 14.3 14.3 14 13.2 12.2 14.3 15.7 14.2 14.6 14.5 14.3 15.3 14.4 13.7 14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.559701	-4.2991	3.3e-05
2	-0.033556	-0.2577	0.398749
3	0.328855	2.526	0.007121
4	-0.218334	-1.6771	0.049411
5	-0.07042	-0.5409	0.295305
6	0.264747	2.0336	0.023251
7	-0.31012	-2.3821	0.010229
8	0.125703	0.9655	0.169106
9	0.14598	1.1213	0.133354
10	-0.238536	-1.8322	0.035983
11	0.137181	1.0537	0.148156
12	-0.05153	-0.3958	0.346835
13	-0.126666	-0.9729	0.167278
14	0.178609	1.3719	0.087641
15	-0.087418	-0.6715	0.252271
16	-0.138365	-1.0628	0.146102
17	0.234361	1.8002	0.038474
18	-0.080632	-0.6193	0.269036
19	-0.018113	-0.1391	0.444913
20	-0.004577	-0.0352	0.486035
21	0.127716	0.981	0.165297
22	-0.223905	-1.7198	0.045351
23	0.262617	2.0172	0.024116
24	-0.147441	-1.1325	0.131
25	-0.101795	-0.7819	0.2187
26	0.230627	1.7715	0.040823
27	-0.149369	-1.1473	0.127939
28	-0.035376	-0.2717	0.39339
29	0.14962	1.1493	0.127545
30	-0.162939	-1.2516	0.107835
31	0.031788	0.2442	0.403975
32	0.143096	1.0991	0.138085
33	-0.258486	-1.9855	0.025873
34	0.097871	0.7518	0.227592
35	0.129648	0.9958	0.161696
36	-0.216099	-1.6599	0.051122
37	0.180611	1.3873	0.085284
38	-0.013308	-0.1022	0.459464
39	-0.128416	-0.9864	0.163987
40	0.207905	1.5969	0.05781
41	-0.1056	-0.8111	0.210276
42	-0.064813	-0.4978	0.310225
43	0.126164	0.9691	0.168229
44	-0.036963	-0.2839	0.388732
45	-0.030423	-0.2337	0.408018
46	0.069168	0.5313	0.298606
47	-0.047015	-0.3611	0.359647
48	0.00105	0.0081	0.496796
49	0.033514	0.2574	0.398874
50	-0.060875	-0.4676	0.320901
51	0.014429	0.1108	0.456062
52	0.020878	0.1604	0.436569
53	-0.023841	-0.1831	0.427663
54	0.007889	0.0606	0.475943
55	-0.003017	-0.0232	0.490794
56	-0.004625	-0.0355	0.48589
57	0.002901	0.0223	0.49115
58	-0.000654	-0.005	0.498005
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.559701	-4.2991	3.3e-05
2	-0.505029	-3.8792	0.000133
3	0.035036	0.2691	0.394389
4	0.110611	0.8496	0.199486
5	-0.091332	-0.7015	0.242863
6	0.076982	0.5913	0.278286
7	-0.173999	-1.3365	0.093257
8	-0.110378	-0.8478	0.199979
9	0.099438	0.7638	0.224015
10	0.055258	0.4244	0.336393
11	0.05569	0.4278	0.33519
12	-0.216208	-1.6607	0.051037
13	-0.329051	-2.5275	0.007094
14	-0.14438	-1.109	0.135964
15	0.028143	0.2162	0.414801
16	-0.072479	-0.5567	0.289911
17	-0.095619	-0.7345	0.232787
18	-0.020329	-0.1562	0.438224
19	0.150821	1.1585	0.125668
20	-0.079172	-0.6081	0.272718
21	0.194678	1.4954	0.070076
22	-0.091597	-0.7036	0.242234
23	0.099838	0.7669	0.223109
24	0.017044	0.1309	0.448142
25	-0.24715	-1.8984	0.031269
26	-0.081281	-0.6243	0.267408
27	-0.213059	-1.6365	0.053525
28	-0.082385	-0.6328	0.26465
29	-0.002949	-0.0227	0.491003
30	-0.04943	-0.3797	0.352774
31	-0.015808	-0.1214	0.451884
32	-0.048219	-0.3704	0.356214
33	-0.030737	-0.2361	0.407089
34	-0.1099	-0.8442	0.200996
35	-0.049911	-0.3834	0.35141
36	-0.055734	-0.4281	0.335068
37	-0.002977	-0.0229	0.490918
38	-0.044727	-0.3436	0.366202
39	-0.068785	-0.5283	0.299621
40	-0.115655	-0.8884	0.188976
41	-0.018181	-0.1397	0.444706
42	-0.038139	-0.293	0.385293
43	0.008076	0.062	0.475372
44	0.000105	8e-04	0.499679
45	0.009843	0.0756	0.469994
46	-0.042864	-0.3292	0.371568
47	-0.050105	-0.3849	0.350862
48	0.092079	0.7073	0.241091
49	-0.057151	-0.439	0.331139
50	-0.050747	-0.3898	0.349046
51	-0.006758	-0.0519	0.47939
52	0.01034	0.0794	0.468483
53	0.075502	0.5799	0.28208
54	-0.018105	-0.1391	0.444934
55	-0.049351	-0.3791	0.352997
56	-0.025248	-0.1939	0.423447
57	0.055097	0.4232	0.336842
58	-0.097262	-0.7471	0.22899
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620044232pxjewby4kh779t/10kir1262004383.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620044232pxjewby4kh779t/10kir1262004383.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620044232pxjewby4kh779t/2rqwm1262004383.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620044232pxjewby4kh779t/2rqwm1262004383.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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