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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sat, 19 Dec 2009 09:36:28 -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/19/t1261240606eu7l462ddyucqjs.htm/, Retrieved Sat, 19 Dec 2009 17:36:49 +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/19/t1261240606eu7l462ddyucqjs.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 «

6.8 7.5 7.6 7.8 8 8.1 8.2 8.3 8.2 8 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3

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	0.373004	3.4591	0.000423
2	-0.231675	-2.1485	0.017244
3	-0.546771	-5.0705	1e-06
4	-0.406873	-3.7732	0.000148
5	0.084523	0.7838	0.217645
6	0.459523	4.2614	2.6e-05
7	0.294713	2.7331	0.003808
8	-0.089875	-0.8335	0.203444
9	-0.322579	-2.9915	0.001811
10	-0.263902	-2.4473	0.008213
11	0.060986	0.5656	0.286583
12	0.504423	4.6778	5e-06
13	0.166895	1.5477	0.062681
14	-0.069321	-0.6429	0.261013
15	-0.194577	-1.8044	0.037332
16	-0.1735	-1.609	0.055644
17	0.009236	0.0856	0.465973
18	0.151988	1.4095	0.08115
19	0.05323	0.4936	0.31141
20	-0.072653	-0.6738	0.251137
21	-0.125291	-1.1619	0.124246
22	-0.088816	-0.8236	0.20621
23	0.028452	0.2638	0.396264
24	0.267394	2.4797	0.00755
25	-0.00314	-0.0291	0.488418
26	-0.087315	-0.8097	0.210165
27	-0.115096	-1.0674	0.144399
28	-0.075182	-0.6972	0.243777
29	0.053616	0.4972	0.310155
30	0.125506	1.1639	0.123843
31	0.037693	0.3495	0.363765
32	-0.09327	-0.865	0.194735
33	-0.13211	-1.2251	0.111933
34	-0.07613	-0.706	0.241049
35	0.024214	0.2246	0.411431
36	0.226141	2.0971	0.019458
37	-0.00488	-0.0453	0.482006
38	-0.107818	-0.9999	0.160091
39	-0.118205	-1.0962	0.138029
40	-0.019073	-0.1769	0.43001
41	0.136108	1.2622	0.105143
42	0.191816	1.7788	0.0394
43	-0.00657	-0.0609	0.47578
44	-0.222935	-2.0674	0.02085
45	-0.249033	-2.3094	0.011658
46	-0.088458	-0.8203	0.207149
47	0.168892	1.5662	0.060483
48	0.380551	3.5291	0.000336
49	0.073546	0.682	0.248523
50	-0.212312	-1.9689	0.026092
51	-0.298954	-2.7724	0.003411
52	-0.14647	-1.3583	0.08896
53	0.122567	1.1366	0.129424
54	0.286894	2.6605	0.004653
55	0.12177	1.1292	0.130967
56	-0.125161	-1.1607	0.124489
57	-0.235762	-2.1864	0.015753
58	-0.177084	-1.6422	0.052099
59	0.039028	0.3619	0.359145
60	0.261162	2.4219	0.00877

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.373004	3.4591	0.000423
2	-0.430736	-3.9945	6.8e-05
3	-0.374338	-3.4715	0.000406
4	-0.194259	-1.8015	0.037565
5	0.100228	0.9295	0.177622
6	0.162417	1.5062	0.067841
7	-0.12608	-1.1692	0.122774
8	-0.094082	-0.8725	0.192688
9	0.011362	0.1054	0.458166
10	-0.001384	-0.0128	0.494896
11	0.047536	0.4408	0.330222
12	0.396438	3.6764	0.000205
13	-0.395772	-3.6702	0.00021
14	0.308977	2.8653	0.002618
15	0.196369	1.821	0.036039
16	-0.011046	-0.1024	0.459324
17	-0.099949	-0.9269	0.178288
18	-0.060218	-0.5584	0.288999
19	0.02489	0.2308	0.409003
20	-0.046228	-0.4287	0.334605
21	-0.131983	-1.224	0.112156
22	-0.059661	-0.5533	0.290757
23	-0.058163	-0.5394	0.29551
24	0.074281	0.6889	0.246385
25	-0.103765	-0.9623	0.169305
26	-0.056138	-0.5206	0.301991
27	-0.074004	-0.6863	0.247189
28	0.052595	0.4877	0.313484
29	0.052063	0.4828	0.315227
30	-0.026063	-0.2417	0.404796
31	0.026193	0.2429	0.404329
32	-0.09089	-0.8429	0.200816
33	0.08322	0.7718	0.221188
34	0.05167	0.4792	0.316518
35	-0.060703	-0.5629	0.28747
36	-0.016262	-0.1508	0.440241
37	-0.061666	-0.5719	0.284451
38	-0.065252	-0.6051	0.273345
39	0.061796	0.5731	0.284044
40	0.062088	0.5758	0.283134
41	0.022025	0.2043	0.419318
42	0.056553	0.5244	0.300658
43	-0.159463	-1.4788	0.071424
44	-0.026662	-0.2473	0.402649
45	-0.062737	-0.5818	0.281112
46	-0.085592	-0.7937	0.214765
47	0.14744	1.3673	0.087546
48	-0.042882	-0.3977	0.34593
49	-0.035282	-0.3272	0.372158
50	-0.085754	-0.7953	0.214328
51	0.008589	0.0797	0.46835
52	-0.022767	-0.2111	0.416641
53	-0.134237	-1.2449	0.108282
54	-0.053872	-0.4996	0.309321
55	-0.003822	-0.0354	0.485905
56	0.061344	0.5689	0.285459
57	-0.039745	-0.3686	0.356672
58	-0.060437	-0.5605	0.288308
59	-0.019437	-0.1803	0.428689
60	-0.044108	-0.409	0.341764

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240606eu7l462ddyucqjs/1x3je1261240585.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240606eu7l462ddyucqjs/1x3je1261240585.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240606eu7l462ddyucqjs/24hi71261240585.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240606eu7l462ddyucqjs/24hi71261240585.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 2 ; par9 = 1 ;

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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