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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: Thu, 16 Dec 2010 14:11:45 +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/16/t1292508754nuogl9d5wwkky8l.htm/, Retrieved Thu, 16 Dec 2010 15:12:36 +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/16/t1292508754nuogl9d5wwkky8l.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 «

2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2539 2069 2063 2565 2442 2194 2798 2074 2628 2289 2154 2466 2137 1846 2072 1786 1754 2226 1947 1823 2521 2072 2368 2164 2095 1834 1856 2017

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.537085	-4.1602	5.1e-05
2	0.058893	0.4562	0.324952
3	0.113967	0.8828	0.190437
4	-0.08852	-0.6857	0.24778
5	-0.030892	-0.2393	0.40585
6	0.00111	0.0086	0.496586
7	-0.064673	-0.501	0.309117
8	0.027042	0.2095	0.417397
9	0.104089	0.8063	0.211635
10	-0.070937	-0.5495	0.292359
11	-0.056153	-0.435	0.332576
12	0.117926	0.9134	0.182331
13	-0.08062	-0.6245	0.26734
14	0.048354	0.3746	0.354658
15	-0.011161	-0.0865	0.465698
16	-0.058451	-0.4528	0.326179
17	0.116505	0.9024	0.185216
18	-0.028831	-0.2233	0.41202
19	-0.075465	-0.5845	0.280522
20	-0.03046	-0.2359	0.407141
21	0.076347	0.5914	0.278242
22	-0.040651	-0.3149	0.376973
23	-0.094707	-0.7336	0.233027
24	0.081099	0.6282	0.266131
25	0.10017	0.7759	0.220424
26	-0.138378	-1.0719	0.144035
27	0.152954	1.1848	0.120389
28	-0.071041	-0.5503	0.292085
29	0.003746	0.029	0.488475
30	0.015729	0.1218	0.451718
31	-0.079773	-0.6179	0.269482
32	0.094327	0.7307	0.233918
33	-0.060371	-0.4676	0.320872
34	0.041727	0.3232	0.373828
35	-0.053309	-0.4129	0.340565
36	0.024329	0.1885	0.425579
37	0.025065	0.1942	0.423357
38	-0.084581	-0.6552	0.257433
39	0.123799	0.9589	0.170718
40	-0.119752	-0.9276	0.178666
41	0.097245	0.7533	0.22712
42	-0.036204	-0.2804	0.390055
43	0.033801	0.2618	0.397178
44	-0.038608	-0.2991	0.382965
45	-0.005815	-0.045	0.48211
46	0.027899	0.2161	0.414819
47	-0.104577	-0.81	0.210556
48	0.06839	0.5297	0.299122
49	-0.004856	-0.0376	0.485061
50	-0.002755	-0.0213	0.491522
51	0.014624	0.1133	0.455095
52	0.032914	0.2549	0.399818
53	-0.007087	-0.0549	0.478203
54	-0.01499	-0.1161	0.453976
55	-0.011458	-0.0888	0.464788
56	-0.005175	-0.0401	0.48408
57	-0.005129	-0.0397	0.48422
58	0.005177	0.0401	0.484073
59	0.005238	0.0406	0.483887
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.537085	-4.1602	5.1e-05
2	-0.322634	-2.4991	0.007603
3	-0.027419	-0.2124	0.416262
4	-0.001776	-0.0138	0.494534
5	-0.085976	-0.666	0.253993
6	-0.138342	-1.0716	0.144097
7	-0.21178	-1.6404	0.053073
8	-0.172826	-1.3387	0.092858
9	0.063805	0.4942	0.311473
10	0.09281	0.7189	0.237495
11	-0.105033	-0.8136	0.209551
12	-0.078698	-0.6096	0.272217
13	-0.078657	-0.6093	0.272321
14	0.04844	0.3752	0.354413
15	0.080375	0.6226	0.26796
16	-0.037213	-0.2883	0.387074
17	0.028435	0.2203	0.413209
18	0.069957	0.5419	0.294952
19	0.007978	0.0618	0.475464
20	-0.149841	-1.1607	0.125188
21	-0.101869	-0.7891	0.216589
22	-0.018564	-0.1438	0.443072
23	-0.147623	-1.1435	0.12869
24	-0.160344	-1.242	0.109531
25	0.08578	0.6644	0.254475
26	-0.053713	-0.4161	0.339427
27	0.034022	0.2635	0.396522
28	0.054117	0.4192	0.338286
29	0.047395	0.3671	0.357412
30	-0.004874	-0.0378	0.485004
31	-0.103166	-0.7991	0.213686
32	0.119741	0.9275	0.178689
33	0.101071	0.7829	0.218384
34	0.058481	0.453	0.326095
35	-0.060725	-0.4704	0.319897
36	-0.080804	-0.6259	0.266876
37	0.036293	0.2811	0.389791
38	-0.043098	-0.3338	0.369834
39	0.035837	0.2776	0.39114
40	-0.042544	-0.3295	0.371447
41	-0.024474	-0.1896	0.425142
42	-0.129413	-1.0024	0.160081
43	0.03037	0.2352	0.407409
44	0.064355	0.4985	0.309979
45	-0.010243	-0.0793	0.468513
46	-0.064382	-0.4987	0.309908
47	-0.113105	-0.8761	0.192234
48	-0.000204	-0.0016	0.499371
49	-0.01468	-0.1137	0.454922
50	0.036086	0.2795	0.390404
51	0.01765	0.1367	0.445858
52	0.035213	0.2728	0.392988
53	0.014536	0.1126	0.455363
54	-0.027752	-0.215	0.415262
55	-0.003401	-0.0263	0.489535
56	-0.00131	-0.0101	0.49597
57	-0.063456	-0.4915	0.312424
58	-0.054521	-0.4223	0.337152
59	-0.004238	-0.0328	0.486962
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292508754nuogl9d5wwkky8l/1ujgq1292508702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292508754nuogl9d5wwkky8l/1ujgq1292508702.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292508754nuogl9d5wwkky8l/2ujgq1292508702.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292508754nuogl9d5wwkky8l/2ujgq1292508702.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (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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