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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: Fri, 24 Dec 2010 12:12:12 +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/24/t1293192620714p4jnn6ty5vqq.htm/, Retrieved Fri, 24 Dec 2010 13:10:22 +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/24/t1293192620714p4jnn6ty5vqq.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 «

1143.94 1227.85 1261.26 1408.95 1162.58 1259.39 1253.85 1475.32 1211.75 1303.83 1299.37 1430.73 1244.95 1318.58 1318.74 1525.05 1275.88 1360.09 1349.81 1574.04 1294.58 1380.60 1369.22 1565.98 1338.96 1457.57 1456.21 1654.44 1428.47 1530.39 1514.13 1698.25 1454.22 1578.06 1526.53 1714.21 1492.86 1593.42 1555.50 1820.55 1534.57 1636.03 1594.58 1805.13 1565.37 1679.57 1638.26 1854.64 1628.72 1744.97 1694.35 1920.88 1680.26 1778.62 1740.89 2010.56

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	0.269431	1.9429	0.028726
2	0.178041	1.2839	0.102439
3	0.087002	0.6274	0.266578
4	-0.321452	-2.318	0.012208
5	-0.091348	-0.6587	0.25649
6	-0.115837	-0.8353	0.203683
7	-0.07014	-0.5058	0.307573
8	-0.096904	-0.6988	0.243899
9	0.022613	0.1631	0.435548
10	0.114377	0.8248	0.206631
11	0.103265	0.7447	0.229917
12	0.14273	1.0292	0.154065
13	-0.009316	-0.0672	0.473349
14	-0.076651	-0.5527	0.291404
15	-0.17275	-1.2457	0.109226
16	-0.181935	-1.312	0.097649
17	-0.165515	-1.1935	0.119037
18	-0.090362	-0.6516	0.258761
19	-0.040293	-0.2906	0.386272
20	0.060251	0.4345	0.332871
21	0.094256	0.6797	0.249858
22	0.041804	0.3014	0.382137
23	0.089399	0.6447	0.26099
24	0.156459	1.1282	0.132199
25	-0.005936	-0.0428	0.483009
26	0.04438	0.32	0.375115
27	0.011234	0.081	0.467872
28	-0.180072	-1.2985	0.099919
29	0.060698	0.4377	0.331709
30	0.076473	0.5515	0.291842
31	0.051422	0.3708	0.356143
32	0.11886	0.8571	0.197658
33	-0.052259	-0.3768	0.353911
34	-0.03785	-0.2729	0.392989
35	-0.090224	-0.6506	0.259081
36	-0.039225	-0.2829	0.389206
37	-0.007445	-0.0537	0.478695
38	-0.05085	-0.3667	0.357672
39	-0.004713	-0.034	0.486509
40	0.024163	0.1742	0.431175
41	-0.036736	-0.2649	0.396065
42	-0.023902	-0.1724	0.431913
43	-0.043009	-0.3101	0.378845
44	-0.113884	-0.8212	0.207633
45	-0.035212	-0.2539	0.40028
46	-0.025397	-0.1831	0.427701
47	0.004807	0.0347	0.48624
48	0.018569	0.1339	0.446998
49	-0.051472	-0.3712	0.356009
50	-0.01389	-0.1002	0.460299
51	-0.025654	-0.185	0.426978
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.269431	1.9429	0.028726
2	0.113702	0.8199	0.208003
3	0.015131	0.1091	0.456767
4	-0.399642	-2.8819	0.002867
5	0.079985	0.5768	0.283288
6	0.000753	0.0054	0.497844
7	0.037192	0.2682	0.394805
8	-0.264048	-1.9041	0.03122
9	0.153882	1.1097	0.136126
10	0.128999	0.9302	0.178276
11	0.087776	0.633	0.264765
12	-0.134379	-0.969	0.16851
13	-0.050432	-0.3637	0.35879
14	-0.00951	-0.0686	0.472794
15	-0.085143	-0.614	0.270954
16	-0.119962	-0.8651	0.195491
17	-0.102324	-0.7379	0.231955
18	0.072347	0.5217	0.302046
19	-0.059704	-0.4305	0.334295
20	0.054617	0.3938	0.347651
21	-0.069406	-0.5005	0.309419
22	-0.000785	-0.0057	0.497751
23	-0.012291	-0.0886	0.464859
24	0.272102	1.9622	0.027553
25	-0.165237	-1.1915	0.119425
26	0.051167	0.369	0.356823
27	-0.016577	-0.1195	0.452655
28	0.03534	0.2548	0.399925
29	0.075249	0.5426	0.294853
30	0.07471	0.5387	0.296183
31	-0.030427	-0.2194	0.413595
32	-0.050265	-0.3625	0.359236
33	-0.084636	-0.6103	0.272155
34	0.011007	0.0794	0.46852
35	-0.052331	-0.3774	0.353719
36	-0.045339	-0.3269	0.372512
37	0.048043	0.3464	0.365203
38	0.011184	0.0806	0.468017
39	0.013289	0.0958	0.462012
40	0.038328	0.2764	0.391672
41	-0.10223	-0.7372	0.23216
42	-0.041945	-0.3025	0.38175
43	-0.027045	-0.195	0.423066
44	-0.036704	-0.2647	0.396152
45	0.035266	0.2543	0.400131
46	0.014931	0.1077	0.457335
47	0.005672	0.0409	0.483767
48	-0.055795	-0.4023	0.34454
49	-0.10485	-0.7561	0.226505
50	-0.112428	-0.8107	0.210608
51	0.043059	0.3105	0.378709
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192620714p4jnn6ty5vqq/1ioc21293192729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192620714p4jnn6ty5vqq/1ioc21293192729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192620714p4jnn6ty5vqq/2ioc21293192729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192620714p4jnn6ty5vqq/2ioc21293192729.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 95% ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 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 (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='lags',ylab='ACF')

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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