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autocorrelation function

*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: Tue, 16 Dec 2008 14:14:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229462099ok20g63mtj5af8w.htm/, Retrieved Tue, 16 Dec 2008 22:15:00 +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/2008/Dec/16/t1229462099ok20g63mtj5af8w.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

91.2 99.2 108.2 101.5 106.9 104.4 77.9 60 99.5 95 105.6 102.5 93.3 97.3 127 111.7 96.4 133 72.2 95.8 124.1 127.6 110.7 104.6 112.7 115.3 139.4 119 97.4 154 81.5 88.8 127.7 105.1 114.9 106.4 104.5 121.6 141.4 99 126.7 134.1 81.3 88.6 132.7 132.9 134.4 103.7 119.7 115 132.9 108.5 113.9 142 97.7 92.2 128.8 134.9 128.2 114.8

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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.102513	0.7941	0.215145
2	-0.102028	-0.7903	0.21623
3	0.228519	1.7701	0.040896
4	0.053331	0.4131	0.340503
5	0.127185	0.9852	0.164249
6	0.227823	1.7647	0.041351
7	0.070332	0.5448	0.29396
8	0.054266	0.4203	0.337868
9	0.165545	1.2823	0.102334
10	-0.186272	-1.4429	0.077131
11	0.031098	0.2409	0.405234
12	0.565409	4.3796	2.4e-05
13	-0.037461	-0.2902	0.386342
14	-0.244997	-1.8977	0.031272
15	0.067304	0.5213	0.302026
16	-0.054954	-0.4257	0.335934
17	-0.023036	-0.1784	0.429491
18	0.059774	0.463	0.322516
19	-0.006792	-0.0526	0.479109
20	-0.060872	-0.4715	0.319493
21	0.081897	0.6344	0.264126
22	-0.234008	-1.8126	0.037447
23	-0.012885	-0.0998	0.460416
24	0.346704	2.6856	0.004675
25	-0.065447	-0.5069	0.307025
26	-0.153126	-1.1861	0.120128
27	0.0285	0.2208	0.413015
28	-0.082317	-0.6376	0.263072
29	-0.02281	-0.1767	0.430175
30	0.045077	0.3492	0.364095
31	-0.020385	-0.1579	0.437533
32	-0.032621	-0.2527	0.400688
33	-0.018916	-0.1465	0.442
34	-0.149348	-1.1568	0.12596
35	-0.035136	-0.2722	0.393214
36	0.160848	1.2459	0.108818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.102513	0.7941	0.215145
2	-0.113732	-0.881	0.190926
3	0.257836	1.9972	0.025173
4	-0.022483	-0.1742	0.431165
5	0.199293	1.5437	0.063958
6	0.144854	1.122	0.133158
7	0.071775	0.556	0.290151
8	0.030427	0.2357	0.40724
9	0.100005	0.7746	0.220799
10	-0.301666	-2.3367	0.011406
11	0.075077	0.5815	0.281526
12	0.46299	3.5863	0.000337
13	-0.148268	-1.1485	0.127664
14	-0.263868	-2.0439	0.02268
15	-0.078017	-0.6043	0.273955
16	-0.033322	-0.2581	0.398602
17	-0.084127	-0.6516	0.25856
18	-0.089296	-0.6917	0.245902
19	0.136199	1.055	0.14783
20	-0.080838	-0.6262	0.266789
21	0.088608	0.6864	0.247567
22	-0.044604	-0.3455	0.365464
23	0.11995	0.9291	0.178273
24	-0.054022	-0.4185	0.338555
25	0.084106	0.6515	0.258612
26	0.108648	0.8416	0.201682
27	-0.034851	-0.27	0.39406
28	-0.154185	-1.1943	0.118528
29	0.049002	0.3796	0.352803
30	-0.037404	-0.2897	0.386512
31	-0.051833	-0.4015	0.34474
32	-0.063993	-0.4957	0.310963
33	-0.069864	-0.5412	0.295198
34	0.057502	0.4454	0.328814
35	-0.067322	-0.5215	0.301977
36	-0.079579	-0.6164	0.269977

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229462099ok20g63mtj5af8w/12hbt1229462041.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229462099ok20g63mtj5af8w/12hbt1229462041.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229462099ok20g63mtj5af8w/2py5h1229462041.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229462099ok20g63mtj5af8w/2py5h1229462041.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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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