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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: Sat, 20 Dec 2008 13:03:50 -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/20/t1229803519m5vrx5syk3r2zk3.htm/, Retrieved Sat, 20 Dec 2008 21:05:21 +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/20/t1229803519m5vrx5syk3r2zk3.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 «

103.3 101.2 107.7 110.4 101.9 115.9 89.9 88.6 117.2 123.9 100 103.6 94.1 98.7 119.5 112.7 104.4 124.7 89.1 97 121.6 118.8 114 111.5 97.2 102.5 113.4 109.8 104.9 126.1 80 96.8 117.2 112.3 117.3 111.1 102.2 104.3 122.9 107.6 121.3 131.5 89 104.4 128.9 135.9 133.3 121.3 120.5 120.4 137.9 126.1 133.2 151.1 105 119 140.4 156.6 137.1 122.7

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	0.494125	3.4234	0.000637
2	0.505508	3.5023	0.000504
3	0.560776	3.8852	0.000156
4	0.428268	2.9671	0.002338
5	0.429949	2.9788	0.002264
6	0.411981	2.8543	0.003175
7	0.218775	1.5157	0.068075
8	0.253637	1.7573	0.042626
9	0.258959	1.7941	0.039547
10	-0.013646	-0.0945	0.462535
11	0.064784	0.4488	0.327785
12	0.023457	0.1625	0.435793
13	-0.069624	-0.4824	0.315869
14	-0.088466	-0.6129	0.271415
15	-0.101562	-0.7036	0.242528
16	-0.195582	-1.355	0.090875
17	-0.108044	-0.7485	0.228891
18	-0.192912	-1.3365	0.093838
19	-0.251942	-1.7455	0.043648
20	-0.193462	-1.3403	0.093222
21	-0.187177	-1.2968	0.10045
22	-0.241384	-1.6724	0.05048
23	-0.166912	-1.1564	0.126621
24	-0.258385	-1.7901	0.03987
25	-0.234798	-1.6267	0.055171
26	-0.09424	-0.6529	0.258463
27	-0.198539	-1.3755	0.087678
28	-0.153029	-1.0602	0.147177
29	-0.090582	-0.6276	0.266629
30	-0.148176	-1.0266	0.154879
31	-0.056861	-0.3939	0.347683
32	-0.094116	-0.6521	0.258738
33	-0.156635	-1.0852	0.141627
34	-0.062609	-0.4338	0.3332
35	-0.063601	-0.4406	0.330725
36	-0.156527	-1.0845	0.14179

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.494125	3.4234	0.000637
2	0.345771	2.3956	0.010271
3	0.340367	2.3581	0.011244
4	0.043561	0.3018	0.382055
5	0.055784	0.3865	0.350424
6	0.03308	0.2292	0.40985
7	-0.230204	-1.5949	0.058649
8	-0.061538	-0.4263	0.33588
9	0.053183	0.3685	0.357074
10	-0.307551	-2.1308	0.019129
11	-0.05197	-0.3601	0.360191
12	0.003515	0.0244	0.490337
13	0.023448	0.1625	0.435815
14	-0.075734	-0.5247	0.301102
15	0.047599	0.3298	0.371503
16	-0.005987	-0.0415	0.483543
17	0.046753	0.3239	0.373704
18	-0.063239	-0.4381	0.331628
19	-0.028902	-0.2002	0.421071
20	-0.068353	-0.4736	0.318979
21	0.037836	0.2621	0.397169
22	-0.051112	-0.3541	0.362401
23	0.060296	0.4177	0.338999
24	-0.153931	-1.0665	0.145774
25	-0.023881	-0.1654	0.434642
26	0.138086	0.9567	0.171759
27	0.005898	0.0409	0.483788
28	-0.008129	-0.0563	0.47766
29	0.022625	0.1567	0.43805
30	-0.072475	-0.5021	0.308939
31	0.079743	0.5525	0.291594
32	-0.168744	-1.1691	0.12407
33	-0.072003	-0.4988	0.310082
34	-0.083111	-0.5758	0.283717
35	-0.023732	-0.1644	0.435046
36	-0.085264	-0.5907	0.278737

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229803519m5vrx5syk3r2zk3/1xugl1229803428.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229803519m5vrx5syk3r2zk3/1xugl1229803428.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229803519m5vrx5syk3r2zk3/2vyzu1229803428.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229803519m5vrx5syk3r2zk3/2vyzu1229803428.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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