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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: Tue, 01 Dec 2009 09:52:15 -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/01/t1259686395lb7zma9y0eydio2.htm/, Retrieved Tue, 01 Dec 2009 17:53:17 +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/01/t1259686395lb7zma9y0eydio2.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 «

101.3 106.3 94 102.8 102 105.1 92.4 81.4 105.8 120.3 100.7 88.8 94.3 99.9 103.4 103.3 98.8 104.2 91.2 74.7 108.5 114.5 96.9 89.6 97.1 100.3 122.6 115.4 109 129.1 102.8 96.2 127.7 128.9 126.5 119.8 113.2 114.1 134.1 130 121.8 132.1 105.3 103 117.1 126.3 138.1 119.5 138 135.5 178.6 162.2 176.9 204.9 132.2 142.5 164.3 174.9 175.4 143

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.242672	-1.864	0.03365
2	-0.28492	-2.1885	0.016302
3	0.057508	0.4417	0.330149
4	-0.136823	-1.051	0.148781
5	0.214763	1.6496	0.052167
6	-0.025234	-0.1938	0.42349
7	0.050196	0.3856	0.350602
8	-0.007801	-0.0599	0.47621
9	-0.006827	-0.0524	0.479177
10	-0.312357	-2.3993	0.009803
11	-0.039862	-0.3062	0.380272
12	0.485486	3.7291	0.000217
13	-0.149931	-1.1516	0.127058
14	-0.097795	-0.7512	0.227765
15	-0.036765	-0.2824	0.389312
16	-0.104813	-0.8051	0.212001
17	0.120648	0.9267	0.178924
18	0.06062	0.4656	0.321598
19	-0.016288	-0.1251	0.45043
20	0.047503	0.3649	0.358253
21	0.062039	0.4765	0.317727
22	-0.324734	-2.4943	0.00772
23	0.035452	0.2723	0.393167
24	0.332199	2.5517	0.006666
25	-0.090342	-0.6939	0.245224
26	-0.001772	-0.0136	0.494592
27	-0.094618	-0.7268	0.235118
28	-0.063764	-0.4898	0.313054
29	0.09915	0.7616	0.224671
30	-0.012766	-0.0981	0.461109
31	-0.025231	-0.1938	0.423497
32	0.121861	0.936	0.176536
33	-0.01356	-0.1042	0.458698
34	-0.253288	-1.9455	0.02824
35	0.057792	0.4439	0.329365
36	0.140095	1.0761	0.143135

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.242672	-1.864	0.03365
2	-0.365324	-2.8061	0.003391
3	-0.153949	-1.1825	0.120874
4	-0.339766	-2.6098	0.005732
5	0.032404	0.2489	0.40215
6	-0.110409	-0.8481	0.199914
7	0.166182	1.2765	0.103396
8	0.038739	0.2976	0.383542
9	0.233191	1.7912	0.039197
10	-0.424608	-3.2615	0.000922
11	-0.286821	-2.2031	0.015752
12	0.046949	0.3606	0.359836
13	-0.033531	-0.2576	0.398822
14	-0.0526	-0.404	0.343826
15	0.026561	0.204	0.419519
16	-0.028952	-0.2224	0.41239
17	-0.105581	-0.811	0.210317
18	0.039061	0.3	0.382604
19	-0.078638	-0.604	0.27407
20	-0.03725	-0.2861	0.387894
21	0.093516	0.7183	0.237701
22	-0.079653	-0.6118	0.271502
23	-0.102112	-0.7843	0.21799
24	0.060846	0.4674	0.320978
25	0.023073	0.1772	0.429968
26	0.002119	0.0163	0.493535
27	0.015878	0.122	0.451673
28	0.075758	0.5819	0.281424
29	-0.025375	-0.1949	0.423068
30	-0.044649	-0.343	0.366427
31	-0.065194	-0.5008	0.309199
32	-0.001093	-0.0084	0.496665
33	-0.076508	-0.5877	0.279497
34	0.024999	0.192	0.424192
35	-0.016685	-0.1282	0.449229
36	-0.040012	-0.3073	0.379834

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259686395lb7zma9y0eydio2/1khsj1259686333.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259686395lb7zma9y0eydio2/1khsj1259686333.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259686395lb7zma9y0eydio2/2e8d71259686333.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259686395lb7zma9y0eydio2/2e8d71259686333.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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