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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: Mon, 14 Dec 2009 03:10:41 -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/14/t12607855041b0pvokb84k2yze.htm/, Retrieved Mon, 14 Dec 2009 11:11:46 +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/14/t12607855041b0pvokb84k2yze.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 «

95,1 97,0 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99,0 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102,0 106,0 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100,0 110,7 112,8 109,8 117,3 109,1 115,9 96,0 99,8 116,8 115,7 99,4 94,3

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	0.019259	0.1334	0.447205
2	0.209728	1.453	0.07636
3	0.27158	1.8816	0.032984
4	0.041854	0.29	0.386542
5	0.137803	0.9547	0.17225
6	0.131167	0.9088	0.18401
7	-0.031635	-0.2192	0.413722
8	0.06642	0.4602	0.323735
9	0.078139	0.5414	0.295382
10	-0.096778	-0.6705	0.252876
11	0.048765	0.3379	0.368473
12	-0.051848	-0.3592	0.360506
13	-0.050276	-0.3483	0.36456
14	-0.093837	-0.6501	0.259357
15	0.012485	0.0865	0.465715
16	-0.153869	-1.066	0.14587
17	-0.037308	-0.2585	0.398571
18	-0.033291	-0.2306	0.409285
19	-0.167336	-1.1593	0.126027
20	-0.071402	-0.4947	0.311538
21	-0.083611	-0.5793	0.282557
22	-0.250703	-1.7369	0.044408
23	0.121975	0.8451	0.201133
24	-0.259312	-1.7966	0.039349
25	-0.128243	-0.8885	0.189354
26	-0.019309	-0.1338	0.447068
27	-0.130405	-0.9035	0.185394
28	-0.075683	-0.5243	0.301225
29	-0.068718	-0.4761	0.318083
30	-0.119001	-0.8245	0.206877
31	-0.132938	-0.921	0.180823
32	-0.038997	-0.2702	0.39409
33	-0.160954	-1.1151	0.135174
34	-0.005351	-0.0371	0.48529
35	-0.061104	-0.4233	0.336968
36	0.046343	0.3211	0.374775

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.019259	0.1334	0.447205
2	0.209435	1.451	0.076641
3	0.276583	1.9162	0.030651
4	0.005759	0.0399	0.48417
5	0.02954	0.2047	0.419351
6	0.060669	0.4203	0.338062
7	-0.079406	-0.5501	0.292387
8	-0.022792	-0.1579	0.437595
9	0.057338	0.3973	0.346472
10	-0.094145	-0.6523	0.258674
11	-0.007609	-0.0527	0.479087
12	-0.047198	-0.327	0.372546
13	-0.011575	-0.0802	0.468208
14	-0.115447	-0.7998	0.213873
15	0.059801	0.4143	0.340246
16	-0.088241	-0.6113	0.271927
17	-0.018392	-0.1274	0.449568
18	0.017703	0.1227	0.451447
19	-0.085287	-0.5909	0.278684
20	-0.076353	-0.529	0.299625
21	-0.022931	-0.1589	0.43722
22	-0.176055	-1.2197	0.11426
23	0.198045	1.3721	0.088207
24	-0.196863	-1.3639	0.089479
25	-0.041357	-0.2865	0.387854
26	-0.048649	-0.3371	0.368774
27	0.044043	0.3051	0.380791
28	-0.050419	-0.3493	0.364191
29	-0.059654	-0.4133	0.340616
30	-0.056134	-0.3889	0.349532
31	-0.113536	-0.7866	0.217692
32	-0.073165	-0.5069	0.307271
33	-0.043328	-0.3002	0.382665
34	-0.013862	-0.096	0.461946
35	0.003518	0.0244	0.490328
36	0.0598	0.4143	0.340249

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607855041b0pvokb84k2yze/103ww1260785439.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607855041b0pvokb84k2yze/103ww1260785439.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607855041b0pvokb84k2yze/20qtw1260785439.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607855041b0pvokb84k2yze/20qtw1260785439.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 2.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 2.0 ; par3 = 0 ; par4 = 1 ; 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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