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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, 22 Dec 2009 03:45:15 -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/22/t12614787779fliorttuw7s4yw.htm/, Retrieved Tue, 22 Dec 2009 11:46:19 +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/22/t12614787779fliorttuw7s4yw.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:

paper, TRA, inflatie1

Dataseries X:

» Textbox « » Textfile « » CSV «

1,1 1,2 1,1 1,2 1,4 1,5 1,5 1,8 1,6 1,5 1,4 1,4 1,4 1,4 1,5 1,4 1,1 1,1 0,9 0,9 0,9 0,9 1,1 1,3 1 1,1 1,4 1,4 1,3 1,4 1 1,8 1,5 1,5 1,4 1,6 1,6 1,6 1,4 1,7 1,8 1,9 2,2 2,1 2,4 2,6 2,8 2,7 2,6 2,9 2,8 2,2 2,2 2,2 2 2 1,7 1,4 1,3 1,4 1,3

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	0.903559	7.057	0
2	0.843185	6.5855	0
3	0.768485	6.0021	0
4	0.683886	5.3413	1e-06
5	0.587588	4.5892	1.1e-05
6	0.493235	3.8523	0.000142
7	0.380247	2.9698	0.002128
8	0.32078	2.5054	0.007459
9	0.237047	1.8514	0.034477
10	0.153294	1.1973	0.117918
11	0.081444	0.6361	0.263546
12	0.028249	0.2206	0.413058
13	0.014125	0.1103	0.456259
14	-0.006811	-0.0532	0.478874
15	-0.030813	-0.2407	0.405315
16	-0.039968	-0.3122	0.377993
17	-0.05233	-0.4087	0.342092
18	-0.059163	-0.4621	0.322834
19	-0.088378	-0.6903	0.246326
20	-0.138152	-1.079	0.142418
21	-0.171175	-1.3369	0.093107
22	-0.202976	-1.5853	0.059036
23	-0.247841	-1.9357	0.028771
24	-0.266537	-2.0817	0.020786
25	-0.318836	-2.4902	0.007754
26	-0.330119	-2.5783	0.006179
27	-0.324611	-2.5353	0.006907
28	-0.327779	-2.56	0.00648
29	-0.334693	-2.614	0.005628
30	-0.302395	-2.3618	0.010698
31	-0.304503	-2.3782	0.010271
32	-0.252328	-1.9707	0.026648
33	-0.22011	-1.7191	0.045332
34	-0.187252	-1.4625	0.074371
35	-0.147581	-1.1526	0.126777
36	-0.120353	-0.94	0.175466

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.903559	7.057	0
2	0.145801	1.1387	0.129632
3	-0.078151	-0.6104	0.27194
4	-0.118626	-0.9265	0.178918
5	-0.13716	-1.0713	0.144137
6	-0.070791	-0.5529	0.291177
7	-0.159818	-1.2482	0.10836
8	0.20465	1.5984	0.057564
9	-0.070989	-0.5544	0.290651
10	-0.110963	-0.8667	0.194765
11	-0.030482	-0.2381	0.406311
12	0.039873	0.3114	0.378272
13	0.235886	1.8423	0.035144
14	-0.041664	-0.3254	0.372995
15	-0.038329	-0.2994	0.382842
16	-0.055937	-0.4369	0.33187
17	-0.10351	-0.8084	0.210989
18	0.010794	0.0843	0.466545
19	-0.155416	-1.2138	0.114744
20	-0.125688	-0.9817	0.165074
21	-0.059073	-0.4614	0.323086
22	-0.02207	-0.1724	0.431859
23	-0.025669	-0.2005	0.420886
24	0.135589	1.059	0.146891
25	-0.122687	-0.9582	0.170869
26	0.07497	0.5855	0.280175
27	0.106936	0.8352	0.203434
28	0.007804	0.061	0.475798
29	-0.085745	-0.6697	0.252791
30	0.062897	0.4912	0.312509
31	-0.204172	-1.5946	0.057982
32	0.10181	0.7952	0.214801
33	0.045958	0.3589	0.360437
34	-0.008363	-0.0653	0.474068
35	-0.009797	-0.0765	0.469629
36	-0.150763	-1.1775	0.121786

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/22/t12614787779fliorttuw7s4yw/1s8381261478713.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/22/t12614787779fliorttuw7s4yw/1s8381261478713.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/22/t12614787779fliorttuw7s4yw/2b0ve1261478713.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/22/t12614787779fliorttuw7s4yw/2b0ve1261478713.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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